ICMP 2003

Condensed matter physics

Session organized by J. Yngvason (Wien), Y. Avron (Haïfa).


A. ElgartNew York
J. FeldmanVancouver
G. M. GrafZürich
M. SalmhoferLeipzig
R. SeiringerPrinceton
S. TeufelTU München, Germany
Alexander Elgart
Courant Institute

Adiabatic transport, Kubo formula and Anderson localization in some lattice and continuum models

The different explanations of Quantum Hall Effect rely on the validity of the linear response theory for a system that has infinite extent. We will present recent results on the adiabatic charge transport in this context for two dimensional lattice (joint work with M. Aizenman and J. Schenker) and continuum (joint work with B. Schlein) models of a non interacting electron gas. It is proved that if the Fermi energy falls in the localization regime then Hall transport is correctly described by the linear response Kubo formula. The localization condition is set forth by fractional moment method, which is by now extended also to continuum models (joint work with M. Aizenman, S. Naboko, J. Schenker and G. Stoltz). In the present talk, besides of the localization criteria, we will discuss some ideas -- Nenciu's asymptotic expansion, generalized space-momentum inequalities, and finite speed of propagation estimates which enter the proof.

Joel Feldman

Construction of a 2-d Fermi liquid: the results

This is one of two self-contained talks at ICMP 2003 concerning the proof (of Horst Knoerrer, Eugene Trubowitz and J. F.) that the temperature zero renormalized perturbation expansions of a class of interacting many-fermion models in two space dimensions have nonzero radius of convergence. The models have "asymmetric" Fermi surfaces and short range interactions. One consequence of the convergence is the existence of a discontinuity in the particle number density at the Fermi surface. The detailed proof is now available on the net at http://www.math.ubc.ca/~feldman/. This talk will concentrate on the statement of results. The other, which is in the session on Equilibrium Statistical Mechanics, will highlight the strategy of the construction.

Gian Michele Graf
ETH Zuerich

Adiabatic charge pumping in open quantum systems

Transport between coupled reservoirs at equilibrium occurs if the junction between them is externally driven. We consider such pumps in the case where they are connected to reservoirs of independent electrons, and the driving is slow compared to the dwell time of particles in the pump. The charge transport associated with a given change of pump parameters is characterized in terms of S-matrices pertaining to time-independent junctions. In fact, several transport properties (charge, dissipation and, at positive temperature, noise and entropy production) may be expressed in terms of the matrix of energy shift which, like Wigner's time delay to which it is dual, is determined by the S-matrix.

This is joint work with J. Avron, A. Elgart, L. Sadun, K. Schnee.

Manfred Salmhofer
University Leipzig

Fermi systems in two dimensions and fermi surface flows

A proof of Fermi liquid behaviour of weakly coupled Hubbard--like models in two spatial dimensions at positive temperature, in the sense of finiteness of the quasiparticle interactions and regularity of the selfenergy, is discussed. The proof is by a renormalization group flow in which the Fermi surface gets adjusted dynamically during the flow, so that no counterterms are needed. To show the required regularity properties of the selfenergy and the Fermi surface, the technique of improving power counting by single and double overlaps is implemented in a nonperturbative setting.

This is joint work with Walter de Siqueira Pedra (University and MPI--MIS, Leipzig).

Roebert Seiringer
Princeton University

One-dimensional behavior of dilute, trapped Bose gases

Recent experimental and theoretical work has shown that under certain conditions trapped, low-density Bose gases behave like one-dimensional systems, which are typically described by an (exactly solvable) model of a 1D Bose gas with delta-function interaction. This one-dimensional behavior is an intrinsically quantum-mechanical phenomenon because it is not necessary to have a trap width that is of the order of the size of an atom - as might have been supposed - but it suffices merely that the trap width is small compared to the "healing length". We give a rigorous proof of the one-dimensional behavior, at least as far as the ground state is concerned, and determine the relevant parameter regimes. In particular, we derive the 1D Bose gas with delta-function interaction as a limit of a 3D Bose gas of hard spheres. We also investigate the phenomenon of Bose-Einstein condensation for these effectively one-dimensional systems.

(Joint work with E.H. Lieb and J. Yngvason.)

Stefan Teufel
TU München, Germany

Effective dynamics for Bloch Electrons: Peierls substitution and beyond

The semiclassical equations of motion of a quantum particle in a slowly perturbed periodic potential are discussed. Based on recent results from a joint work with G. Panati and H. Spohn I explain how the well known "semiclassical model" of solid state physics is related to the Schrödinger equation. I also present a rigorous result concerning the first order corrections to the "semiclassical model" recently discovered by Niu et al. These corrections involve, in particular, a contribution from the curvature of the Berry connection defined by the Bloch eigenfunctions. They provide a semiclassical explanation for the quantization of the Hall conductivity in quantum Hall systems.

(Joint work with G. Panati and H. Spohn)


P.S. Goldbaum

Lower bound for the segregation energy in the Falicov-Kimball model

E. Langmann
KTH, Stockolm

A class of exactly solvable models of 2D correlated fermions

E. Palentova, Z. Masakova
Czech Tech. Univ., Czech Republic

The Meyer property for quasicrystals

S.Teufel, G.Panati, H.Spohn
Tech. Univ. Munchen, Germany

Effective dynamics for Bloch electrons: Peierls substitution and beyond

V. Geyler
Mordovian State U., Russia

Fractal properties of the spectrum of the three-dimensional periodic Landau operators

P. Zeiner

Coincidence site lattices for cubic lattices

J. Lages, P.D. Sacramento, Z. Tesanovic
CFIF, IST, Lisbon; CFIF, IST, Lisbon and Johns Hopkins Univ., USA

Disorder and vortices in unconventional superconductors

V. Zagrebnov
CPT, Marseille, France

Do bosons condense in a homogeneous magnetic field?

A. Suto
Res. ISSPO, Budapeste, Hungary

Bose condensation of trapped bosons

K. Watanabe, K. Nakamura, H. Ezawa
Meisei, Tokyo; Meiji Univ., Tokyo and Honkomagame, Tokyo

A condition for Bose-Einstein condensation in a trap

C. Brouder
Lab. Mineralogie-Cristallographie, U. Paris 6 et 7, France

Quantum field theory of degenerate systems

O. Vertsanova
Nat. Tech. Univ. Ukraine, Kyiv, Ukraine

Mathematical simulation of photoacoustic effect in layered solid structures

M. Angelova
Northumbria Univ., Newcastle upon Tyne

Algebraic thermodynamic properties of anharmonic molecules and linear chains

J. Riess
CRTBT, CNRS Grenoble, France

On the theory of electric DC-conductivity: linear and non-linear microscopic evolution vs. macroscopic behaviour