Introduction Study of the dynamics

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Introduction Study of the dynamics Thermodynamics properties Random repeated interaction quantum systems Collaboration with A. Joye and M. Merkli L. Bruneau Univ. Cergy-Pontoise January 2009 L. Bruneau Random repeated interaction quantum systems

  • langevin equation

  • cergy pontoise

  • interaction quantum

  • bruneau random repeated

  • introduction study

  • spectral analysis


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Random
Introduction Study of the dynamics Thermodynamics properties
repeated Collaboration
quantum nd M. Merkli
interaction with A. Joye a
L.
Univ.
Bruneau
Cergy-Pontoise
January
L. Bruneau
2009
systems
Random repeated interaction quantum systems
Open Systems
Introduction Study of the dynamics Thermodynamics properties
A “small” (or confined) systemSinteracts with an environmentR. Goal:understand the asymptotic (t+) behaviour of the systemS (asymptotic state, thermodynamical properties).
S
L. Bruneau
R
Random repeated interaction quantum systems
Open Systems
Introduction Study of the dynamics Thermodynamics properties
A “small” (or confined) systemSinteracts with an environmentR. Goal:understand the asymptotic (t+) behaviour of the systemS (asymptotic state, thermodynamical properties).
S
2 approaches: Hamiltonian / Markovian
L. Bruneau
R
Random repeated interaction quantum systems
Open Systems
Introduction Study of the dynamics Thermodynamics properties
A “small” (or confined) systemSinteracts with an environmentR. Goal:understand the asymptotic (t+) behaviour of the systemS (asymptotic state, thermodynamical properties).
S
R
2 approaches: Hamiltonian / Markovian Hamiltonian:full description, spectral analysis, scattering theory.
L. Bruneau
Random repeated interaction quantum systems
Open Systems
Introduction Study of the dynamics Thermodynamics properties
A “small” (or confined) systemSinteracts with an environmentR. Goal:understand the asymptotic (t+) behaviour of the systemS (asymptotic state, thermodynamical properties).
S
R
2 approaches: Hamiltonian / Markovian Hamiltonian:full description, spectral analysis, scattering theory. Markovian:effective description ofS, obtained by weak-coupling type limits or ifSundergoes stochastic forces (Langevin equation).
L. Bruneau
Random repeated interaction quantum systems
Repeated
A
Introduction Study of the dynamics Thermodynamics properties Interaction Quant
“small” syst Quantum
emS: system
governed
by
L. Bruneau
um
some
Systems
hamiltonian
(RIQS)
HS
acting
Random repeated interaction quantum systems
on
HS.
Repeated
Introduction Study of the dynamics Thermodynamics properties Interaction Quantum
Systems
(RIQS)
HS
A “small” systemS: Quantum system governed by some hamiltonianHSacting on A chainCof quantum sub-systemsEk(k= 12   ): C=E1+E2+   EachEkis governed by some hamiltonianHEkacting onHEk.
L. Bruneau
Random repeated interaction quantum systems
.