On the approach to equilibrium in quantum systems

Ross Dorner

This thesis is a study of non-equilibrium phenomena in quantum systems. Emphasis is given to the recently derived non-equilibrium fluctuation theorems, which relate the non-equilibrium response of a system to its equilibrium thermodynamic properties. We investigate the validity and importance of these theorems, from both a theoretical and experimental perspective, in systems ranging from a single atom to an ensemble of interacting particles. We also investigate the potential role of quantum dynamics in biological processes.

Oscar E. Lanford, Derek W. Robinson

Takaaki Monnai

The irreversible relaxation to equilibrium is explained for macroscopic quantum systems with an emphasis on the behavior of expectation values and extremely high dimensionality of the Hilbert space. We consider a large but isolated system that is initially out of equilibrium and eventually relaxes to equilibrium. The relaxation is described by the deviation of the expectation value of the quantity of interest from the long-time average. After relaxation, the amount of deviation from equilibrium is discussed based on probabilistic arguments, which are available for nonintegrable systems. We also evaluate how long the system stays near equilibrium.

Rudolf Haag

Gérard G. Emch, Chuang Liu

Sheldon Goldstein, David A. Huse, Joel L. Lebowitz +1 more

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (MITE). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between MITE and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and MITE. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but MITE fails to hold for any phase point.