Mathematics Department - Mathematical Physics Seminar - Fall 2014

Mathematical Physics Seminar - Fall 2014



Organizer(s)

Joel Lebowitz, Michael Kiessling

Archive

Website

http://www.math.rutgers.edu/~lebowitz/Fall2014seminars.html




Past Talks


Thursday, December 11th

Wei Min Wang, University of Paris Sud

"Quasi-periodic solutions for nonlinear wave equations"

Time: 12:00 PM
Location: Hill 705
Abstract: We construct time quasi-periodic solutions to NLW on the torus in arbitrary dimensions. This extends our method developed in the limit-elliptic setting of NLS to the hyperbolic setting. The additional ingredient is a Diophantine property of algebraic numbers.

Only one seminar today - no brown bag lunch


Thursday, December 4th

Pedro L. Garrido , Universidad de Granada

"Thermodynamic versus statistical local equilibrium in hard disk systems"

Time: 2:00 PM
Location: Hill 705
Abstract: We use extensive computer simulations to probe local thermodynamic equilibrium (LTE) in a  quintessential model fluid, the two-dimensional hard-disks system. We show that macroscopic LTE  is a very strong property, even in the presence of important finite size effects, revealing a remarkable  bulk-boundary decoupling phenomenon in fluids out of equilibrium. These properties allow us  to measure the hard disks equation of state in simulations far from equilibrium, with a stunning  accuracy comparable to the best equilibrium simulations. Subtle corrections to LTE are found in  the fluctuations of the total energy which strongly point out to the nonlocality of the nonequilibrium  potential governing the fluid macroscopic behavior out of equilibrium. Moreover, we can show that  the temperature and density profiles obeys strikingly simple universal scaling laws predicted by the  Fourier law.


Thursday, December 4th

A.Shadi Tahvildar-Zadeh, Rutgers University

"The Dirac electron and the Kerr-Newman spacetime"

Time: 12:00 PM
Location: Hill 705
Abstract: In this joint work with Michael Kiessling, Dirac's wave equation for a  point electron in the --topologically nontrivial-- maximal analytically  extended Kerr-Newman spacetime is studied in the zero-gravity limit;  here, "zero-gravity" means G --> 0, where G is Newton's constant of  universal gravitation. The following results are obtained: The formal  Dirac Hamiltonian on the static spacelike slices is essentially  self-adjoint; the spectrum of the self-adjoint extension is symmetric  about zero, featuring a continuous spectrum with a gap about zero that,  under two smallness conditions, contains a point spectrum. We will  explain how this is connected with a new quantum-mechanical  interpretation of the Dirac equation, proposed by us, in which the  electron and the positron are not distinct individual particles (though  already related by abstract symmetry operations), but merely two  "topological-spin" states of a single, more fundamental particle.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM!


Thursday, November 20th

Ian Jauslin , Università degli studi di Roma La Sapienza

"Renormalization group approach to bilayer graphene (joint work with A.Giuliani)"

Time: 2:00 PM
Location: Hill 705
Abstract: Bilayer graphene is a recently discovered 2-dimensional crystal with interesting electronic properties. In the present work, we compute the free energy and two-point correlation functions for a generalized Hubbard model of bilayer graphene with a small interaction, and show that they are analytically close to the non-interacting ones. We use a constructive renormalization group technique, in which we compute tight bounds adapted to different energy regimes. This allows us to consider temperatures lower than those accessible using a more naive approach.


Thursday, November 20th

Stefano Olla , Université Paris Dauphine

"Isothermal and adiabatic thermodynamic transformations from microscopic dynamics"

Time: 12:00 PM
Location: Hill 705
Abstract: Isothermal and adiabatic transformations are the basic thermodynamics transitions composing Carnot cycles. I will illustrate how to obtain them from a microscopic dynamics under a diffusive space-time scaling limit. The deterministic irreversible thermodynamic transformations are given by a set of diffusive equations, and the quasi-static reversible transformations are obtained by a further time scaling for limiting slow variation of the applied force. I will also deal with 'isothermal' transitions between stationary non equilibrium state.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM


Thursday, November 13th

Valerio Lucarini , University of Hamburg

"Response Theory in Geophysical Fluid Dynamics: Climate Change Prediction and Parametrizations"

Time: 3:30 PM
Location: Hill 705
Abstract: The climate is a complex, chaotic, non-equilibrium system featuring a limited horizon of predictability, variability on a vast range of temporal and spatial scales, instabilities resulting into energy transformations, and mixing and dissipative processes resulting into entropy production. Despite great progresses, we still do not have a complete theory of climate dynamics able to encompass instabilities, equilibration processes, and response to changing parameters of the system. We will outline some possible applications of the response theory developed by Ruelle for non-equilibrium statistical mechanical systems, showing how it allows for setting on firm ground and on a coherent framework concepts like climate sensitivity, climate response, and climate tipping points. We will show results for simple yet instructive models such as that presented by Lorenz in 1996, and for comprehensive global circulation models. The results are promising in terms of suggesting new ways for approaching the problem of climate change prediction and for using more efficiently the enormous amounts of data produced by modeling groups around the world. We will then show how response theory can be used for constructing parametrizations for multiscale systems, providing explicit formulas for the effective dynamics identical to what can be obtained using a perturbative Mori-Zwanzig approach. This might be relevant for constructing practical parametrizations for weather and climate models.

