# 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…

## 53 Citations

### A note on the Landauer principle in quantum statistical mechanics

- Physics
- 2014

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

- Physics
- 2006

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

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- 2006

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

- Physics
- 2006

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

- Physics
- 2009

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

- Physics
- 2007

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

- Mathematics
- 2008

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

- PhysicsArXiv
- 2011

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

- Mathematics
- 2021

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

- Mathematics, Physics
- 2006

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…

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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…

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