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  • 1.
    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.

  • 2.
    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.

  • 3.
    Herper, H. C.
    et al.
    Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden.
    Ahmed, T.
    Institute for Materials Science, Los Alamos National Laboratory, Los Alamos New Mexico, USA.
    Wills, J. M.
    Theoretical Division, Los Alamos National Laboratory, Los Alamos New Mexico, USA.
    Di Marco, I.
    Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden.
    Björkman, T.
    Department of Natural Sciences, Åbo Akademi, Turku, Finland.
    Iusan, D.
    Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden.
    Balatsky, A. V.
    Institute for Materials Science, Los Alamos National Laboratory, Los Alamos New Mexico, USA; AlbaNova University Center Nordita, Stockholm, Sweden.
    Eriksson, Olle
    Örebro University, School of Science and Technology. Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden.
    Combining electronic structure and many-body theory with large databases: A method for predicting the nature of 4 f states in Ce compounds2017In: Physical Review Materials, ISSN 2475-9953, Vol. 1, no 3, article id 033802Article in journal (Refereed)
    Abstract [en]

    Recent progress in materials informatics has opened up the possibility of a new approach to accessing properties of materials in which one assays the aggregate properties of a large set of materials within the same class in addition to a detailed investigation of each compound in that class. Here we present a large scale investigation of electronic properties and correlated magnetism in Ce-based compounds accompanied by a systematic study of the electronic structure and 4f-hybridization function of a large body of Ce compounds. We systematically study the electronic structure and 4f-hybridization function of a large body of Ce compounds with the goal of elucidating the nature of the 4f states and their interrelation with the measured Kondo energy in these compounds. The hybridization function has been analyzed for more than 350 data sets (being part of the IMS database) of cubic Ce compounds using electronic structure theory that relies on a full-potential approach. We demonstrate that the strength of the hybridization function, evaluated in this way, allows us to draw precise conclusions about the degree of localization of the 4f states in these compounds. The theoretical results are entirely consistent with all experimental information, relevant to the degree of 4f localization for all investigated materials. Furthermore, a more detailed analysis of the electronic structure and the hybridization function allows us to make precise statements about Kondo correlations in these systems. The calculated hybridization functions, together with the corresponding density of states, reproduce the expected exponential behavior of the observed Kondo temperatures and prove a consistent trend in real materials. This trend allows us to predict which systems may be correctly identified as Kondo systems. A strong anticorrelation between the size of the hybridization function and the volume of the systems has been observed. The information entropy for this set of systems is about 0.42. Our approach demonstrates the predictive power of materials informatics when a large number of materials is used to establish significant trends. This predictive power can be used to design new materials with desired properties. The applicability of this approach for other correlated electron systems is discussed.

  • 4.
    Morfeldt, Johannes
    Örebro University, School of Science and Technology.
    Optically Selective Surfaces in low concentrating PV/T systems2009Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    One of the traditional approaches to reduce costs of solar energy is to use inexpensive reflectors to focus the light onto highly efficient solar cells. Several research projects have resulted in designs, where the excess heat is used as solar thermal energy.

    Unlike a solar thermal system, which has a selective surface to reduce the radiant heat loss, a CPV/T (Concentrating PhotoVoltaic/Thermal) system uses a receiver covered with solar cells with high thermal emittance.

    This project analyzes whether the heat loss from the receiver can be reduced by covering parts of the receiver surface, not already covered with solar cells, with an optically selective coating. Comparing different methods of applying such a coating and the long-term stability of low cost alternatives are also part of the objectives of this project.

    To calculate the heat loss reductions of the optically selective surface coating a mathematical model was developed, which takes the thermal emittances and the solar absorptances of the different surfaces into account. Furthermore, a full-size experiment was constructed to verify the theoretical predictions.

    The coating results in a heat loss reduction of approximately 20 % in such a CPV/T system and one of the companies involved in the study is already changing their design to make use of the results.

  • 5.
    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.

  • 6.
    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)
  • 7. 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.

  • 8.
    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.

  • 9.
    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).

  • 10.
    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)
  • 11.
    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.))
  • 12.
    Ögren, Magnus
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Lärarhandledning [Teacher's manual] till: Kvantvärldens fenomen: teori och begrepp2006Book (Other academic)
  • 13.
    Ögren, Magnus
    Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Problem med lösningar till kvantmekanik: fördjupningskurs2006Book (Other academic)
  • 14.
    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)
  • 15.
    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.

  • 16.
    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.

  • 17.
    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.

  • 18.
    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 - 18 of 18
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