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Accueil du site > Séminaires > Séminaires 2011 > Emergence of non-thermal statistics in isolated quantum spin clusters under non-adiabatic perturbations

mardi 8 mars — 14:00

Emergence of non-thermal statistics in isolated quantum spin clusters under non-adiabatic perturbations

Boris Fine (University of Heidelberg)

par Pierre Pujol - 8 mars 2011

The statistical behavior of completely isolated quantum systems having not too large number of particles, but a large number of quantum levels is interesting both on its own and in the context of the foundations of macroscopic thermodynamics. An isolated system of ten q-bits already fits into the above category. Other relevant examples are small clusters of nuclear spins, or the systems of a few cold atoms. I will present numerical evidence[1] that, if a finite isolated cluster of interacting spins 1/2 with the initial thermal occupations of energy eigenstates is subjected to a series of small non-adiabatic perturbations by external magnetic field, then the resulting occupations are no longer describable by the exponential thermal statistics. The emerging non-thermal occupations are significantly higher than the thermal ones on both the low and the high ends of the energy spectra. This behavior semi-quantitatively agrees with the unconventional statistics predicted for the so-called ”quantum micro-canonical” (QMC) ensemble[2], which includes all possible quantum superpositions with a given energy expectation value. The properties and the possible experimental implications of the QMC ensemble are to be described in this talk in some detail. I will also present evidence that the eigenstates of the non-adiabatic perturbation operators are generically localized in the energy basis of the unperturbed Hamiltonian. This kind of localization possibly protects the conventional thermal behavior in the macroscopic limit.

[1] K. Ji and B. V. Fine, arXiv:1102.3651

[2] B. V. Fine, Phys. Rev. E 80, 051130 (2009).

http://www.thphys.uni-heidelberg.de/ fine/