Topics in nonequilibrium quantum statistical mechanics

@inproceedings{Aschbacher2006TopicsIN,
  title={Topics in nonequilibrium quantum statistical mechanics},
  author={Walter H. Aschbacher and Vojkan Jaksic and Yan Pautrat and Claude-Alain Pillet},
  year={2006}
}
These notes are an expanded and revised version of the lectures given by the second and fourth autor in the summer school "Open Quantum System" held in Grenoble, June 16-July 4, 2003. They provide an introduction to recent developments in non-equilibrium statistical mechanics of open quantum systems, including a completely worked out (simple) example. We discuss non-equilibrium steady states (NESS) and their structural properties, entropy production, linear response theory and weak coupling… 
View via Publisher
link.springer.com
53 Citations
Background Citations
2

53 Citations

A note on the Landauer principle in quantum statistical mechanics

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than kT log 2. We discuss…

Quantum Dynamical Systems

This notes are an expanded version of the lectures given by the author at the Grenoble "Open Quantum Systems" summer school in 2003. They provide a short introduction to quantum dynamical systems and…

Mathematical Theory of the Wigner-Weisskopf Atom

These notes provide an introduction to the spectral theory of the Friedrichs model. This model is used in quantum physics to describe the coupling of a discrete set of energy levels to a continuum of…

Linear Response Theory for Thermally Driven Quantum Open Systems

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys.…

Thermal Relaxation of a QED Cavity

We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time…

Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production

A general argument leading from the formula for currents through an open noninteracting mesoscopic system given by the theory of nonequilibrium steady states to the Landauer-Buttiker formula is…

Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States

We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively).…

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics

The large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time is related to the large deviation rule for quantum uncertainty in the W*-algebraic setting.

Energy Full Counting Statistics and Return to Equilibrium

We consider a finite dimensional quantum system S in an arbitrary initial state coupled to an infinitely extended quantum thermal reservoir R in equilibrium at inverse temperature β. The coupling is…

The Landauer-Büttiker formula and resonant quantum transport

We give a short presentation of two recent results. The first one is a rigorous proof of the Landauer-Buttiker formula, and the second one concerns resonant quantum transport. The detailed results…
...

References

SHOWING 1-10 OF 82 REFERENCES

Introduction to quantum statistical mechanics

Problem Non Ideal Bose Gas, Superfluidity and Fundamental Aspects of Quasiaverages Application Quasiaverages in the Theory of Superconductivity Correlations Weakening and Theorems on Singularities of…

Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in refs. 1–7. In the algebraic formalism of quantum statistical mechanics we…

Positive Commutators in Non-Equilibrium Quantum Statistical Mechanics

Abstract: The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum…

Mathematical Theory of the Wigner-Weisskopf Atom

These notes provide an introduction to the spectral theory of the Friedrichs model. This model is used in quantum physics to describe the coupling of a discrete set of energy levels to a continuum of…

Topics in quantum statistical mechanics and operator algebras

The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to…

Spectral theory of thermal relaxation

We review some results obtained in a recent series of papers on thermal relaxation in classical and quantum dissipative systems. We consider models where a small system I, with a finite number of…

The approach to equilibrium in quantum statistics: A perturbation treatment to general order

Dynamical Ensembles in Nonequilibrium Statistical Mechanics.

This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.

Natural Nonequilibrium States in Quantum Statistical Mechanics

A quantum spin system is discussed where a heat flow between infinite reservoirs takes place in a finite region. A time-dependent force may also be acting. Our analysis is based on a simple technical…

Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics

This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view which has emerged…
...