Thermal Pure States for Finite and Isolated Quantum Systems

Abstract

We study an ensemble of quantum pure states, the thermalization resilient ensemble (TRE), providing the statistical characterization of the thermal equilibrium of isolated quantum systems. Following a previous work where the ensemble was defined based on the invariance of the average populations upon thermal contact of identical systems, here we introduce a general methodology to generate quantum states according to the TRE statistic. The sampling is employed to characterize the ensemble distribution of thermodynamic functions like the entropy, internal energy, and temperature. The possibility of defining the temperature also for isolated quantum systems with a limited number of degrees of freedom is a distinctive feature of the TRE statistic which has no counterpart in other quantum statistical ensembles. The results are illustrated by explicit calculations for spin model systems.

Signatures of Anderson localization and delocalized random quantum states

“…Such an issue has been examined in the past from different points of view with the purpose of providing well defined rules for the random sampling of pure states within the Bloch hypersphere. [44][45][46][47] In the following, we shall employ the Random Pure State Ensemble which has been proposed and analyzed in detail elsewhere. 12, 31 The initial state (0)  is parameterized according to the set of phases  , while for the population an efficient algorithm based on the independent sampling of ( 1) N  variables in the domain [0,1) is available as reported in ref 26 .…”

“…Such an issue has been examined in the past from different points of view with the purpose of providing well defined rules for the random sampling of pure states within the Bloch hypersphere. [44][45][46][47] In the following, we shall employ the Random Pure State Ensemble which has been proposed and analyzed in detail elsewhere. 12,31 The initial state (0)  is parameterized according to the set of phases The uniform distribution on the Bloch hypersphere of the pure states is recovered from the uniform distribution on N -dimensional torus for the phases and the uniform distribution on ( 1) N  -dimensional simplex for the eigenstate populations taking into account the constraints of normalization,  , while for the population an efficient algorithm based on the independent sampling of ( 1) N  variables in the domain [0,1) is available as reported in ref 26 .…”