caa a22 4500 46789311X CHVBK 20180406152754.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10955-006-9210-z doi (NATIONALLICENCE)springer-10.1007/s10955-006-9210-z On the Distribution of the Wave Function for Systems in Thermal Equilibrium [Elektronische Daten] [Sheldon Goldstein, Joel Lebowitz, Roderich Tumulka, Nino Zanghì] For a quantum system, a density matrix ρ that is not pure can arise, via averaging, from a distribution μ of its wave function, a normalized vector belonging to its Hilbert space ℋ. While ρ itself does not determine a unique μ, additional facts, such as that the system has come to thermal equilibrium, might. It is thus not unreasonable to ask, which μ, if any, corresponds to a given thermodynamic ensemble? To answer this question we construct, for any given density matrix ρ, a natural measure on the unit sphere in ℋ, denoted GAP(ρ). We do this using a suitable projection of the Gaussian measure on ℋ with covariance ρ. We establish some nice properties of GAP(ρ) 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 ρβ = (1/Z) exp (−β H). GAP(ρ) may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems, where distributions on ℋ are often used. Springer Science+Business Media, LLC, 2006 Canonical ensemble in quantum theory nationallicence probability measures on Hilbert space nationallicence Gaussian measures nationallicence density matrices nationallicence Goldstein Sheldon Departments of Mathematics and Physics, Rutgers, The State University of New Jersey, Hill Center, 110 Frelinghuysen Road, 08854-8019, Piscataway, NJ, USA aut Lebowitz Joel Departments of Mathematics and Physics, Rutgers, The State University of New Jersey, Hill Center, 110 Frelinghuysen Road, 08854-8019, Piscataway, NJ, USA aut Tumulka Roderich Mathematisches Institut, Eberhard-Karls-Universität, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut Zanghì Nino Dipartimento di Fisica and INFN sezione di Genova, dell'Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1193-1221 0022-4715 125:5-6<1193 2006 125 10955 https://doi.org/10.1007/s10955-006-9210-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9210-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goldstein Sheldon Departments of Mathematics and Physics, Rutgers, The State University of New Jersey, Hill Center, 110 Frelinghuysen Road, 08854-8019, Piscataway, NJ, USA aut NATIONALLICENCE 700 1- Lebowitz Joel Departments of Mathematics and Physics, Rutgers, The State University of New Jersey, Hill Center, 110 Frelinghuysen Road, 08854-8019, Piscataway, NJ, USA aut NATIONALLICENCE 700 1- Tumulka Roderich Mathematisches Institut, Eberhard-Karls-Universität, Auf der Morgenstelle 10, 72076, Tübingen, Germany aut NATIONALLICENCE 700 1- Zanghì Nino Dipartimento di Fisica and INFN sezione di Genova, dell'Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/5-6(2006-12-01), 1193-1221 0022-4715 125:5-6<1193 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer