Mathematical Physics
Seminar
December Schedule
Please join us every Thursday in the kitchen of room 705 for
cookies & coffee
Speaker: V. Rom-Kedar, Weizmann Institute
Date:Thursday, Dec. 7, 2006
Time/Place:12-1pm; Hill 705
Title:
"From Forced NLS to Resonant Surface Waves-Towards Classifying
the Structure of Chaotic Solutions"
Abstract: The
study of near-integrable Hamiltonian systems by the hierarchy of
bifurcations framework will be described. It will be shown that it
leads to new insights regarding the solution structure of quite
complicated, non-integrable systems, such as the forced NLS on a
periodic segment and of resonant surface waves interactions. For the
forced NLS case we show that depending on the forcing frequency, for
low amplitude solutions which are close to the plane wave solution,
three different chaotic scenarios (homoclinic chaos, hyperbolic
resonance and parabolic resonance) may emerge. The analysis is
performed on a truncated model and it is numerically demonstrated that
similar behavior appears in the full system. The analysis leads to the
judicious choice of the initial profiles and parameter values which
produce these different types of solutions of the forced NLS equation.
Similar strategy is employed for analyzing the interaction of surface
waves near certain resonances. We show that the above three scenarios
appear in a truncated version of this problem as well, and discuss
their implications on the form of the surface waves.
Based on joint works with E. Shlizerman and M. Radnovic.
THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM
Speaker: P. Garrido, University of Granada
Date:Thursday, Dec. 7, 2006
Time/Place:2-3pm; Hill 705
Title:"Boundary Dissipation in a Driven Hard Disk System"
Abstract: Bulk dissipation is often assumed to explain
stationary states in driven systems as in the well known example of
Drude's
theory of electrical conduction where three mechanisms act over a
given interacting particle system in order to have a well defined
stationary state:
(1) a constant force that accelerates the particles in a given
direction,
(2) a thermal bath (typically acting in the bulk) that should drive
the system to an equilibrium state absorbing energy excess due
to the action of the driving and
(3) an array of bulk impurities that introduce a strong chaotic
behavior on the particle dynamics.
Existence of a stationary state is, however, not so clear if the
action of the thermostat is at the system boundaries and no impurities
are present.
We present the computer simulation results of a system of hard disks
under the action of a driving field. We check that, within the range
of external force strength that we are able to simulate, the system
appears to reach a well defined stationary state. Even for ``strong''
driving fields, although the thermostat acts only near the system
boundaries, i.e.through very short range forces (in fact we
consider hard core forces) between pairs of particles of the system
and of the thermostats and between``mixed pairs'' of system and
thermostats particles.
Speaker: S. Chakravarty, UCLA
Date:Thursday, Dec. 14, 2006
Time/Place:12-1pm; Hill 705
Title:"Replacing energy by Von Neumann entropy in quantum phase transitions"
Abstract: In the thermodynamic limit two distinct states
of matter cannot be analytic continuations of each other. Classical
phase transitions are characterized by non-analyticities of the free
energy. For quantum phase transitions (QPTs) the ground state energy
often assumes the role of the free energy. But in a number of
important cases this criterion fails to predict a QPT, such as the
three-dimensional metal-insulator transition of non-interacting
electrons in a random potential (Anderson localization). It is
therefore essential that we find alternative criteria that can track
fundamental changes in the internal correlations of the ground state
wavefunction. Here we propose that QPTs are generally accompanied by
non-analyticities of the von Neumann (entanglement) entropy. In
particular, the entropy is non-analytic at the Anderson transition,
where it exhibits unusual fractal scaling. Similar results a;so hold
for the Von Neumann entropy for quantum Hall plateau transitions. We
also examine two dissipative quantum systems of considerable
interest to the study of decoherence and find that non-analyticities
occur if and only if the system undergoes a QPT.
THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM
Speaker:C. Toninelli, LPT, ENS
Date:Thursday, Dec. 14, 2006
Time/Place:2-3pm; Hill 705
Title: "Relaxation Times of Kinetically Constrained Spin
Models with Glassy Dynamics"
Abstract: We discuss some kinetically constrained spin
models (KCSM)
which were introduced in physical literature to model liquid/glass
and jamming transitions. We present a novel multi-scale approach
through
which we can determine the scaling with the system size of their
relaxation time and establish exponential decay to equilibrium in the
whole ergodic regime. This excludes the stretched exponential
relaxation
conjectured by previous numerical simulations. On the other hand, we
prove that relaxation times diverges faster than any power law as
density
goes to one, in a way which is very reminiscent of the Vogel-Fulcher
law
for supercooled liquids.