On the Distribution of the Wave Function for Systems in Thermal Equilibrium

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dc.creatorGoldstein, Sheldon
dc.creatorLebowitz, Joel L.
dc.creatorTumulka, Roderich
dc.creatorZanghi, Nino
dc.date2003-09-01
dc.date2005-08-13
dc.date.accessioned2026-07-07T07:36:08Z
dc.date.available2026-07-07T07:36:08Z
dc.descriptionFor a quantum system, a density matrix rho that is not pure can arise, via averaging, from a distribution mu of its wave function, a normalized vector belonging to its Hilbert space H. While rho itself does not determine a unique mu, additional facts, such as that the system has come to thermal equilibrium, might. It is thus not unreasonable to ask, which mu, if any, corresponds to a given thermodynamic ensemble? To answer this question we construct, for any given density matrix rho, a natural measure on the unit sphere in H, denoted GAP(rho). We do this using a suitable projection of the Gaussian measure on H with covariance rho. We establish some nice properties of GAP(rho) and show that this measure arises naturally when considering macroscopic systems. In particular, we argue that it is the most appropriate choice for systems in thermal equilibrium, described by the canonical ensemble density matrix rho_beta = (1/Z) exp(- beta H). GAP(rho) may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems, where distributions on H are often used.
dc.description31 pages LaTeX, 1 figure; v3 minor improvements; v2 completely revised with major extensions
dc.identifierhttps://arxiv.org/abs/quant-ph/0309021
dc.identifierhttp://arxiv.org/abs/quant-ph/0309021
dc.identifierJ. Statist. Phys. 125 (2006) 1193-1221
dc.identifierdoi:10.1007/s10955-006-9210-z
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120324
dc.subjectQuantum Physics
dc.titleOn the Distribution of the Wave Function for Systems in Thermal Equilibrium
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