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  • 1.
    Abdullaev, Farakhulla
    et al.
    Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal.
    Konotop, V. V.
    Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal.
    Ögren, Magnus
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Sørensen, M. P.
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Zeno effect and switching of solitons in nonlinear couplers2011In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 36, no 23, p. 4566-4568Article in journal (Refereed)
    Abstract [en]

    The Zeno effect is investigated for soliton type pulses in a nonlinear directional coupler with dissipation. The effect consists in increase of the coupler transparency with increase of the dissipative losses in one of the arms. It is shown that localized dissipation can lead to switching of solitons between the arms. Power losses accompanying the switching can be fully compensated by using a combination of dissipative and active (in particular, parity-time-symmetric) segments.

  • 2.
    Abdullaev, Fatkhulla
    et al.
    Physical-Technical Institute, Uzbek Academy of Sciences, Tashkent, Uzbekistan; Instituto de Fisica Teorica, Universidade Estadual Paulista Júlio de Mesquita Filho, São Paulo, Brazil.
    Ögren, Magnus
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Sørensen, M. P.
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures2013In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, no 2, article id 023616Article in journal (Refereed)
    Abstract [en]

    The generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are considered: a variation of the fermion-boson scattering length and the boson-boson scattering length. We predict the properties of the generated Faraday patterns and study the parameter regions where they can be excited.

  • 3.
    Brack, M.
    et al.
    Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany.
    Ögren, Magnus
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Yu, Y.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Reimann, S. M.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 46, p. 9941-9967Article in journal (Refereed)
    Abstract [en]

    We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small ε in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary ε which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit ε (or energy) →0 restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios ωrφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.

  • 4.
    Carlsen, Martin
    et al.
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Darula, Radoslav
    Aalborg University, Aalborg, Denmark.
    Gravesen, Jens
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Hjorth, Poul G.
    Dynamical systems, Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Jørgensen, H. B.
    University of Southern Denmark, Odense, Denmark.
    Nguyen, Dang Manh
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Nielsen, Peter Nørtoft
    Geometry, Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Olsen, J.
    Joltech, Sønderborg, Denmark.
    Petersen, H. G.
    University of Southern Denmark, Odense, Denmark.
    Røgen, Peter
    Geometry, Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Ögren, Magnus
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Efficiency of a gyroscopic device for conversion of mechanical wave energy to electric energy: Technical report from ESGI-83 workshop in industrial mathematics 20112011Report (Other academic)
    Abstract [en]

    We consider a recently proposed gyroscopic device for conversion of mechanical ocean wave energy to electrical energy. Two models of the device derived from standard engineering mechanics from the literature are analysed, and a model is derived from analytical mechanics considerations. From these models, estimates of the power production, efficiency, forces and moments are made. We find that it is possible to extract a significant amount of energy from an ocean wave using the described device. Further studies are required for a full treatment of the device.

  • 5.
    Corboz, Philippe
    et al.
    School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Ögren, Magnus
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Kheruntsyan, Karén
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Corney, Joel F.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Phase-space methods for fermions2013In: Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics / [ed] Davis, M.; Gardiner, S.; Proukakis, N.; Szymańska, M., London: Imperial College Press, 2013, p. 407-416Chapter in book (Other academic)
    Abstract [en]

    We review phase-space simulation techniques for fermions, showing how a Gaussian operator basis leads to exact calculations of the evolution of a many-body quantum system in both real and imaginary time. We apply such techniques to the Hubbard model and to the problem of molecular dissociation of bosonic molecules into pairs of fermionic atoms.

  • 6.
    Kavoulakis, G. M.
    et al.
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Yu, Y.
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Ögren, Magnus
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Reimann, S. M.
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Superfluidity in a gas of strongly interacting bosons2006In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 76, no 2, p. 215-221Article in journal (Refereed)
    Abstract [en]

    We consider small systems of bosonic atoms rotating in a toroidal trap. Using the method of exact numerical diagonalization of the many-body Hamiltonian, we examine the transition from the Bose-Einstein condensed state to the Tonks-Girardeau state. The system supports persistent currents in a wide range between the two limits, even in the absence of Bose-Einstein condensation.

