Violations of local equilibrium and linear response in classical lattice theories (熱場の量子論とその応用)

Kenichiro Aoki, Dimitri Kusnezov

Jan Naudts, J. V. Pul�, André F. Verbeure

Abraham Nitzan

Abstract This chapter introduces linear response theory, a general way to describe non-equilibrium system in the vicinity of equilibrium. (1) Classical static and dynamic linear response theory. (2) Quantum static and dynamic linear response theory. (3) Causality and the Kramers–Kronig relations (4) Examples: Mobility, conductivity and diffusion. (5) Thermal noise.

Akira Shimizu, Kyota Fujikura

Abstract We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.

S. Jain

Sergei Skorik

We study the partition functions of quantum impurity problems in the domain of complex applied bias for its relation to the non-equilibrium current suggested by Fendley, Lesage and Saleur (cond-mat/9510055). The problem is reformulated as a certain generalization of the linear response theory that accomodates an additional complex variable. It is shown that the mentioned relation holds in a rather generic case in the linear response limit, or under certain condition out of equilibrium. This condition is trivially satisfied by the quadratic Hamiltonians and is rather restrictive for the interacting models. An example is given when the condition is violated.