Aspects of Integrability in a Classical Model for Non-Interacting Fermionic Fields

• Authors: S. Grosse-Holz , T. Engl , K. Richter , J. Urbina
• Languages of publication: EN

Abstracts

EN

In this work we investigate the issue of integrability in a classical model for non-interacting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrable in general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle.

Keywords

EN

03.65.Sq; 05.45.Mt; 67.85.-d; 72.15.Rn

Discipline

• 72.15.Rn: Localization effects (Anderson or weak localization)
• 03.65.Sq: Semiclassical theories and applications
• 67.85.-d: Ultracold gases, trapped gases(see also 03.75.-b Matter waves in quantum mechanics)
• 05.45.Mt: Quantum chaos; semiclassical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 128
• Issue: 6
• Pages: 994-1001

Dates

published

2015-12

Contributors

author

S. Grosse-Holz

• Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

author

T. Engl

• Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

author

K. Richter

• Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

author

J. Urbina

• Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

References

• [1] M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer Science & Business Media, New York 2013
• [2] K. Richter, Semiclassical Theory of Mesoscopic Quantum Systems, Springer, Berlin 2000
• [3] J.J. Sakurai, J. Napolitano, Modern Quantum Mechanics, Pearson, Boston 2011
• [4] L.S. Schulman, Techniques and Applications of Path Integration, Dover, Mineola (NY) 2005
• [5] M. Brack, R.K. Bhaduri, Semiclassical Physics, Addison-Wesley, Reading (MA) 1997
• [6] J.W. Negele, H. Orland, Quantum Many-Particle Systems, Westview Press, Boulder (CA) 2009
• [7] T. Van Voorhis, D.R. Reichman, J. Chem. Phys. 120, 579 (2004), doi: 10.1063/1.1630963
• [8] T. Engl, Ph.D. Thesis, Universität Regensburg, 2015
• [9] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, J.D. Urbina, Phys. Rev. Lett. 112, 140403 (2014), doi: 10.1103/PhysRevLett.112.140403
• [10] T. Engl, P. Plößl, J.D. Urbina, K. Richter, Theor. Chem. Acc. 133 (11), (2014), doi: 10.1007/s00214-014-1563-9
• [11] M. Tabor, Chaos and Integrability in Nonlinear Dynamics, Wiley, New York 1989

Identifiers

DOI

10.12693/APhysPolA.128.994