  • 7.
    Lockby, Andreas
    et al.
    School of Science and Technology, Örebro University, Örebro, Sweden..
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems2016In: Comsol Conference 2016, 2016Conference paper (Refereed)
    Abstract [en]

    The dynamical functional particle method(DFPM) is a method for solving equations, e.g. PDEs, using a second order damped dynamical system. We show how the method can be extended to include constraints both explicitly as global constraints and adding the constraints as additional damped dynamical equations. These methods are implemented in Comsol and we show numerical tests for finding the stationary solution of a nonlinear heat equation with and without constraints (global and dynamical). The results show that DFPM is a very general and robust way of solving PDEs and it should be of interest to implement the approach more generally in Comsol.

  • 8.
    Møller-Andersen, Jakob
    et al.
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
    Ögren, Magnus
    Örebro University, School of Science and Technology. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark; Nano Science Center, Department of Chemistry, University of Copenhagen, København, Denmark.
    Perturbative semiclassical trace formulae for harmonic oscillators2015In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 75, no 3, p. 359-382Article in journal (Refereed)
    Abstract [en]

    In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn the conclusion that the gross structure of the quantum spectrum is determined from only classical circular and diameter orbits for this class of systems.

  • 9.
    Nyström, Marcus
    et al.
    Humanities Lab, Lund University, Lund, Sweden.
    Ögren, Magnus
    Department of Mathematics, Technical University of Denmark, Kgs. Lyngby, Denmark.
    A pilot study of problem solving in vector calculus using eye-tracking2011In: Utvecklingskonferens 11 LU: Proceedings, Lund University , 2011, p. 118-123Conference paper (Refereed)
  • 10. Nyström, Marcus
    et al.
    Ögren, Magnus
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    How illustrations influence performance and eye movement behaviour when solving problems in vector calculus2012In: Conference on Teaching and Learning 2012: Proceedings, Lund University , 2012Conference paper (Refereed)
    Abstract [en]

    Mathematical formulas in vector calculus often have direct visual representations, which in form of illustrations are used extensively during teaching and when assessing students’ levels of understanding. However, there is very little, if any, empirical evidence of how the illustrations are utilized during problem solving and whether they are beneficial to comprehension. In this paper we collect eye movements and performance scores (true or false answers) from students while solving eight problems in vector calculus; 20 students solve illustrated problems whereas 16 students solve the same problems, but without the illustrations. Results show no overall performance benefit for illustrated problems even though they are clearly visually attended. Surprisingly, we found a significant effect of whether the answer to the problem was true of false; students were more likely to answer that the question was true given an illustrated problem. We interpret this finding as if the illustrations persuade the students that the answer is true, irrespective of whether or not it in fact is. These results may question the tacit consensus among teachers of vector calculus that illustrations are generally beneficial for comprehending a problem.

  • 11.
    Puig Von Friesen, M.
    et al.
    Mathematical Physics, Lund University, Lund, Sweden.
    Ögren, Magnus
    Mathematical Physics, Lund University, Lund, Sweden.
    Åberg, S.
    Mathematical Physics, Lund University, Lund, Sweden.
    Quantum chaos and regularity in ultracold Fermi gases2007In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 76, no 5, article id 057204Article in journal (Refereed)
    Abstract [en]

    Quantum fluctuation of the energy is studied for an ultracold gas of interacting fermions trapped in a three-dimensional potential. Periodic-orbit theory is explored, and energy fluctuations are studied versus the particle number for generic regular and chaotic systems, as well as for a system defined by a harmonic confinement potential. Temperature effects on the energy fluctuations are investigated.

