Numerical Stability of Solution of Recursion Relation for Ideal Quantum Gases Containing Finite Number of Harmonically Trapped Particles

• Authors: T. Paszkiewicz , S. Wolski
• Languages of publication: EN

Abstracts

EN

The numerical stability of the solution of recursion relation for mean occupation numbers derived by Schönhammer for ideal Fermi gas trapped in 1D harmonic potential is studied. In low temperature region there exists a solution of this recursion relation. In high temperature region the iteration becomes unstable. In low and high temperature regions with growing number of particles the region of numerical instability diminishes.

Keywords

EN

05.30.Fk; 03.75.Ss

Discipline

• 03.75.Ss: Degenerate Fermi gases
• 05.30.Fk: Fermion systems and electron gas(see also 71.10.-w Theories and models of many-electron systems; see also 67.10.Db Fermion degeneracy in quantum fluids)

• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 128
• Issue: 2
• Pages: 204-207

Dates

published

2015-08

Contributors

author

T. Paszkiewicz

• Retired from Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, Rzeszów, Poland

author

S. Wolski

• Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, PL-35959 Rzeszów, Poland

References

• [1] L.P. Pitaevskii, S. Stringari, Einstein Condensation, Clarendon, Oxford 2003.
• [2] L.P. Pitaevskii, S. Stringari, Bose-Einstein Condensation, Clarendon, Oxford 2003.
• [3] S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008), doi: 10.1103/RevModPhys.80.1215
• [4] R. Denton, B. Muhlschlegel, D.J. Scalapino, Phys. Rev. B 7, 3589 (1973), doi: 10.1103/PhysRevB.7.3589
• [5] J. Arnaud, J.M. Boé, L. Chusseau, F. Philippe, Am. J. Phys. 67, 215 (1999), doi: 10.1119/1.19228
• [6] J. Arnaud, L. Chusseau, F. Philippe, Phys. Rev. B 62, 13482 (2000), doi: 10.1103/PhysRevB.62.13482
• [7] S. Grossmann, M. Holthaus, Phys. Rev. E 54, 3495 (1996), doi: 10.1103/PhysRevE.54.3495
• [8] S. Grossmann, M. Holthaus, Chaos Solitons Fractals 10, 795 (1999), doi: 10.1016/S0960-0779(98)00029-0
• [9] J.-M. Boé, F. Philippe, J. Comb. Theor. Series A 92, 173 (2000), doi: 10.1006/jcta.2000.3059
• [10] A. Kubasiak, J.K. Korbicz, J. Zakrzewski, M. Lewenstein, Europhys. Lett. 72, 506 (2005), doi: 10.1209/epl/i2005-10278-8
• [11] H.-J. Schmidt, J. Schnack, Am. J. Phys. 70, 53 (2002), doi: 10.1119/1.1412643
• [12] M. Ligare, Am. J. Phys. 66, 185 (1998), doi: 10.1119/1.18843
• [13] M. Ligare, Am. J. Phys. 70, 76 (2002), doi: 10.1119/1.1412649
• [14] M. Holthaus, E. Kalinowski, K. Kirsten, Ann. Phys. (New York) 270, 198 (1998), doi: 10.1006/aphy.1998.5852
• [15] M.N. Tran, M.V.N. Murthy, R.K. Badhuri, Phys. Rev. E 63, 031105 (2001), doi: 10.1103/PhysRevE.63.031105
• [16] F. Philippe, J. Arnoud, L. Chusseau, arXiv: math-ph/0211029v1, 2002
• [17] K. Schönhammer, Am. J. Phys. 68, 1032 (2000), doi: 10.1119/1.1286116
• [18] R. Shankar, Principles of Quantum Mechanics, Kluwer Academic, Plenum Publ., New York 2004
• [19] W.J. Mullin, J.P. Fernandez, Am. J. Phys. 71, 661 (2003), doi: 10.1119/1.1544520
• [20] E.D. Trifonov, S.N. Zagoulaev, Phys.-Usp. 53, 83 (2010), doi: 10.3367/UFNe.0180.201001e.0089
• [21] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York 1976

Identifiers

DOI

10.12693/APhysPolA.128.203