%0 Generic
%A Hahn, Walter
%D 2016
%F heidok:21802
%K quantum statistical ensemble
%R 10.11588/heidok.00021802
%T Stability of Quantum Statistical Ensembles with Respect to Local Measurements
%U https://archiv.ub.uni-heidelberg.de/volltextserver/21802/
%X An open problem in the foundations of quantum statistical physics is the missing justification for using statistical ensembles with narrow energy distributions such as the canonical or microcanonical ensembles.    In this thesis, we resolve this problem by introducing a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called “stable” when a small number of local measurements cannot significantly modify the probability distribution of the total energy of the system. We apply this criterion to lattices of spins-1/2, thereby showing that the canonical ensemble is nearly stable, whereas statistical ensembles with much broader energy distributions are not stable.    We test the analytical estimates numerically by investigating the stability of quantum statistical ensembles for generic interacting spin systems. Although the finite-size effects with respect to local measurements are rather pronounced for the microscopic system sizes available in numerical simulations, the results of the numerical studies are consistent with the analytical results.    Finally, we introduce a macroscopicity measure for quantum superpositions. A quantum superposition is called macroscopic if one local measurement can induce a significant change of a macroscopic number of the subsystems’ density matrices.