  • 12.
    Roussou, Alexandra
    et al.
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Smyrnakis, Ioannis
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, Manolis
    Technological Education Institute of Crete, Heraklion, Greece.
    Efremidis, Nikolaos
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Kavoulakis, Georgios
    Technological Education Institute of Crete, Heraklion, Greece.
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry2018In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 045006Article in journal (Refereed)
    Abstract [en]

    We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

  • 13.
    Sandin, Patrik
    et al.
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology. Sch Sci & Technol, Univ Örebro, Örebro, Sweden.
    Numerical solution of the stationary multicomponent nonlinear Schrodinger equation with a constraint on the angular momentum2016In: Physical Review E, ISSN 2470-0045, Vol. 93, no 3, article id 033301Article in journal (Refereed)
    Abstract [en]

    We formulate a damped oscillating particle method to solve the stationary nonlinear Schrodinger equation (NLSE). The ground-state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self-interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so-called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.

  • 14.
    Sandin, Patrik
    et al.
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Smyrnakis, J.
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Kavoulakis, G. M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength2017In: Physical Review E, ISSN 2470-0045, Vol. 95, no 1, article id 012142Article in journal (Refereed)
    Abstract [en]

    Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

  • 15.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Chadalavada, Ravi
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Creativity in the eye of the student: Refining investigations of mathematical creativity using eye-tracking goggles2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (PME) / [ed] C. Csíkos, A. Rausch, & J. Szitányi, 2016Conference paper (Refereed)
    Abstract [en]

    Mathematical creativity is increasingly important for improved innovation and problem-solving. In this paper, we address the question of how to best investigate mathematical creativity and critically discuss dichotomous creativity scoring schemes. In order to gain deeper insights into creative problem-solving processes, we suggest the use of mobile, unobtrusive eye-trackers for evaluating students’ creativity in the context of Multiple Solution Tasks (MSTs). We present first results with inexpensive eye-tracking goggles that reveal the added value of evaluating students’ eye movements when investigating mathematical creativity—compared to an analysis of written/drawn solutions as well as compared to an analysis of simple videos.

  • 16.
    Sørensen, Mads Peter
    et al.
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Falsig Pedersen, Niels
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    The dynamics of magnetic vortices in type II superconductors with pinning sites studied by the time dependent Ginzburg–Landau model2017In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 533, p. 40-43Article in journal (Refereed)
    Abstract [en]

    We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg–Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.

  • 17.
    Yu, Y.
    et al.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Ögren, Magnus
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Åberg, S.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Reimann, S. M.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Brack, M.
    Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany.
    Supershell structure in trapped dilute Fermi gases2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, no 5, article id 051602Article in journal (Refereed)
    Abstract [en]

    We show that a dilute harmonically trapped two-component gas of fermionic atoms with a weak repulsive interaction has a pronounced super-shell structure: The shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the "magic numbers" occurring between the beat nodes by half a period. The length and amplitude of this beating mode depend on the strength of the interaction. We give a simple interpretation of the beat structure in terms of a semiclassical trace formula for the symmetry breaking U(3)→SO(3).

  • 18.
    Ögren, Magnus
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    ESGI-88 (European Study Group with Industry) workshop on industrial mathematics: Report2012Report (Other academic)
  • 19.
    Ögren, Magnus
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Klassisk mekanik vs kvantmekanik2010In: Forskning, ISSN 1654-8876, no 3-4, p. 50-54Article, review/survey (Other (popular science, discussion, etc.))
  • 20.
    Ögren, Magnus
    Örebro University, School of Science and Technology. Nano Science Center, Department of Chemistry, University of Copenhagen, Denmark.
    Local boundary conditions for NMR-relaxation in digitized porous media2014In: The European Physical Journal B, ISSN 1434-6028, Vol. 87, no 11, p. 255-Article in journal (Refereed)
    Abstract [en]

    We narrow the gap between simulations of nuclear magnetic resonance dynamics on digital domains (such as CT-images) and measurements in D-dimensional porous media. We point out with two basic domains, the ball and the cube in D dimensions, that due to a digital uncertainty in representing the real pore surfaces of dimension D − 1, there is a systematic error in simulated dynamics. We then reduce this error by introducing local Robin boundary conditions.

