Mathematical Physics Seminar - Fall 2009
|
 |
Organizer(s) | Joel Lebowitz | Archive | |
Website | http://www.math.rutgers.edu/~lebowitz/ |
Thursday, December 3rd |
Vieri Mastropietro, University of Rome |
"Developments in the theory of universality" |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: Between the two seminars, there will be a brown bag lunch from 1-2:00pm
|
Thursday, December 3rd |
Chris Stucchio, Courant Institute of Mathematical Sciences, New York University |
"TBA" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: Coffee and cookies will be available in Hill 705 at 11:45 am |
Thursday, November 19th |
Milton D. Jara, CEREMADE, University of Paris-Dauphine |
"Density and current fluctuations for anomalous diffusive systems" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: We consider one-dimensional interacting particle systems with reversible dynamics whose scaling limits are not diffusive. As a prototype of these models we consider the zero-range process with long jumps and the zero-range process with degenerated bond disorder. We obtain a central limit theorem for the density of particles and for the current through a bond on those systems. The scaling limit is given by a fractional Brownian motion of Hurst parameter H in (0,1/2). |
Thursday, November 12th |
Edward Gerjuoy, University of Pittsburgh |
" An Introduction To Dense Coding" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: Coffee and Cookies will be available in Hill 705 at 11:45 AM
|
Thursday, November 5th |
Mikko Stenlund, Courant Institute of Mathematical Sciences, New York University |
" A pair correlation bound implies the Central Limit Theorem for Sinai Billiards " |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: It is an open problem in the study of dynamical systems whether fast decay of correlations alone is sufficient for the Central Limit Theorem (CLT) to hold. On the one hand, there are no examples of dynamical systems for which correlations decay quickly but the CLT fails. On the other, existing CLT proofs rely on statistical properties much stronger than correlation decay. In the talk I will discuss a prime class of physically relevant systems, called Sinai Billiards, and show that a single bound on correlations indeed implies the CLT directly. As a byproduct, the CLT is obtained for observables possessing remarkably little regularity. |
Thursday, October 29th |
Giovanni Gallavotti, University of Rome, "La Sapienza, and Rutgers University |
" Thermostats,constants of motion and heat in nonequilibrium statistical mechanics " |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: Thermostats are a contrivance designed to keep temperature constant in regions with which a system subject to nonconservative forces is in contact. In nonequilibrium statistical mechanics thermostat models can be Hamiltonian and infinite or artificial and finite. The problem examined is the equivalence between some Hamiltonian and artificial model: the artificial models considered are not the stochastic thermostats but the iso-ernergetic or isokinetic thermostats which introduce artificial forces to maintain the constrained temperatures: such thermostats are interesting because they are employed in simulations leading to recent developments in nonequilibrium theory. Connection heat conduction and Fourier law might find a place in the talk if time permits. |
Thursday, October 29th |
Luc Rey-Bellet, University of Massachusetts |
"Some problems in large deviations for quantum systems" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: Coffee and Cookies will be available in
Hill 705 at 11:45 AM
We discuss several issues in quantum large deviations.
The first problem
we discuss is a generalization of Laplace-Vardhan lemma to quantum spin
systems or in the language of statistical mechanics a proof of a
variational principle for systems with short range and mean field
interactions. (Joint work with W. De Roeck, C. Maes and K. Netockny).
The second problem we address is a proof a large deviation principle for
macroscopic observables in quantum systems. We apply to the quantum case
an approach to large deviations which goes back to
Lanford and Ruelle and use direct sub additivity arguments. (Joint work
with Y. Ogata).
Finally we will discuss some open problems.
THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM BETWEEN THE TWO SEMINARS, PLEASE JOIN US |
Wednesday, October 28th |
| Special Mathematical Physics Seminar |
Jared Speck, Cambridge University, England, UK |
"THE STABILITY OF THE IRROTATIONAL EULER-EINSTEIN SYSTEM WITH A POSITIVE COSMOLOGICAL CONSTANT" |
| Time: 10:20 AM |
| Location: Hill 425 |
| Abstract: The irrotational Euler-Einstein system models the evolution of a dynamic spacetime containing a perfect fluid with vanishing vorticity. In this talk, which is a summary of recent joint work with Igor Rodnianski, I will discuss the stability of a family of background cosmological solutions to the irrotational Euler-Einstein system in 1 + 3 dimensions with a positive cosmological constant $Lambda$. The background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. Our main result is a proof that under the equation of state p = c^2_s; 0 < c^2_s < 1/3, the background solutions are globally future-stable under small irrotational perturbations. In particular, the perturbed spacetimes, which have the topological structure [0,infty) times bbT^3, are future casually geodesically complete. It is of special interest to note that the behavior of the fluid in an exponentially expanding spacetime diff ers drastically from the case of flat spacetime. More speci cally, Christodoulou has recently shown that on the Minkowski space background, irrotational data arbitrarily close to that of an initially quiet uniform fluid can lead to solutions that form shocks. In view of this fact, we remark that the proof of our main result can be used to show the following: exponentially expanding spacetime backgrounds can stabilize irrotational fluids. This work is an extension of recent work by Ringstrom. |
Thursday, October 22nd |
Yves Elskens, CNRS-University of Provence, Marseille |
" Diffusion limit for many particles in a periodic stochastic acceleration field" |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: The one-dimensional motion of any number $N$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener processes. In the limit of vanishing particle mass $m to 0$, or equivalently of large noise intensity, we show that the momenta of all $N$ particles converge weakly to $N$ independent Brownian motions, and this convergence holds even if the noise is periodic. This justifies the usual application of the diffusion equation to a family of particles in a unique stochastic force field. The proof rests on the ergodic properties of the relative velocity of two particles in the scaling limit. Y. Elskens and E. Pardoux. |
Thursday, October 22nd |
S. Olla, Ceremade, UMR CNR University of Paris, Daupphine |
"On anomalous thermal conductivity in stochastic models" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: I will review some recent analitical and numerical results on the thermal conductivity for one dimensional chain of coupled oscillators with noise conserving energy and momentum. |
Thursday, October 15th |
Marcello Lucia, City University of NY, CSI |
" Uniqueness and symmetry of equilibria in a chemotaxis model " |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: Coffee and Cookies will be available in the kitchen of
Hill 705 prior to the start of the Seminar AT 11:45 am
We consider in a disc a class of parameter-dependent, nonlocal elliptic boundary value problems that describe the steady states of some chemotaxis systems. If the appearing parameter is less than an explicit critical value, we establish several uniqueness results for solutions that are invariant under a group of rotations. Furthermore, we discuss the associated consequences for the time asymptotic behavior of the solutions to the corresponding time dependent chemotaxis systems. Our results also provide optimal constants in some Moser-Trudinger type inequalities. |
Thursday, October 8th |
TBA, TBA |
"TBA" |
| Time: 2:00 PM |
| Location: Hill 705 |
Thursday, October 8th |
TBA, TBA |
"TBA" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM BETWEEN THE TWO SEMINARS. PLEASE JOIN US |
Thursday, October 1st |
Jean-Pierre Eckmann, University of Geneva |
"A topological glass" |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: I will describe some work about a model which captures properties of 2D glasses of soft disks. In particular I will show that much of the results of Procaccia et al. comes from purely topological considerations (with Metropolis structure). Finally, this work also sheds light on what can be considered the "ultrametric properties" of glassy systems. |
Thursday, October 1st |
Kenneth Golden, University of Utah |
" Climate Change and the Thermal Evolution of Fluid Permeability and Microstructure in Sea Ice" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: There will be Coffee and Cookies in Room 705 at 11:45 AM prior to the beginning of the seminars.
There will also be a "Brown Bag Lunch" between the seminars from 1:00 PM to 2:00 PM Sea ice is both an indicator and agent of climate change. It also hosts extensive microbial communities which sustain life in the polar oceans. Fluid flow through porous sea ice mediates a broad range of processes such as the growth and decay of seasonal ice, the evolution of melt ponds and ice pack reflectance, and biomass build-up. We will describe recent advances in using percolation, hierarchical, and network models to predict the fluid permeability of sea ice, and rigorous methods for bounding such transport coefficients. We'll also discuss X-ray CT imaging of the brine microstructure and connectivity analysis of random graphs derived from the tomographic images. Our work will help in predicting how global warming may affect Earth's sea ice packs and how polar ecosystems may respond. Related results on electromagnetic properties will help in monitoring ice thickness and the impact of climate change on the polar marine environment. Video from a 2007 Antarctic expedition where we measured fluid and electrical transport in sea ice will be shown. |
Thursday, September 24th |
O.Costin, Ohio State University |
" Integrability versus chaos in differential systems" |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: We analyze ordinary differential equations from the point of view of integrability, in the broad sense of existence of well behaved global conserved quantities (constants of motion). A century old and very powerful practical criterion of integrability is the Painleve property, the absence of branched movable (initial condition-dependent) singularities. We discuss why global integrals exist in this case, and their implications on global control of solutions. Simple examples such as Abel's equation, y'=y3+t, and in fact generic equations do not satisfy Painleve property. Using Borel summability methods we show that this implies a form of ergodicity: for an open set of complex initial conditions, every trajectory is dense in an open set of solutions. When this is the case, solvability in any explicit sense, and even precise control of the solution in large complex regions of the phase space are virtually precluded. Work in collaboration with R.D. Costin, L. Zhang, and F. Fauvet. |
Thursday, September 24th |
R. Tumulka, Rutgers University |
" On the Free Will Theorem of Conway and Kochen Abstract: " |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: John Horton Conway and Simon Kochen have presented a "free will theorem"
which they claim shows that "if indeed we humans have free will, then [so
do] elementary particles." In a more precise fashion, they claim it shows
that for certain quantum experiments in which the experimenters can choose
between several options, no deterministic or stochastic model can account
for the observed outcomes without violating a condition "MIN" motivated by
relativistic symmetry.
