Document Type
Article
Publication Date
9-1-1990
Publication Title
Physical Review A
Abstract
Starting from quantum Langevin equations for operators we study thermal properties of a one-dimensional harmonic chain to whose ends independent heat baths are attached. In this paper, we mainly discuss the thermal equilibrium state that the chain eventually approaches if the heat baths are at equal temperatures. In the classical limit, this state is determined by the Gibbs ensemble of the free chain, whereas in the quantal case, this is only true if the strength of coupling between chain and heat baths is made infinitely small. We find that corrections for finite coupling strength are appreciable only in boundary layers near both ends of the chain. The thickness of the boundary layers depends only on the temperature and not on the damping constant. Outside these boundary layers we find an analogy between thermal properties of the chain and a discrete random walk.
Repository Citation
Zürcher, Ulrich and Talkner, Peter, "Quantum-Mechanical Harmonic Chain Attached to Heat Baths I: Equilibrium Properties" (1990). Physics Faculty Publications. 275.
https://engagedscholarship.csuohio.edu/sciphysics_facpub/275
DOI
10.1103/PhysRevA.42.3267
Version
Publisher's PDF
Publisher's Statement
©1990 American Physical Society
Volume
42