  • 21.
    Ögren, Magnus
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Lärarhandledning [Teacher's manual] till: Kvantvärldens fenomen: teori och begrepp2006Book (Other academic)
  • 22.
    Ögren, Magnus
    Nano Science Center, Department of Chemistry, University of Copenhagen, Denmark.
    Predicting the Petrophysical Parameters from the Nanoscale Properties of Chalk2013Report (Other academic)
  • 23.
    Ögren, Magnus
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Problem med lösningar till kvantmekanik: fördjupningskurs2006Book (Other academic)
  • 24.
    Ögren, Magnus
    et al.
    Örebro University, School of Science and Technology.
    Abdullaev, Fatkhulla
    Physical-Technical Institute, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan .
    Konotop, Vladimir
    Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal .
    Solitons in a 𝒫𝒯-symmetric 𝜒(2) coupler2017In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 42, no 20, p. 4079-4082Article in journal (Refereed)
    Abstract [en]

    We consider the existence and stability of solitons in a 𝜒(2) coupler. Both the fundamental and second harmonics (SHs) undergo gain in one of the coupler cores and are absorbed in the other one. The gain and loss are balanced, creating a parity-time (𝒫𝒯) symmetric configuration. We present two types of families of 𝒫𝒯-symmetric solitons having equal and different profiles of the fundamental and SHs. It is shown that the gain and loss can stabilize solitons. The interaction of stable solitons is shown. In the cascading limit, the model is reduced to the 𝒫𝒯-symmetric coupler with effective Kerr-type nonlinearity and the balanced nonlinear gain and loss.

  • 25.
    Ögren, Magnus
    et al.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Bengtsson, Ragnar
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Vektoranalys: övningar2009Book (Other academic)
  • 26.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Carlsson, M.
    Mathematics Department, Purdue University, West Lafayette IN, United States.
    An exact lower energy bound for the infinite square well potential2011In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 32, no 2, p. L3-L6Article in journal (Refereed)
    Abstract [en]

    We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the Schrödinger equation and illustrates an example where the wavefunction is obtained directly by energy minimization. The derivation presented can serve as an example of a variational method in an undergraduate level university course in quantum mechanics.

  • 27.
    Ögren, Magnus
    et al.
    Department of Mathematics, Technical University of Denmark, Kgs. Lyngby, Denmark.
    Carlsson, M.
    Center for Mathematical Sciences, Lund University, Lund, Sweden.
    On the dynamics of the Fermi-Bose model2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 1, article id 015005Article in journal (Refereed)
    Abstract [en]

    We consider the exponential matrix representing the dynamics of the Fermi-Bose model in an undepleted bosonic field approximation. A recent application of this model is molecular dimers dissociating into its atomic compounds. The problem is solved in D spatial dimensions by dividing the system matrix into blocks with generalizations of Hankel matrices, here referred to as D-block-Hankel matrices. The method is practically useful for treating large systems, i.e. dense computational grids or higher spatial dimensions, either on a single standard computer or a cluster. In particular the results can be used for studies of three-dimensional physical systems of arbitrary geometry. We illustrate the generality of our approach by giving numerical results for the dynamics of Glauber type atomic pair correlation functions for a non-isotropic three-dimensional harmonically trapped molecular Bose-Einstein condensate.

  • 28.
    Ögren, Magnus
    et al.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Heiselberg, H.
    University of Southern Denmark, Odense, Denmark.
    Supershell structures and pairing in ultracold trapped Fermi gases2007In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 76, no 2, article id 021601Article in journal (Refereed)
    Abstract [en]

    We calculate level densities and pairing gaps for an ultracold dilute gas of fermionic atoms in harmonic traps under the influence of mean field and anharmonic quartic trap potentials. Supershell nodes, which were found in Hartree-Fock calculations, are calculated analytically within periodic orbit theory as well as from WKB calculations. For attractive interactions, the underlying level densities are crucial for pairing and supershell structures in gaps are predicted.

