Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics

Martin Bodo Plenio

N. S. Tonchev, J.G. Brankov

We present some aspects of the fidelity approach to phase transitions based on lower and upper bounds on the fidelity susceptibility that are expressed in terms of thermodynamic quantities. Both commutative and non commutative cases are considered. In the commutative case, in addition, a relation between the fidelity and the nonequilibrium work done on the system in a process from an equilibrium initial state to an equilibrium final state has been obtained by using the Jarzynski equality.

Shusa Deng

Aditya Shashi

Traditionally the study of quantum mechanical ensembles was focused on the exploration of their equilibrium properties: the program has consisted of the classification of the quantum mechanical states of matter, and the identification of the striking phase transitions between them. On the other hand, questions about the out of equilibrium properties of quantum ensembles have largely remained academic until fairly recently. Particularly, the rapid technological progress in the field of atomic physics has enabled experimental demonstrations of nontrivial out of equilibrium phenomena which moreover are describable in terms of relatively simple theoretical models with a few parameters. Thus the time is ripe for a theoretical exploration of nonequilibrium physics. To this end, quantum impurity models offer a natural and simple starting point for studying nonequilibrium phenomena in the context of ultracold atoms, and pave the way toward the study of more complicated systems. I will discuss how the impurity-bath model offers a clean, simple realization of rich phenomenology including the dynamics of polaron formation as well as the orthogonality catastrophe, and can be engineered using dilute mixtures of cold atomic gases. Moreover I will demonstrate how impurity models are also embedded in the more complicated physics of the response of a one-dimensional system to an external perturbation, or a sudden local parameter change. Lastly, I will describe the approach to equilibrium of a more\ncomplicated system, the one dimensional Bose gas, following a sudden parameter change, and discuss some of the important questions which arise in this connection: does a quantum mechanical system thermalize? What is the appropriate asymptotic description of a nonequilibrium state? Does such a system retain a memory of its initial state?

K. Sengupta