Mathematical Physics
Seminar
November Schedule
Please join us every Thursday in the kitchen of room 705 for
cookies & coffee
Speaker: J. Cardy,University of Oxford
Date:Thursday, Nov. 2, 2006
Time/Place:12-1pm; Hill 705
Title: "Percolation and Integer Flows"
Abstract: Some time ago Arrowsmith, Mason and Essam pointed out a connection between the connectedness probability of oriented (directed) percolation on the square lattice and a peculiar limit of the so-called integer flow problem on the same lattice. I will review this result and show that the connection holds for a wide range of models on an arbitrary oriented lattice. Extensions to ordinary non-oriented percolation are also discussed. This work was done in part with F. Colaiori.
PLEASE NOTE THERE WILL BE A BROWN BAG LUNCH FROM 1-2 PM.
PLEASE BRING YOUR LUNCH
Speaker: T. Banks, Rutgers University
Date:Thursday, Nov. 2, 2006
Time/Place:2-3pm; Hill 705
Title: "A Heterodox View of the State of String Theory"
Abstract:I will argue that string theory, much like quantum
field theory, is a collection of DIFFERENT quantum models, all of
which include gravity. The different models are distinguished by the
asymptotics of space-time, the amount of supersymmetry, and other
quantum numbers. Well understood models have the property that a
conventional low energy field theoretic treatment of the dynamics in
space-time is valid only when supersymmetry is asymptotically (both at
large energy and at large distance) restored. Theories of
asymptotically flat space-time have exact supersymmetry. The models
allow us to understand a number of mechanisms relevant to the real
world - in particular the appearance of non-abelian gauge theory and
chiral fermions.
The implications of these observations for the real world are
profound, and change our view of the cosmological constant . In the
context of these observations, the so-called "Landscape of String
Theory", seems like a naive conjecture based on low energy field
theory, though it cannot be definitively ruled out. If I have time I
will present a brief introduction to my own ideas about how to
generalize the formalism of string theory to make a model of the real world.
Speaker: D. Brydges, University of British Columbia
Date: Thursday, Nov. 9, 2006
Time/Place: 12-1pm; Hill 705
Title:"Self-avoiding loop correlations and loop erasure"
Abstract: Ratios of generating functions for disjoint
oriented
loops in a finite graph can be expressed in terms of the generating
function of a single path in the graph weighted according to loops in
the path. It is a little combinatoric miracle about the Mayer
expansion
and it is also a generalisation of Cramer's formula for the
inverse of a matrix. It was discovered in 1993 by Xavier Viennot and
recently rediscovered by Abdesselam and Brydges.
PLEASE NOTE THERE WILL BE A BROWN BAG LUNCH FROM 1-2 PM.
PLEASE BRING YOUR LUNCH
Speaker: E. Carlen, Georgia Tech.
Date: Thursday, Nov. 9, 2006
Time/Place: 2-3pm; Hill 705
Title:"Long Time Behavior of Solutions of Some Fourth
Order Equations"
Abstract:A number of physical problems lead to the
consideration
of fourth order parabolic evolution equations. The lack of a maximum
principle for these equations is the source of interesting challenges,
and places a premium on finding as many Lyapunov funcions as possible.
I will discuss the general background on this area, and then will
discuss recent results, some of which have been obtained
in collaboration with Suleyman Ulusoy.
Speaker: L. Rey-Bellet, University of Massachusetts
Date: Thursday, Nov. 16, 2006
Time/Place: 12-1pm; Hill 705
Title: "Large deviations in nonuniformly dynamical systems"
Abstract: We discuss large deviations results for deterministic dynamical systems which are non-uniformly hyperbolic in the sens they admit a symbolic description by a so-called Young tower. Such systems are for example quadratic maps of the interval, Henon maps, billiards.
PLEASE NOTE THERE WILL BE A BROWN BAG LUNCH FROM 1-2 PM.
