"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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