Klaus Richter

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Concepts based on multi-particle interference have been proven very fruitful for better understanding
various different many-body phenomena, including quantum dynamics of cold atoms, "many-body localization",
correlated transport through molecules, or scattering in photonic networks. We will consider such phenomena
using semiclassical techniques based on interfering Feynman paths.
A major objective of such approaches to an interacting many-body system is to combine
information of its two complementary classical limits, namely a classical system of particles
and/or a classical field theory, into a unified framework, providing a picture of many-body interference
based on coherent sums over classical solutions.
Following this direction we will illustrate recent progress in the semiclassical analysis of many-body
interference using a prime example of integrable quantum field theory, the Lieb-Liniger model, describing
interacting bosons on a ring. We show that, in the limit of high excitations, its spectrum can be
understood by means of suitable generalizations of the so-called Weyl expansion for the smooth part, and a
trace formula for the oscillatory part, revealing a spectral shell structure in terms of many-body periodic
orbits.
We will then show how for large particle number the complementary classical limit of the Lieb-Liniger model,
given by a nonlinear Schroedinger equation, admits as well an analysis as an integrable classical system,
now near its ground state. This enables the description of a sequence of quantum phase transitions arising
for increasing (attractive) interaction, along with an understanding of numerical results for the spreading
of information around criticallity.
In the opposite case of non-integrable systems, applications of many particle interference comprise
coherent backscattering and echo phenomena in Fock space.

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University of Regensburg
TP seminar room 0.03
Contact: Alexander Altland