Canonical typicality

TY - JOUR

T1 - Canonical typicality

AU - Goldstein, Sheldon

AU - Lebowitz, Joel L.

AU - Tumulka, Roderich

AU - Zanghì, Nino

PY - 2006

Y1 - 2006

N2 - It is well known that a system S weakly coupled to a heat bath B is described by the canonical ensemble when the composite S+B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schrödinger in 1952.

AB - It is well known that a system S weakly coupled to a heat bath B is described by the canonical ensemble when the composite S+B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schrödinger in 1952.

UR - https://www.scopus.com/pages/publications/33144456594

UR - https://www.scopus.com/pages/publications/33144456594#tab=citedBy

U2 - 10.1103/PhysRevLett.96.050403

DO - 10.1103/PhysRevLett.96.050403

M3 - Article

SN - 0031-9007

VL - 96

JO - Physical review letters

JF - Physical review letters

IS - 5

M1 - 050403

ER -