### Topical School

## Open quantum Systems (2)

## Nancy, July 9th, 10th and 11th, 2008

#### Speakers

Walter Aschbacher (Munich) |
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A short introduction to the mathematical theory of nonequilibirum quantum statistical mechanics I: General theory |

We give a short introduction to the rigorous mathematical theory of open quantum systems with focus on the nonequilibrium situation. In the first lecture, we briefly present the general theory in its algebraic framework, i.e. the so-called scattering and spectral approaches to nonequilibrium steady states (NESS). |

A short introduction to the mathematical theory of nonequilibirum quantum statistical mechanics II: Some applications |

We give a short introduction to the rigorous mathematical theory of open quantum systems with focus on the nonequilibrium situation. In the second lecture, we illustrate the general theory by means of quasifree fermionic systems, and, in particular, by the prominent XY chain. |

Arnaldo Donoso (Caracas) |

Quantum Dynamics with Particle Methods, a different computational approach |

A phase space approach to quantum dynamics is presented in terms of quasi-probability distribution functions as an attempt to obtain a more intuitive view of simple quantum processes. The equations are solved using particle methods as an alternative to more conventional grid-based schemes. A few examples are presented for illustration. |

Jochen Gemmer (Osnabrueck) |

The careful application of projection methods to transport and relaxation |

Traditionally projection operator methods like the Nakajima-Zwanzig approach have been applied to open system scenarios employing projections onto product states. The validity of this approach is routinely inferred from the separation of relaxation and correlation timescales. It turns out that the approach may fail even if there is separation of timescales, e.g., in the context of finite environments. This can be (possibly) fixed by projection onto non-product states. This generalized class of projections than also allows for a direct approach to transport problems by projecting onto density waves. |

The typicality approach to thermodynamical relaxation in quantum systems |

In recent years an approach ("typicality") to thermodynamical relaxation that does not rely on projection methods has attracted considerable attention. It is based on the the idea that, in some sense, Hilbert space is "filled" with pure states each of which already individually features equilibrium ensemble properties. Thus relaxation simply appears as the venturing of a pure state into and through this class of states. The approach has been discussed for compound as well as for single system scenarios. We present both and comment on dynamics and the relation to projection methods. |

Bahar Mehmani (Amsterdam) |

System under influence of a varying environment |

A discussion on non adiabatic corrections for a system interacting with a varying environment. |

Theo Nieuwenhuizen (Amsterdam) |

Quantum thermodynamics I |

I will define the field of quantum thermodynamics as the thermodynamics of a small quantum system coupled to a macroscopic bath and a macroscopic work source. In the absence of a thermodynamics limit, the various formulations of the second law remain different and may or may not be valid anymore. Specific cases will be discussed. If time allows, the role of work transfer for the Berry phase will be discussed. |

Quantum thermodynamics II |

Quantum thermodynamics III |

Supermassive black holes as giant Bose-Einstein condensates |

Juan Pablo Paz (Buenos Aires) |

Decoherence, the quantum to classical transition and the environment (1) |

In these lectures I will present an overview of the physics of the process of environment induced decoherence. In the first lecture I will discuss the relevance of this process to understand the emergence of classicality out of a fundamentally quantum substrate. I will discuss general features about the evolution of quantum open systems and focus on the paradigmatic example of quantum Brownian motion to illustrate the main features of decoherence (timescales, pointer states, etc). |

Decoherence, the quantum to classical transition and the environment (2) |

In the second lecture I will analyze the decoherence induced by the interaction with spin baths. The role of the dynamics of the environment will be discussed with some detail. The footprints of critical phenomena in the environment will be analyzed. |

Decoherence, the quantum to classical transition and the environment (3) |

In the third lecture I will examine decoherence from a different perspective: I will focus on the way in which correlations between system and environment are created and develop. Classicality will be related with the existence of redundant records of the state of the system imprinted in the environment. The way in which this can be quantified will be discussed and illustrated for the case of quantum Brownian motion. |

#### Organizing comittee

Bertrand Berche |

Dragi Karevski |

#### Our partners

UFA - DFH | Nancy Université - UHP |