  • 29.
    Ögren, Magnus
    et al.
    Department of Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Kavoulakis, G. M.
    Department of Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Persistent currents in a Bose-Einstein condensate in the presence of disorder2007In: Journal of Low Temperature Physics, ISSN 0022-2291, E-ISSN 1573-7357, Vol. 149, no 3-4, p. 176-184Article in journal (Refereed)
    Abstract [en]

    We examine bosonic atoms that are confined in a toroidal, quasi-one-dimensional trap, subjected to a random potential. The resulting inhomogeneous atomic density is smoothened for sufficiently strong, repulsive interatomic interactions. Statistical analysis of our simulations show that the gas supports persistent currents, which become more fragile due to the disorder.

  • 30.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia; Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Kavoulakis, G. M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Stability of persistent currents in a Bose-Einstein condensate confined in a toroidal trap2009In: Journal of Low Temperature Physics, ISSN 0022-2291, E-ISSN 1573-7357, Vol. 154, no 1-2, p. 30-40Article in journal (Refereed)
    Abstract [en]

    Motivated by recent experiments in Bose-Einstein condensed atoms that have been confined in toroidal traps, we examine the stability of persistent currents in such systems. We investigate the extent that the stability of these currents may be tunable, and the possible difficulties in their creation and detection.

  • 31.
    Ögren, Magnus
    et al.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Kavoulakis, G. M.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Jackson, A. D.
    Niels Bohr Institute, Copenhagen, Denmark.
    Solitary waves in elongated clouds of strongly interacting bosons2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, no 2, article id 021603Article in journal (Refereed)
    Abstract [en]

    We examine the propagation of solitary waves in elongated clouds of trapped bosonic atoms as the confinement, the strength of the interatomic interaction, and the atom density are varied. We identify three different physical regimes and develop a general formalism that allows us to interpolate between them. Finally we pay special attention to the transition to the Tonks-Girardeau limit of strongly interacting bosons.

  • 32.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Atom-atom correlations and relative number squeezing in dissociation of spatially inhomogeneous molecular condensates2008In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 78, no 1, article id 011602Article in journal (Refereed)
    Abstract [en]

    We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.

  • 33.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Atom-atom correlations in colliding Bose-Einstein condensates2009In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, no 2, article id 021606Article in journal (Refereed)
    Abstract [en]

    We analyze atom-atom correlations in the s -wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive- P representation and provide analytic insights into the experimental observations of Perrin [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.

  • 34.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Role of spatial inhomogeneity in dissociation of trapped molecular condensates2010In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 82, no 1, article id 013641Article in journal (Refereed)
    Abstract [en]

    We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair correlations in the short-time limit. Both fermionic and bosonic statistics of the constituent atoms are considered. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the asymptotic behavior of the second-order correlation functions and for the relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparison with the numerical results shows that the analytic approach employed here captures the main underlying physics and provides useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate.

  • 35.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Corney, J. F.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    First-principles quantum dynamics for fermions: Application to molecular dissociation2010In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 92, no 3, article id 36003Article in journal (Refereed)
    Abstract [en]

    We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.

  • 36.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Corney, J. F.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Stochastic simulations of fermionic dynamics with phase-space representations2011In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 182, no 9, p. 1999-2003Article in journal (Refereed)
    Abstract [en]

    A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains well-bounded, which defines a useful simulation time. We analyse the application of the Gaussian phase-space representation to the dynamics of the dissociation of an ultra-cold molecular gas. We show how the choice of mapping to stochastic differential equations can be used to tailor the stochastic behaviour, and thus the useful simulation time. In the phase-space approach, it is only averages of stochastic trajectories that have a direct physical meaning. Whether particular constants of the motion are satisfied by individual trajectories depends on the choice of mapping, as we show in examples.

