Math Phys Seminar: Jeffrey Schenker (IAS) 'Diffusion of wave packets for the Markov Schroedinger equation'

Thu, Mar 29, 2012, 3:00 pm – 4:30 pm

The long time evolution of waves in a homogeneous random environment will be discussed. Proving that the wave amplitude evolves diffusively over any sufficiently long time scales remains an open problem. One obstacle that arises is recurrence -- return of portions of the wave packet to regions previously visited. However, if one removes…

Math Phys Seminar: Sourav Chatterjee (Courant Inst. NYU) 'Invariant measures and the soliton resolution conjecture'

Tue, Mar 27, 2012, 3:30 pm – 5:00 pm

The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution…

Math Phys Seminar: Christian Hainzl (University of Tuebingen) 'Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs'

Tue, Feb 28, 2012, 3:30 pm – 5:00 pm

We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs. This is joint work with Robert Seiringer.

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Math Phys Seminar: Jonathan Breuer (Hebrew University) 'Nonintersecting random walkers with a staircase initial condition'

Tue, Feb 7, 2012, 4:30 pm – 6:00 pm

We study a model of one dimensional particles, performing geometrically weighted random walks that are conditioned not to intersect. The walkers start at equidistant points and end at consecutive integers. A naturally associated tiling model can be viewed as one of placing boxes on a staircase. For a particular value of the parameters we obtain a…

Math Phys Seminar: Ivan Corwin (Courant Inst. NYU) 'Macdonald Processes and Some Applications in Probability and Integrable Systems'

Tue, Nov 29, 2011, 4:30 pm – 6:00 pm

Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two parameters q, t in [0,1). Utilizing the Macdonald difference operators we prove several results about observables these processes, including Fredholm determinant formulas for q…

Math Phys Seminar: Giambattista Giacomin (Université Paris Diderot) "Random natural frequencies, active dynamics and coherence stability in populati

Tue, Nov 22, 2011, 4:30 pm – 6:00 pm

The Kuramoto synchronization model is the reference model for synchronization phenomena in biology (and, to a certain extent, also in other fields). The model is formulated as a dynamical system of interacting plane rotators. Variations of it provide basic models of phenomena beyond synchronization, such as noise induced coherent oscillations…

Math Phys Seminar: Robert Schrader (FU - Berlin) "QED in Half Space"

Tue, Nov 15, 2011, 4:30 pm – 6:00 pm

A proposal for QED in half space is made. Starting from the well known principle of mirror charges in electrostatics, we formulate boundary conditions for electromagnetic fields and charge carrying currents both in the classical and the quantum context. Free classical and quantum fields are constructed, such that the required boundary conditions…

Math Phys Seminar: Michael Damron (Princeton Univ.) "A simplified proof of the relation between scaling exponents in first-passage percolation"

Tue, Nov 8, 2011, 4:30 pm – 6:00 pm

In first passage percolation, we place i.i.d. non-negative weights on the nearest-neighbor edges of Z^d and study the induced random metric. A long-standing conjecture gives a relation between two "scaling exponents": one describes the variance of the distance between two points and the other describes the transversal fluctuations of optimizing…

Math Phys Seminar: Tatyana Shcherbina (Inst. for Low Temp. Phys., Kharkov, Ukraine) "Characteristic polynomials of the hermitian Wigner and sample co

Tue, Nov 1, 2011, 4:30 pm – 6:00 pm

We consider asymptotics of the correlation functions of characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$ and the hermitian sample covariance matrices $X_n=n^{-1}A_{m,n}^*A_{m,n}$. We use the integration over the Grassmann variables to obtain a convenient integral representation. Then we show that the asymptotics of…

Math Phys Seminar: Marija Vucelja (Courant Inst. NYU) "Fractal iso-contours of passive scalar in smooth random flows"

Tue, Oct 25, 2011, 4:30 pm – 6:00 pm

We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new effective semi-analytic algorithm to model the scalar turbulence. We then carry massive numerics of passive…

Math Phys Seminar: Sourav Chatterjee (Courant Inst. NYU) "The universal relation between exponents in first-passage percolation"

Tue, Oct 18, 2011, 4:30 pm – 6:00 pm

It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent \chi and the wandering exponent \xi are related through the universal relation \chi=2\xi -1, irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. I will give a…

Math Phys Seminar: Simone Warzel (Tech. Univ. Munich) "Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder"

Tue, Oct 11, 2011, 4:30 pm – 6:00 pm

We discuss recently established criteria for the formation of extended states on tree graphs in the presence of disorder. These criteria have the surprising implication that for bounded random potentials, as in the Anderson model, in the weak disorder regime there is no transition to a spectral regime of Anderson localization in the form usually…

Y. Avron (Technion) Geometry of quantum response in open systems

Fri, Mar 4, 2011, 11:00 am – 1:00 pm

I shall describe a theory of adiabatic response for controlled open systems governed by Lindblad evolutions. The theory gives quantum response a geometric interpretation induced from the geometry of Hilbert space projections. For a two level system the metric turns out to be the Fubini-Study metric and the symplectic form the adiabatic curvature…

Sir Michael Berry (Univ Bristol) Singularity - dominated strong fluctuations

Tue, Feb 22, 2011, 4:30 pm – 6:00 pm

The fluctuations of a physical quantity can be described by its moments. In many cases, these diverge as an asymptotic parameter becomes large (or small), through the influence of geometric singularities. These large moments are described by power laws whose exponents can be determined from a knowledge of the singularities. Examples are twinkling…

Mathieu Lewin (Universite de Cergy-Pointoise) "Geometric methods for nonlinear quantum many-body systems"

Tue, Dec 14, 2010, 4:30 pm – 6:00 pm

Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schrödinger operators. In this talk I will present a formalism which also allows to study nonlinear systems. I will in particular define a weak topology on many-body states, which appropriately describes the physical behavior of the…

Clement Hongler (Columbia University) "The energy density field of the Ising model"

Tue, Nov 9, 2010, 4:30 pm – 6:30 pm

We consider the planar Ising model on bounded domains from a conformal invariance point of view. We are interested in the scaling limit of the model at critical temperature. Physics theories, notably Conformal Field Theory, predict the existence of two conformal local fields describing the model in the continuum: the spin and the energy density…

Idan Oren (The Weizmann Institute) Trace Formulas for Large Random d-Regular Graphs

Tue, Oct 26, 2010, 4:30 pm – Sun, Sep 26, 2010, 6:30 pm

Trace formulas for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulas depend on a parameter (w) which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only…

Idan Oren (The Weizmann Institute) "Trace Formulas for Large Random d-Regular Graphs"

Tue, Oct 26, 2010, 4:30 pm – 6:30 pm

Trace formulas for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulas depend on a parameter (w) which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only…

Simone Warzel (Tech. Univ. Munich) "Extended States in a Lifshitz Tail Regime for Random Operators on Trees"

Tue, Oct 12, 2010, 4:30 pm – 6:30 pm

We will discuss the spectral properties of random operators on regular tree graphs. The models have have been among the earliest studied for Anderson localization, and they continue to attract attention because of analogies with localization issues for many particles. The talk will focus on the location of the mobility edge. Somewhat…

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