A soluble model for quantum mechanical dissipation

N. G. van Kampen

Masayuki Matsuo, Fumihiko Sakata, Toshio Marumori

Élliott H. Lieb

The early history of exactly soluble models in statistical mechanics and the quantum-mechanical many-body problem, especially in the 1960's, is briefly reviewed.

A. O. Caldeira

G. Crespo, A.M. Kowalski, Angelo Plastino +1 more

Pavel E. Dolgirev, Jamir Marino, Dries Sels +1 more

We study the behavior of an extended fermionic wire coupled to a local stochastic field. Since the quantum jump operator is Hermitian and quadratic in fermionic operators, it renders the model soluble, allowing investigation of the properties of the nonequilibrium steady state and the role of dissipation-induced fluctuations. We derive a closed set of equations of motion solely for the two-point correlator; on the other hand, we find, surprisingly, that the many-body state exhibits non-Gaussian correlations. Density-density correlation function demonstrates a crossover from a regime of weak dissipation characterized by moderate heating and stimulated fluctuations to a quantum Zeno regime ruled by strong dissipation, which tames quantum fluctuations. Instances of soluble dissipative impurities represent an experimentally viable platform to understand the interplay between dissipation and Hamiltonian dynamics in many-body quantum systems.