  • 37.
    Ögren, Magnus
    et al.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Kärkkäinen, K.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Yu, Y.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    Reimann, S. M.
    Mathematical Physics, Lund Institute of Technology, Lund, Sweden.
    On the spin asymmetry of ground states in trapped two-component Fermi gases with repulsive interactions2007In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 40, no 13, p. 2653-2660Article in journal (Refereed)
    Abstract [en]

    We examine the spin asymmetry of ground states for two-dimensional, harmonically trapped two-component gases of fermionic atoms at zero temperature with weakly repulsive short-range interactions. Our main result is that, in contrast to the three-dimensional case, in two dimensions a non-trivial spin-asymmetric phase can only be caused by the shell structure. A simple, qualitative description is given in terms of an approximate single-particle model, comparing well to the standard results of Hartree-Fock or direct diagonalization methods.

  • 38.
    Ögren, Magnus
    et al.
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Nyström, Marcus
    Blick för bättre läromedel?2012In: Manus, ISSN 2000-4028, no 2, p. 6-6Article, review/survey (Other (popular science, discussion, etc.))
  • 39.
    Ögren, Magnus
    et al.
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Nyström, Marcus
    Humanistlaboratoriet, Lunds universitet, Lund, Sweden.
    Med blick på vektoranalys: Ögonrörelsemätning vid problemlösning2011In: Lärande i LTH, Vol. 15, p. 6-7Article, review/survey (Other (popular science, discussion, etc.))
  • 40.
    Ögren, Magnus
    et al.
    Örebro University, School of Science and Technology. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark; Department of Chemistry, Nano-Science Center, University of Copenhagen, Copenhagen, Denmark.
    Nyström, Marcus
    Lund University Humanities Laboratory, Lund, Sweden.
    Jarodzka, Halszka
    Open University, Heerlen, The Netherlands.
    There’s more to the multimedia effect than meets the eye: is seeing pictures believing?2017In: Instructional science, ISSN 0020-4277, E-ISSN 1573-1952, Vol. 45, no 2, p. 263-287Article in journal (Refereed)
    Abstract [en]

    Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students’ attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.

  • 41.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Savage, C. M.
    Department of Quantum Science, ARC Centre of Excellence for Quantum-Atom Optics, Australian National University, Canberra, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Directional effects due to quantum statistics in dissociation of elongated molecular condensates2009In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, no 4, article id 043624Article in journal (Refereed)
    Abstract [en]

    Ultracold clouds of dimeric molecules can dissociate into quantum mechanically correlated constituent atoms that are either both bosons or both fermions. We theoretically model the dissociation of two-dimensional anisotropic molecular condensates for which this difference manifests as complementary geometric structures of the dissociated atoms. Atomic bosons are preferentially emitted along the long axis of the molecular condensate, while atomic fermions are preferentially emitted along the short axis. This anisotropy potentially simplifies the measurement of correlations between the atoms through relative number squeezing.

  • 42.
    Ögren, Magnus
    et al.
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Sørensen, M. P.
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Pedersen, N. F.
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Self-consistent Ginzburg-Landau theory for transport currents in superconductors2012In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 479, p. 157-159Article in journal (Refereed)
    Abstract [en]

    We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in principle also be used for general geometries in three-dimensional superconductors. © 2012 Elsevier B.V. All rights reserved.

  • 43.
    Ögren, Magnus
    et al.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Yu, Y.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Åberg, S.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Reimann, S. M.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Brack, M.
    Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany.
    Super-shell structure in harmonically trapped fermionic gases and its semi-classical interpretation2006In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, no T125, p. 37-40Article in journal (Refereed)
    Abstract [en]

    It was recently shown in self-consistent Hartree–Fock calculations that a harmonically trapped dilute gas of fermionic atoms with a repulsive two-body interaction exhibits a pronounced super-shell structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the 'magic numbers' occurring between the beat nodes by half a period. The length and amplitude of the beating mode depends on the strength of the interaction. We give a qualitative interpretation of the beat structure in terms of a semi-classical trace formula that uniformly describes the symmetry breaking U(3) → SO(3) in a three-dimensional harmonic oscillator potential perturbed by an anharmonic term ∝ r 4 with arbitrary strength. We show that at low Fermi energies (or particle numbers), the beating gross-shell structure of this system is dominated solely by the twofold degenerate circular and (diametrically) pendulating orbits.

1 - 43 of 43
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