Georgia Institute of Technology College of Sciences

I will discuss chaos in quantum many-body systems, specifically how it is relates to thermalization and how it fails in many-body localized states. I will conjecture a new universal form for the spreading of chaos in local systems, and discuss evidence for the conjecture from a variety of sources including new large-scale simulations of quantum dynamics of spin chains.

TBA

The three-dimensional Maxwell-Pauli-Coulomb (MPC) equations are a system of nonlinear, coupled partial differential equations describing the time evolution of a single electron interacting with its self-generated electromagnetic field and a static (infinitly heavy) nucleus of atomic number Z. The time local (and, hence, global) well-posedness of the MPC equations for any initial data is an open problem, even when Z = 0.

Electrons possess both spin and charge. In one dimension, quantum theory predicts that systems of interacting electrons may behave as though their charge and spin are transported at different speeds.We discuss examples of how such many-particle effects may be simulated using neutral atoms and radiation fields. Joint work with Xiao-Feng Shi

Abstract: A number of quantities in quantum many-body systems show remarkable universality properties, in the sense of exact independence from microscopic details. I will present some rigorous result establishing universality in presence of many body interaction in Graphene and in Topological Insulators, both for the bulk and edge transport. The proof uses Renormalization Group methods and a combination of lattice and emerging Ward Identities.

Entanglement is one of the crucial phenomena in quantum theory. The existence of entanglement between two parties allows for notorious protocols, like quantum teleportation and super dense coding. Finding a running time for many quantum algorithms depends on how fast a system can generate entanglement. This raises the following question: given some Hamiltonian and dissipative interactions between two or more subsystems, what is the maximal rate at which an ancilla-assisted entanglement can be generated in time.

The unification of the four fundamental forces remains one of the most important issues in theoretical particle physics. In this talk, I will first give a short introduction to Non-Commutative Spectral Geometry, a bottom-up approach that unifies the (successful) Standard Model of high energy physics with Einstein's General theory of Relativity. The model is build upon almost-commutative spaces and I will discuss the physical implications of the choice of such manifolds.

When P. Anderson introduced a model for the electronic structure in random disordered systems in 1958, such as randomly doped semiconductors, the surprise was his claim of the possibility of absence of diffusion for the electron motion. Today this phenomenon is called Anderson's localization and corresponds to pure point spectrum with exponentially decaying eigenfunctions for certain random Schrödinger operators (or Anderson models). Mathematically this phenomenon is quite well understood.For dimensions d≥3 and small disorder, the existence of diffusion, i.e.

Sources of single photons (as opposed to sources which produce on average a single photon) are of great current interest for quantum information processing. Perhaps surprisingly, it is not easy to produce a single photon efficiently and in a controlled way.

We consider a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at inverse temperature \beta. The system admits the canonical distribution at inverse temperature \beta as the unique equilibrium state.