Subject: [Depfis] invitacion charlas sobre desequilibrio en cadenas de espines

From: Juan Pablo Paz <[email-masked]>
Date: Wed, 04 Mar 2009 14:21:26 -0300

Hola,

Durante los proximos dos meses nos visitara el Profesor Dragi Karevski,
del grupo de Fisica Estadistica de la Facultad de Ciencias de la Universidad
de Nancy 1, Francia. Dragi es un especialista en sistemas de espines acoplados
y dara una serie de charlas a modo de mini-curso. El titulo de este ciclo es
"Lectures on nonequilibrium Ising and XY quantum chains". Consistira de
aproximadamente cuatro o cinco encuentros de 1hs y media cada uno. Los mismos
comenzaran el proximo MARTES 10 DE MARZO a las 14hs en el Aula de Seminarios
del Departamento (segundo piso, Pabellon 1). Estan todos invitados. El curso
es especialmente apropiado para gente interesada en fisica estadistica,
materia condensada, informacion cuantica, etc. Las charlas seran en ingles,
se dictaran a un nivel introductorio, para no-especialistas, con cuentas y
detalles incluidos. Abajo incluyo un resumen del contenido del curso (en
ingles) y un programa abreviado. Saludos y los esperamos,

Juan Pablo

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Lecture on Nonequilibrium Ising and XY quantum chains

Dragi Karevski
Grupo de Fisica Estadistica, Institute Jean Lamour,
Universite Henri Poncare, Nancy 1, France

Abstract:
The series of lectures presented here are devoted to the  
non-equilibrium properties of  simple models: the Ising quantum chain  
and XY chain. Those
models are exactly mapped onto a set of free fermionic oscillators which
in turn leads to the possibility of explicitely solving the Heisenberg
equation of motion. The focus on these simple models is mainly due to
the fact that they present a rich phase diagram with so-called quantum
critical points. The possibility of an exact treatment of the dynamics
in non-equilibrium situations, generated by a quantum quench or the
coupling to quantum reservoirs, gives to these models the statut of a
"garde fou" in the development of general ideas in non-equilibrium
statistical mechanics.
After briefly reviewing the canonical diagonalization procedure and  
the equilibrium properties of the models I will turn on the discussion  
of
quantum quenches, that is starting with a state which is for exemple
the equilibrium (ground) state of an initial Hamiltonian $H_0$ we switch
on rapidly a field which will drive the system out of equilibrium and
focus on the relaxation properties of various local and global quantities.
The most interesting situation for a quantum quench is when the field is
varied such that it crosses the quantum critical point. Such time-dependent
quantum quenches present similarities with spacial quenches, that is when
the quantum control parameter is varying spacially and crosses  the
critical point value at a given spacial locus. A general scaling theory
is developed and a detailed solution is given for the Ising chain. Finally
the last lecture will be devoted to the open quantum chain interacting at
both ends with quantum bathes. The precise description of the bathes will
be discussed and a repeated interaction bath procedure will be presented
and used in order to discuss transport properties of the quantum chains.
This has a relevance to the optical lattice community since the XY chain
is mapped exactly to the Tonks-Girardeau gaz describing a strongly
repulsive bosonic gaz. The Nonequilibrium steady state describing the
system will be discussed in several sitations, including fluctuating
optical lattices.
Finally, the last lecture will be about Gallavotti-Cohen like quantum
fluctuation theorem and the connection between the work distribution
and the Loschmidt echo during a quantum quench. Some results on the
Ising and Heisenberg chains will be discussed and we will finish with
some open questions.

Temario:

1. Ising and XY quantum chains: Equilibrium properties, a reminder
1.1 Jordan-Wigner mapping
1.2 Diagonalization, excitation spectrum
1.3 Critical behaviour
1.4 Time-dependent correlation functions

2. Quench dynamics for the closed system
2.1 Equation of motion
2.2 Relaxation properties of physical quantities
2.3 Transverse magnetization
2.4 Two-time functions
2.5 Entanglement entropy, area law and relaxation
2.6 Disordered systems

3. From temporal to spacial quench
3.1 Scaling theory for gradient critical phenomena
3.2 Exact solution of the Ising chain with a gradient field

4. Open Systems
4.1 Current carrying states
4.2 Coupling to quantum bathes
4.3 Lindblad and repeated interactions
4.4 Exact NESS for the hard core boson model (XX chain)
4.5 Fluctuating optical lattices and transport properties in the NESS

5. Related and open questions
5.1 Quantum Fluctuation theorem in small spin chains
5.2 Work distribution and Loschmidt echo in a quantum quench
5.3 Perspectives and questions

-- 
Juan Pablo Paz
Associate Professor
Department of Physics
FCEyN, UBA
Pabellon 1, Ciudad Universitaria
1428 Buenos Aires, Argentina

Phone: 54-11-45763353
Fax:   54-11-45763357
web:   http://www.df.uba.ar/users/paz
email: [email-masked]