V. Lucarini, R. Blender, C. Herbert, F. Ragone, S. Pascale, J. Wouters, Mathematical and Physical Ideas for Climate Science, Reviews of Geophysics doi: 10.1002/2013RG000446 (2014)


Thursday, November 13th

Jeremy England , Massachusetts Institute of Technology

"Boltzmann's Dog and Darwin's Finch: The statistical thermodynamics of self-replication and evolution"

Time: 2:00 PM
Location: Hill 705
Abstract: Living things operate according to well-known physical laws, yet it is challenging to discern specific, non-trivial consequences of these constraints for how an organism that is a product of evolution must behave. Part of the difficulty here is that life lives very far from thermal equilibrium, where many of our traditional theoretical tools fail us. However, recent developments in nonequilibrium statistical mechanics may help light a way forward. The goal of this talk will be to explain some of these developments, and show how they begin to offer a new perspective on the physics of self-replication, natural selection, and evolution.

THERE WILL BE A COFFEE BREAK FROM 3-3:30PM


Thursday, November 13th

Lai-Sang Young, Courant Institute

"Attempting to understand visual cortex"

Time: 12:00 PM
Location: Hill 705
Abstract: In this talk, I will report on my attempts to understand the functioning of a region of the brain called the primary visual cortex, or V1. A nontrivial fraction of a primate’s nervous system is devoted to the processing of visual information. From the time that light hits the receptors in our retina, information is passed in the form of electrical signals from our retina to a region located at the back of our heads called V1. This is where the first stage of information processing in cortex takes place. I propose to view V1 as a large dynamical system, comprised of a network of spiking neurons. This system is bombarded by changing signals in one's visual field, hence is perpetually out of equilibrium. A goal is to explain V1 phenomena in terms of feedforward inputs and neuron-to-neuron interactions -- in the spirit of statistical mechanics. I will discuss the many challenges that come with such an approach, and report on some preliminary results from a computational study.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM


Thursday, November 6th

David Ruelle, IHES, France

"Non-Equilibrium Statistical Mechanics of Turbulence"

Time: 12:00 PM
Location: Hill 705
Abstract: The macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow for a suitable mechanical system. This leads to a new approach to (part of) turbulence theory. Turbulent fluctuations (intermittency) correspond to thermal fluctuations, and this allows to estimate the exponents $zeta_p$ associated with velocity fluctuations. In particular we can derive probability distributions at finite Reynolds number for the dissipation and velocity fluctuations, and the latter permit an interpretation of numerical experiments. Specifically, if $p(z)dz$ is the probability distribution of the radial velocity gradient we can explain why, when the Reynolds number ${cal R}$ increases, $ln p(z)$ passes from a concave to a linear then to a convex profile for large $z$ as observed. We show that the central limit theorem applies to the dissipation and velocity distribution functions, so that a logical relation with the lognormal theory of Kolmogorov and Obukhov is established. We find however that the lognormal behavior of the distribution functions fails at large value of the argument, so that a lognormal theory cannot correctly predict the exponents $zeta_p$.

References:

''Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics.'' Proc. Nat. Acad. Sci. {bf 109},20344-20346(2012). arXiv:1210.2374 ''Non-equilibrium statistical mechanics of turbulence.'' J. Statist. Phys. {bf 157},205-218(2014). arXiv:1405.5746 end _______________________________________________________


Thursday, October 23rd

Roderich Tumulka, Rutgers University

"Novel type of Hamiltonians without ultraviolet divergence for quantum field theories"

Time: 12:00 PM
Location: Hill 705


Thursday, October 9th

Roderich Tumulka , Rutgers University

"Novel type of Hamiltonians without ultraviolet divergence for quantum field theories"

Time: 2:00 PM
Location: Hill 705
Abstract: In quantum field theories, the terms in the Hamiltonian governing particle creation and annihilation are usually ultraviolet (UV) divergent. The problem can be circumvented by either discretizing space or attributing a nonzero radius to the electron (or other particles). I describe a novel way of defining a Hamiltonian, to our knowledge not previously considered in the literature; these Hamiltonians are well defined, involve particle creation and annihilation, treat space as a continuum, and give radius zero to electrons. They are defined in the particle-position representation of Fock space by means of a new kind of boundary condition on the wave function, which we call an interior-boundary condition (IBC) because it relates values of the wave function on a boundary of configuration space to values in the interior. Here, the relevant configuration space is that of a variable number of particles, the relevant boundary consists of the collision configurations (i.e., those at which two or more particles meet), and the relevant interior point lies in a sector with fewer particles. I will describe results about Schrodinger and Dirac operators with IBCs.

