Mathematics Department - Mathematical Physics Seminar - Spring 2016

Mathematical Physics Seminar - Spring 2016


Joel Lebowitz, Michael Kiessling



Upcoming Talks

Thursday, February 11th

Roger Nussbaum , Rutgers University

"Analyticity Versus Infinite Differentiability: Case Studies and Open Questions"

Time: 12:00 PM
Location: Hill 705
Abstract: This talk considers differential-delay equations, but no prior knowledge will be assumed.

The topics to be discussed represent joint work with John Mallet-Paret.

If x: (-(infinity), T) --> (complex numbers) is infinitely differentiable and bounded, let N denote the subset of the domain of x(.) where x is not real analytic and A denote the set of points t in the domain such that x(.) is real analytic on an open neighborhood of t. We shall describe a simple-looking class of differential-delay equations, defined by real analytic functions. The equations in question have periodic solutions x(.) for which the set N is uncountable and the set A is open and nonempty. Under slightly more restrictive assumptions, N has empty interior. Time permitting, we shall also consider a class of differential delay equations which have bounded, infinitely differentiable solutions x(.) defined on (-(infinity), (infinity)). The solutions in question also have a nonzero limit as t approaches (-infinity). We conjecture that these solutions are nowhere real analytic, but no proofs have been given even for simple equations like x'(t) = exp(it^2)x(t-1)or x'(t) = sin(t^2)x(t-1).

Past Talks

Thursday, February 4th

Eugene Speer, Rutgers University

"Translation invariant extensions of finite volume measures"

Time: 2:00 PM
Location: Hill 705
Abstract: Given a probability measure on the set of particle configurations on a finite subset of a lattice, can it be extended to a translation invariant measure on configurations on the entire lattice? When the answer is yes, what are the properties, e.g., the entropy, of such an extension? We give reasonably complete answers for the one-dimensional case; in higher dimensions we can say much less.

This is joint work with S. Goldstein, J. L. Lebowitz, and T. Kuna.

Thursday, February 4th

Haim Brezis , Rutgers University

"Sobolev inequalities: the work of Sobolev, Nirenberg and beyond"

Time: 12:00 PM
Location: Hill 705
Abstract: The lecture is concerned with various aspects of the Sobolev inequalities on R^N in the border line cases p=1 and p=N, starting with the contributions of S. Sobolev and L. Nirenberg. I will explain how new results when p=N are connected to the solvability of linear elliptic equations with data in L^1 (based joint work with J. Bourgain). I also plan to discuss elliptic equations involving critical nonlinearities (revisiting a joint work with L. Nirenberg)


Thursday, January 28th

Denys Bonder , Princeton University

"Measurement inspired modeling of quantum and classical dynamical systems"

Time: 2:00 PM
Location: Hill 705
Abstract: In this talk, I will provide an answer to the question:

"What kind of observations and assumptions are minimally needed to formulate a physical theory?" Our answer to this question leads to the new systematic approach of Operational Dynamical Modeling (ODM), which allows to deduce equations of motions from time evolution of observables. Using ODM, we are not only able to re-derive well-known physical theories (such as the Schrodinger and classical Liouville equations), but also infer novel physical dynamics (and solve open problems) in the realm of non-equilibrium quantum statistical mechanics.

Thursday, January 28th

Roderich Tumulka , Rutgers University

"Probability Distribution of the Time at Which an Ideal Detector Clicks"

Time: 12:00 PM
Location: Hill 705
Abstract: We consider a non-relativistic quantum particle surrounded by a detecting surface and ask how to compute, from the particle's initial wave function, the probability distribution of the time and place at which the particle gets detected. In principle, quantum mechanics makes a prediction for this distribution by solving the Schrodinger equation of the particle of interest together with the 10^23 (or more) particles of the detectors, but this is impractical to compute. Is there a simple rule for computing this distribution approximately for idealized detectors? I will argue in favor of a particular proposal of such a rule, the "absorbing boundary rule," which is based on a 1-particle Schrodinger equation with a certain "absorbing" boundary condition on the detecting surface. The mere existence of such a rule may seem surprising in view of the quantum Zeno effect. Time permitting, I may also be able to explain extensions of this rule to the cases of several particles, moving detectors, particles with spin, Dirac particles, curved space-time, and discrete space (a lattice).

Some of the results are based on joint work with Abhishek Dhar and Stefan Teufel.


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