However, the free will theorem itself explicitly refers only to
deterministic models; its upshot is that no deterministic model satisfying
MIN can account for the observations, a fact proven also by John Bell's
inequality argument of 1964. For stochastic models, on the other hand,
Conway and Kochen have not made precise the meaning of MIN. I will present
examples of stochastic models illustrating that, depending on the
interpretation of MIN, either MIN is not a reasonable requirement or the
claim that stochastic models satisfying MIN cannot account for the
observations is wrong.
THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM BETWEEN THE TWO SEMINARS. |
Tuesday, September 22nd |
| Special Mathematical Physics Seminar |
M. Huang, Ohio State University (PLEASE NOTE SPECIAL DAY) |
"Geometry of Quadratic Julia Sets: A Transseries" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: PLEASE NOTE SPECIAL DAY
We introduce convergent transseries expansions for the B"ottcher map near all periodic points on the Julia set of complex quadratic maps. These expansions allow us to study the geometric structure of the fractal. We will discuss the relation between transseries and important properties of Julia sets such as Holder continuity and the Hausdorff dimension. We will also show plots of fractals obtained by combining curve segments calculated using the transseries. They give direct insight into the intricate features of Julia sets. |
Thursday, September 17th |
A. Dhar, Raman Research Institite, India |
"Heat conduction and phonon localization in disordered harmonic crystals" |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: We investigate the system size dependence of the heat current in two and three dimensional disordered harmonic crystals. Both nonequilibrium simulations as well as direct numerical evaluation of phonon transmission coefficients are performed. In the presence of a pinning potential we find that Fourier's law is valid in three dimensions while in two dimensions we obtain a heat insulator. In the absence of pinning the heat conductivity is found to have a power-law divergence with system size and our study suggests the presence of super-diffusive phonon states. Some results on heat conduction in anharmonic crystals will be briefly discussed. |
Thursday, September 17th |
D. Huse, Princeton University |
"Many-body localization, quantum heat baths, thermal equilibration and heat transport" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: As first argued by Anderson (1958) and more recently and thoroughly by Basko, Aleiner and Altshuler, a quantum system of many degrees of freedom with quenched randomness may be localized and fail to thermally equilibrate. There can be a dynamic phase transition, a "mobility edge", as one varies the parameters and/or the energy density of the system, between the ergodic phase where the system can serve as its own heat bath and does equilibrate, and the many-body localized phase where it does not. I will attempt to precisely define what these words mean, and report on our attempts to investigate the nature of this phase transition.
THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM BETWEEN THE TWO SEMINARS. PLEASE JOIN US |
Thursday, September 10th |
Van Vu, Rutgers University |
" Random matrices: Universality of local eigenvalue statistics" |
| Time: 2:00 PM |
| Location: Hill 705 |
| Abstract: THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM BETWEEN THE TWO
SEMINARS.
PLEASE JOIN US
One of the main goals of the theory of random matrices is to establish the limiting distributions of the eigenvalues. In the 1950s, Wigner proved his famous semi-circle law (subsequently extended by L. Arnold, L.A.Pastur and others), which established the global distribution of the eigenvalues of random Hermitian matrices. In the last fifty years or so, the focus of the theory has been on the local distributions, such as the distribution of the gaps between consecutive eigenvalues, the k-point correlations, the local fluctuation of a particular eigenvalue, or the distribution of the least singular value. Many of these problems have connections to other fields of mathematics, such as combinatorics, number theory, statistics and numerical linear algebra. Most of the local statistics can be computed explicitly for random matrices with gaussian entries (GUE or GOE), thanks to Ginibre's formulae of the joint density of eigenvalues. It has been conjectured that these results can be extended to other models of random matrices. This is generally known as the Universality phenomenon, with several specific conjectures posed by Wigner, Dyson, Mehta, etc. In this talk, we would like to discuss recent progresses concerning the Universality phenomenon, focusing on a recent result (obtained jointly with T. Tao), which asserts that all local statistics of eigenvalues of a random matrix are determined by the first four moments of the entries. This (combining with results of Johansson, Erdos-Ramirez-Schlein-Yau and many others) provides answers to several old problems. |
Thursday, September 10th |
Jozsef Beck, Rutgers University |
"Deterministic Approach to the Kinetic Theory of Gases" |
| Time: 12:00 PM |
| Location: Hill 705 |
| Abstract: COFFEE AND COOKIES WILL BE SERVED AT 11:45 AM IN THE KITCHEN OF ROOM 705; ONLY ONE SEMINAR TODAY
In the so-called Bernoulli model of the kinetic theory of gases, where (1) the particles are dimensionless points, (2) they are contained in a cube container, (3) no attractive or exterior forces are acting on them, (4) there is no collision between the particles, (5) the collision against the walls of the container are according to the law of elastic reflection, we deduce from Newtonian mechanics two local probabilistic laws: a Poisson limit law and a central limit theorem. We also prove some global law of large numbers, justifying that ``density" and ``pressure" are constant. Finally, as a byproduct of our research, we prove the surprising super-uniformity of the typical billiard path in a square. |