Seminars and Colloquia by Series

Efficient Representations of Correlated Data as Tensor Networks

Series
Math Physics Seminar
Time
Monday, October 7, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Glen Evenbly – School of Physics, Georgia Tech –
Tensors networks are a formalism for expressing high-order tensors as networks of low-order tensors, thus can offer a compact representation of certain high-dimensional datasets. Originally developed in the context of quantum many-body theory, where they are used to efficiently represent quantum wave-functions, tensor networks have since found application in big data analytics, error correction, classical data compression and machine learning.
 
In this talk I will provide a brief introduction to the theory and application of tensor networks, and outline some of the current research directions in the tensor network program.    
 

Sharp diameter bound on the spectral gap for quantum graphs

Series
Math Physics Seminar
Time
Monday, September 30, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kenny Jones – Emory –

We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity. This is a joint work with D. Borthwick and L. Corsi.

Periodic Dynamics of a Local Perturbation in the Isotropic XY Model

Series
Math Physics Seminar
Time
Monday, September 16, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Livia Corsi – Universita' di Roma 3 –

I will consider the isotropic XY chain with a transverse magnetic field acting on a single site, and analyze the long time behaviour of the time-dependent state of the system when a periodic perturbation drives the impurity. I will show that, under some conditions, the state approaches a periodic orbit synchronized with the forcing. Moreover I will provide the explicit rate of convergence to the asymptotics. This is a joint work with G. Genovese.

Exponential decay of quantum conditional information in thermal states of 1D short-ranged gapped Hamiltonians.

Series
Math Physics Seminar
Time
Friday, April 19, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pavel Svetlichnyy – School of Physics, GaTeach –

I will talk about a conjecture that in Gibbs states of one-dimensional spin chains with short-ranged gapped Hamiltonians the quantum conditional mutual information (QCMI) between the parts of the chain decays exponentially with the length of separation between said parts. The smallness of QCMI enables efficient representation of these states as tensor networks, which allows their efficient construction and fast computation of global quantities, such as entropy. I will present the known partial results on the way of proving of the conjecture and discuss the probable approaches to the proof and the obstacles that are encountered.

Periodic and quasi-periodic attractors of the spin-orbit dynamics of Mercury

Series
Math Physics Seminar
Time
Tuesday, April 9, 2019 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guido Gentile – Universita' di Roma 3 –

Please Note: Unusual time.

Mercury is entrapped in a 3:2 resonance: it rotates on its axis three times for every two revolutions it makes around the Sun. It is generally accepted that this is due to the large value of Mercury's eccentricity. However, the mathematical model commonly used to study the problem -- sometimes called the spin-orbit model -- proved not to be entirely convincing, because of the expression used for the tidal torque. Only recently, a different model for the tidal torque has been proposed, with the advantage of both being more realistic and providing a higher probability of capture into the 3:2 resonance with respect to the previous models. On the other hand, a drawback of the model is that the function describing the tidal torque is not smooth and appears as a superposition of peaks, so that both analytical and numerical computations turn out to be rather delicate. We shall present numerical and analytical results about the nature of the librations of Mercury's spin in the 3:2 resonance, as predicted by the realistic model. In particular we shall provide evidence that the librations are quasi-periodic in time, so that the very concept of resonance should be revisited. The analytical results are mainly based on perturbation theory and leave several open problems, that we shall discuss.

Physical Versus Mathematical Billiards: From Regular Dynamics to Chaos and Back

Series
Math Physics Seminar
Time
Monday, April 8, 2019 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
L.A.Bunimovich – School of Mathematics, Georgia Tech –

Please Note: Unusual time.

In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard sphere moves in the same billiard table, virtually anything may happen. Namely a non-chaotic billiard may become chaotic and vice versa. Moreover, both these transitions may occur softly, i.e. for any (arbitrarily small) positive value of the radius of a physical particle, as well as by a ”hard” transition when radius of the physical particle must exceed some critical strictly positive value. Such transitions may change a phase portrait of a mathematical billiard locally as well as completely (globally). These results are somewhat unexpected because for all standard examples of billiards their dynamics remains absolutely the same after transition from a point particle to a finite size (”physical”) particle. Moreover we show that a character of dynamics may change several times when the size of the particle is increasing. This approach already demonstrated a sensational result that quantum system could be more chaotic than its classical counterpart.

Averaging in a fully coupled system with singularities

Series
Math Physics Seminar
Time
Friday, April 5, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Grigo – Department of Mathematics, University of Oklahoma –

In this talk I will discuss a particular fast-slow system, and describe an averaging theorem. I will also explain how this particular slow-fast system arises in a certain problem of energy transport in an open system of interacting hard-spheres. The technical aspect involved in this is how to deal with singularities present and the fact that the dynamics is fully coupled.

Mixing and the local limit theorem for hyperbolic dynamical systems

Series
Math Physics Seminar
Time
Friday, March 15, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Nandori – University of Maryland –
We present a convenient joint generalization of mixing and the local central limit theorem which we call MLLT. We review results on the MLLT for hyperbolic maps and present new results for hyperbolic flows. Then we apply these results to prove global mixing properties of some mechanical systems. These systems include various versions of the Lorentz gas (periodic one; locally perturbed; subject to external fields), the Galton board and pingpong models. Finally, we present applications to random walks in deterministic scenery. This talk is based on joint work with D. Dolgopyat and partially with M. Lenci.

The interaction of gaps with the boundary in dimer systems --- a heat flow conjecture

Series
Math Physics Seminar
Time
Friday, March 15, 2019 - 14:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mihai Ciucu – Mathematics Department, Indiana University –
We consider a triangular gap of side two in a 90 degree angle on the triangular lattice with mixed boundary conditions: a constrained, zig-zag boundary along one side, and a free lattice line boundary along the other. We study the interaction of the gap with thecorner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its three images in the sides of the angle. This, together with a few other results we worked out previously, provides evidence for a unified way of understanding the interaction of gaps with the boundary under mixed boundary conditions, which we present as a conjecture. Our conjecture is phrased in terms of the steady state heat flow problem in a uniform block of material in which there are a finite number of heat sources and sinks. This new physical analogy is equivalent in the bulk to the electrostatic analogy we developed in previous work, but arises as the correct one for the correlation with the boundary.The starting point for our analysis is an exact formula we prove for the number of lozenge tilings of certain trapezoidal regions with mixed boundary conditions, which is equivalent to a new, multi-parameter generalization of a classical plane partition enumeration problem (that of enumerating symmetric, self-complementary plane partitions).

Field electron emission and the Fowler-Nordheim equation

Series
Math Physics Seminar
Time
Friday, February 22, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ian Jauslin – Princeton University –
Consider a metallic field emitter shaped like a thin needle, at the tip of which a large electric field is applied. Electrons spring out of the metal under the influence of the field. The celebrated and widely used Fowler-Nordheim equation predicts a value for the current outside the metal. In this talk, I will show that the Fowler-Nordheim equation emerges as the long-time asymptotic solution of a Schrodinger equation with a realistic initial condition, thereby justifying the use of the Fowler Nordheim equation in real setups. I will also discuss the rate of convergence to the Fowler-Nordheim regime.

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