Abstract
Further application of embedded ensembles (EEs) is to time dynamics and entropy production in isolated finite interacting many-particle systems. Results here are useful in the study of the stability of a quantum computer against quantum chaos and in the study of issues related to statistical relaxation and thermalization in isolated finite quantum systems. It is also possible to address fidelity and Loschmidt echoes in many-particle quantum systems using EEs. Available results in these topics are briefly discussed.
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References
V.V. Flambaum, Time dynamics in chaotic many-body systems: can chaos destroy a quantum computer? Aust. J. Phys. 53, 489–497 (2000)
L.F. Santos, F. Borgonovi, F.M. Izrailev, Onset of chaos and relaxation in isolated systems of interacting spins: energy shell approach. Phys. Rev. E 85, 036209 (2012)
V.K.B. Kota, A. Relaño, J. Retamosa, M. Vyas, Thermalization in the two-body random ensemble, J. Stat. Mech. P10028 (2011)
G.P. Berman, F. Borgonovi, F.M. Izrailev, A. Smerzi, Irregular dynamics in a one-dimensional Bose system. Phys. Rev. Lett. 92, 030404 (2004)
I. Piz̆orn, T. Prosen, T.H. Seligman, Loschmidt echoes in two-body random matrix ensembles. Phys. Rev. B 76, 035122 (2007)
V.V. Flambaum, F.M. Izrailev, Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems. Phys. Rev. E 64, 036220 (2001)
V.K.B. Kota, R. Sahu, Structure of wavefunctions in (1+2)-body random matrix ensembles. Phys. Rev. E 64, 016219 (2001)
M. Abramowtiz, I.A. Stegun (eds.), Handbook of Mathematical Functions, NBS Applied Mathematics Series, vol. 55 (U.S. Govt. Printing Office, Washington, D.C., 1972)
A. Bohr, B.R. Mottelson, Nuclear Structure, Single-Particle Motion, vol. I (Benjamin, New York, 1969)
I. Dreier, S. Kotz, A note on the characteristic function of the t-distribution. Stat. Probab. Lett. 57, 221–224 (2002)
R. Jördens, N. Strohmaier, K. Günter, H. Moritz, T. Esslinger, A Mott insulator of fermionic atoms in an optical lattice. Nature 455, 204–207 (2008)
U. Schneider et al., Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322, 1520–1525 (2008)
L. Perfetti et al., Time evolution of the electronic structure of 1T-TaS2 through the insulator-metal transition. Phys. Rev. Lett. 97, 067402 (2006)
M. Srednicki, Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994)
J.M. Deutsch, Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046–2049 (1991)
M.V. Berry, Regular and irregular semiclassical wavefunctions. J. Phys. A 10, 2083–2091 (1977)
M. Rigol, V. Dunjko, M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems. Nature (London) 452, 854–858 (2008)
M. Rigol, Breakdown of thermalization in finite one-dimensional systems. Phys. Rev. Lett. 103, 100403 (2009)
L.F. Santos, M. Rigol, Onset of quantum chaos in one dimensional bosonic and fermionic systems and its relation to thermalization. Phys. Rev. E 81, 036206 (2010)
L.F. Santos, M. Rigol, Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems. Phys. Rev. E 82, 031130 (2010)
L.F. Santos, F. Borgonovi, F.M. Izrailev, Chaos and statistical relaxation in quantum systems of interacting particles. Phys. Rev. Lett. 108, 094102 (2012)
V.K.B. Kota, Embedded random matrix ensembles for complexity and chaos in finite interacting particle systems. Phys. Rep. 347, 223–288 (2001)
J.M.G. Gómez, K. Kar, V.K.B. Kota, R.A. Molina, A. Relaño, J. Retamosa, Many-body quantum chaos: recent developments and applications to nuclei. Phys. Rep. 499, 103–226 (2011)
V.V. Flambaum, A.A. Gribakina, G.F. Gribakin, I.V. Ponomarev, Quantum chaos in many-body systems: what can we learn from the Ce atom. Physica D 131, 205–220 (1999)
P. Reimann, Foundation of statistical mechanics under experimentally realistic conditions. Phys. Rev. Lett. 101, 190403 (2008)
S. Goldstein, J.L. Lebowitz, C. Mastrodonato, R. Tumulka, N. Zanghi, Approach to thermal equilibrium of macroscopic quantum systems. Phys. Rev. E 81, 011109 (2010)
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Kota, V.K.B. (2014). Time Dynamics and Entropy Production to Thermalization in EGOE. In: Embedded Random Matrix Ensembles in Quantum Physics. Lecture Notes in Physics, vol 884. Springer, Cham. https://doi.org/10.1007/978-3-319-04567-2_15
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DOI: https://doi.org/10.1007/978-3-319-04567-2_15
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