Density Operators and Other Tools of Quantum Statistics

И. Д. Феранчук, A. A. Ivanov, Van-Hoang Le +1 more

Tomaž Prosen, Marko Žnidarič

We propose to quantify the complexity of nonequilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of the level spacing distribution of their spectra. Based on extensive numerical studies in a variety of models, some solvable and some unsolved, we conjecture that the integrability of density operators (e.g., the existence of an algebraic procedure for their construction in finitely many steps) is signaled by a Poissonian level statistics, whereas in the generic nonintegrable cases one finds level statistics of a Gaussian unitary ensemble of random matrices. Eigenvalue statistics can therefore be used as an efficient tool to identify integrable quantum nonequilibrium systems.

W. Ebeling, Thorsten Pöschel

In this chapter, basic quantum tools such as time-evolution operators, transition rates and amplitudes, statistical and projector operators, and interaction and density matrix representations are employed to characterize the open and interacting quantum systems with the aid of Schrödinger, quantum master, Fokker-Planck, and Feynman path integral equations and formulations.

F. Becattini, Matteo Buzzegoli, Eduardo Grossi

In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions.

Raj K. Pathria, Paul D. Beale