This is joint work with Stefan Teufel, Julian Schmidt, and Jonas Lampart.


Thursday, October 9th

Giovanni Gallavotti, Rutgers University

"Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model"

Time: 12:00 PM
Location: Hill 705
Abstract: We construct different equivalent non-equilibrium statistical ensembles in a $N$-degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. The purpose is to test conjectures on a theory of ensembles in non equilibrium statistical mechanics and turbulence as well as the chaotic hypothesis and the fluctuation relation. This leads to the proposal that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.


Thursday, October 2nd

Alex Kontorovich , Rutgers University

"Dynamics and Number Theory"

Time: 2:00 PM
Location: Hill 705
Abstract: We will give an informal discussion of some interactions between dynamics on homogeneous spaces and number theory, focussing specifically on conjectures of McMullen and Einsiedler-Lindenstrauss-Michel-Venkatesh.


Thursday, October 2nd

Yanyan Li, Rutgers University

"The Nirenberg problem and its generalizations: A unified approach"

Time: 12:00 PM
Location: Hill 705
Abstract: Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations $P_sigma(v)= K v^{ frac{n+2sigma}{n-2sigma} }$ on the standard sphere $S^n$ for $sigmain (0, n/2)$, where $P_sigma$ is the conformal fractional Laplacian of order $2sigma$. Finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric with prescribed certain curvatures. When $sigma=1$, it is the prescribing scalar curvature problem of the Nirenberg problem, and when $sigma=2$, it is the prescribing $Q-$curvature problem.

This is a joint work with Tianling Jin and Jingang Xiong.

BROWN BAG LUNCH AT 1PM


Thursday, September 18th

Ivan Sudakov , University of Utah

"Critical Phenomena in Planetary Climate: Statistical Physics Approach"

Time: 2:00 PM
Location: Hill 705
Abstract: Planetary climate is the result of interactions between multiple physical systems. Current climate simulation techniques require much computational power based on scientifically sound but highly sophisticated computer models. Hence in many situations it is desirable to find simpler approaches to reduce the computational cost, in particular those based on classical statistical physics. I will explain the new approach that focuses on defining of free energy for the various patterns of tipping elements in the climate system (e.g., melt ponds, permafrost lakes, tropical convection patterns etc.). It is used to explain many of the recently observed geometric properties of these patterns, in particular the onset of pattern complexity and the distribution of pattern sizes. Moreover, applications of this approach help to identify phase transitions and other critical phenomena in the climate system, which may be of considerable theoretical interest.


Thursday, September 18th

Ofer Zeitouni, University of Minnesota

"Freezing and decorated Poisson point processes"

Time: 12:00 PM
Location: Hill 705
Abstract: The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point processes (SDPPP). In the proofs of those results, the Laplace functional of the limiting extremal process is shown to satisfy $L(theta_{y}f]=g(y-tau_{f})$ for any nonzero, nonnegative, compactly supported, continuous function $f$, where $theta_{y}$ is the shift operator, $tau_{f}$ is a real number that depends on $f$, and $g$ is a real function that is independent of $f$. We show that, under some assumptions, this property characterizes the structure of SDPPP. Moreover, when it holds, we show that $g$ has to be a convolution of the Gumbel distribution with some measure. The above property of the Laplace functional is closely related to a `freezing phenomenon' that is expected by physicists to occur in a wide class of log-correlated fields, and which has played an important role in the analysis of various models. Our results shed light on this intriguing phenomenon and provide a natural tool for proving an SDPPP structure in these and other models.

Joint work with Eliran Subag.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM.


Thursday, September 11th

Jozsef Beck , Rutgers University

"How long does it take for a large dynamical system to reach complete randomness?"

Time: 2:00 PM
Location: Hill 705
Abstract: Consider a large system of point billiards in a box, or many particles moving on a sphere, starting from some far-from equilibrium state (e.g., Big Bang). Assuming a reasonable initial velocity distribution (e.g., Maxwellian, meaning the 3-dim normal), how long does it take for the typical time evolution to reach "complete randomness"? We study "time-lapse randomness" and "snapshot randomness". I will talk about some surprising, counter-intuitive results, for which I cannot give a "plausible explanation".


Thursday, September 11th

Ido Kanter , Bar-Ilan University, Israel

"Ultrafast Physical random number generators"

Time: 12:00 PM
Location: Hill 705
Abstract: The generation of random bit sequences based on non-deterministic physical mechanisms is of paramount importance for cryptography and secure communications. High data rates also require extremely fast generation rates and robustness to external perturbations. Physical generators based on stochastic noise sources have been limited in bandwidth to 100 Mbit/s generation rates. We present a physical random bit generator, based on a chaotic semiconductor laser, having time-delayed self-feedback, which operates reliably at rates up to 300 Gbit/s. The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM.


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