PLEASE BRING YOUR LUNCH
Speaker: F. Toninelli, ENS, France
Date: Thursday, Nov. 16, 2006
Time/Place: 2-3pm; Hill 705
Title: "Critical properties of the depinning transition of random directed polymers"
Abstract:Directed polymers interacting with a one-dimensional defect line show a delocalization-localization phase transition. I will discuss some rigorous results on the critical properties (i.e., inequalities for critical exponents) for models both with and without disorder. In particular, I will focus on the question of when is disorder "relevant" or "irrelevant" in the sense of the Harris criterion.
Speaker: D. Ruelle, IHES/Rutgers Univ.
Date: Tuesday, Nov. 21, 2006 <--- PLEASE NOTE DATE
Time/Place: 12-1pm; Hill 705
Title: "Nonequilibrium Statistical Mechanics of Infinite
Systems, and Entropy Production"
Abstract:We discuss infinite classical systems (rotators) and quantum systems
(quantum spins) and ask if it is possible to define entropy and rate of
entropy production for finite subsets of the infinite system.
PLEASE NOTE THERE WILL BE A BROWN BAG LUNCH FROM 1-2 PM.
PLEASE BRING YOUR LUNCH
Speaker: J. Lukkarinen, Technical University Munich
Date: Tuesday, Nov. 21, 2006 <--- PLEASE NOTE DATE
Time/Place: 2-3pm; Hill 705
Title:"Energy Transport in a Weakly Anharmonic
Chain"
Abstract:I will discuss a joint work with Kenichiro Aoki and Herbert Spohn on heat conduction in a certain anharmonic chain [J. Stat. Phys. 124 (2006) 1105-1129]. We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular values of the coupling parameters before, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level, we employ the Boltzmann-Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for the finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations, and in the range of weak anharmonicity, respectively low temperatures, reasonable quantitative agreement is observed.
PLEASE NOTE THERE WILL BE NO SEMINAR THURSDAY, NOVEMBER 23, 2006
Speaker: G. Milton, University of Utah
Date: Thursday, Nov. 30, 2006
Time/Place: 12-1pm; Hill 705
Title: "Cloaking: a New Phenomena in Electomagnetism and
Elasticity"
Abstract: The making of an object invisible through
some cloaking device
until recently was commonly regarded as science fiction. Two
quite different types of electromagnetic cloaking have been proposed
early this year. In our cloaking scenario a collection of arbitrarily
many
polarizable dipoles becomes essentially invisible when
they are within a certain critical distance of a superlens.
Superlenses have attracted attention because they promise resolution
on a length scale finer than can be achieved using conventional
lenses, i.e.,
finer than the wavelength. The radiation scattered by the polarizable
dipoles resonates with the superlens and acts back on the dipoles to
essentially cancel the field incident on them, which is why they
become invisible. Dipolar energy sources supplying constant power also
become invisible. A second type of cloaking was proposed by Pendry,
Schurig and Smith and Leonhardt. In this scenario a shield cloaks
objects to incident electromagnetic waves. This work is related
to the earlier work of Greenleaf, Lassas and Uhlmann, on cloaking
for conductivity. Here we will review these developments and also
discuss how cloaking might be extended to elasticity using these
ideas. This requires new materials, in particular materials with
anisotropic mass density. We show how such materials can be made.
This is joint work with Nicolae Nicorovici, Ross McPhedran, Mark
Briane and John Willis.
PLEASE NOTE THERE WILL BE A BROWN BAG LUNCH FROM 1-2 PM.
PLEASE BRING YOUR LUNCH
Speaker: N. Zanghi, INFN, Italy
Date: Thursday, Nov. 30, 2006
Time/Place: 2-3pm; Hill 705
Title: "On the Common Structure of Bohmian Mechanics and
the Ghirardi--Rimini--Weber Theory"
Abstract:Bohmian mechanics and the
Ghirardi--Rimini--Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional
variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave
function by a nonlinear and stochastic modification of Schroedinger's
equation. Still, both theories, when understood appropriately, share
the following structure: They are ultimately not about wave functions
but about "matter'' moving in space, represented by either particle
trajectories, fields on space-time, or a discrete set of space-time
points. The role of the wave
function then is to govern the motion of the matter. (Work in
collaboration with Valia Allori, Shelly Goldstein and Roderich Tumulka.)