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# Documents  Pillet, Claude-Alain | enregistrements trouvés : 4

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## Nonequilibrium statistical mechanics of harmonic networks Pillet, Claude-Alain | CIRM H

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Research talks;Mathematical Physics

We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence and uniqueness of the steady state of the resulting process, we construct a canonical entropy production functional $S(t)$ which satisfies the Gallavotti-Cohen fluctuation theorem. More precisely, we prove that cumulant generating function of $S(t)$ has a large-time limit $e(a)$ which is finite on a closed interval centered at $a=1/2$, infinite on its complement and satisfies the Gallavotti-Cohen symmetry $e(1-a)=e(a)$ for all $a$. It follows from well known results that $S(t)$ satisfies a global large deviation principle with a rate function $I(s)$ obeying the Gallavotti-Cohen fluctuation relation $I(-s)-I(s)=s$ for all $s$. We also consider perturbations of $S(t)$ by quadratic boundary terms and prove that they satisfy extended fluctuation relations, i.e., a global large deviation principle with a rate function that typically differs from $I(s)$ outside a finite interval. This applies to various physically relevant functionals and, in particular, to the heat dissipation rate of the network. Our approach relies on the properties of the maximal solution of a one-parameter family of algebraic matrix Ricatti equations. It turns out that the limiting cumulant generating functions of $S(t)$ and its perturbations can be computed in terms of spectral data of a Hamiltonian matrix depending on the harmonic potential of the network and the parameters of the Langevin reservoirs. This makes our approach well adapted to both analytical and numerical investigations. This is joint work with Vojkan Jaksic and Armen Shirikyan. We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence and uniqueness of the steady state of the resulting process, we construct a canonical entropy production functional $S(t)$ which satisfies the Gallavotti-Cohen fluctuation theorem. More precisely, we prove ...

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## Open quantum systems III :recent developments Attal, Stéphane ; Joye, Alain ; Pillet, Claude-Alain | Springer 2006

Ouvrage

- 310 p.
ISBN 978-3-540-30993-2

Lecture notes in mathematics , 1882

Localisation : Collection 1er étage

Systéme ouvert # système quantique physique # propriété de non-équilibre # règle d'or de Fermi # limite à couplage faible # irréversibilité quantique # décohérence # comportement qualitatif des semigroupes de Markov quantiques # mesure quantique continue

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## Open quantum systems II :the markovian approach Attal, Stéphane ; Joye, Alain ; Pillet, Claude-Alain | Springer 2006

Ouvrage

- 239 p.
ISBN 978-3-540-30992-5

Lecture notes in mathematics , 1881

Localisation : Collection 1er étage

système ouvert # systéme quantique physique # processus de Markov # équation différentielle stochastique # formalisme markovien

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## Open quantum systems I :the Hamiltonian approach Attal, Stéphane ; Joye, Alain ; Pillet, Claude-Alain | Springer 2006

Ouvrage

- 329 p.
ISBN 978-3-540-30991-8

Lecture notes in mathematics , 1880

Localisation : Collection 1er étage

système ouvert # système quantique physique # mécanique statistique quantique # analyse spectrale # théorie modulaire # système dynamique quantique

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