Mathematical Physics
Seminar

December Schedule

Organizer: Joel L. Lebowitz
lebowitz@math.rutgers.edu

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.