Beyond quantum microcanonical statistics

Journal Article · Mon Feb 07 00:00:00 EST 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3544218· OSTI ID:21559997

Fresch, Barbara; Moro, Giorgio J ^[1]

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1. Dipartimento di Science Chimiche, Universita di Padova, via Marzolo 1, 35131 Padova (Italy)

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e., the wavefunction, of an isolated system is determined to calculate molecular properties and their time evolution according to the unitary Schroedinger equation. On the other hand a mixed state, i.e., a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem.

• OSTI ID: 21559997
• Journal Information: Journal of Chemical Physics, Vol. 134, Issue 5; Other Information: DOI: 10.1063/1.3544218; (c) 2011 American Institute of Physics; ISSN 0021-9606
• Country of Publication: United States
• Language: English

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