Events Archive

Math Physics Seminar | Michael Aizenman, Princeton | ``Geometric analysis of frustration in a class of SU(2S+1) invariant quantum spin chains’’ | Jadwin A06
Tue, Oct 22, 2019, 4:30 pm4:30 pm


Unlike their classical counterparts, quantum antiferromagnetic systems exhibit ground state frustration effects even in one dimension.  A case in point is the SU(2S+1) invariant spin chain, with the interaction between pairs of neighboring S-spins given by…

Math Physics Seminar | Rodrigo Matos, Michigan State | "Localization in the Disordered Hubbard Model within Hartree-Fock Theory" | Jadwin A06
Tue, Oct 15, 2019, 4:30 pm4:30 pm

We aim at presenting a simple context where known results on Anderson localization for systems of non-interacting particles in a random environment may be extended to systems with weak interactions.

Using the fractional moment method it is shown that, within the Hartree-Fock…

Math Physics Seminar, | Simone Warzel, TU, Munich | "The Quantum Random Energy Model" | Jadwin A06
Tue, Sep 24, 2019, 4:30 pm4:30 pm

The quantum random energy model serves as a simple cornerstone, and a testing ground, for a number of fields.  It is the simplest of all mean-field spin glass models in which quantum effects due to the presence of a transversal field are studied.  Renewed interest in its spectral properties arose recently in…

Math Physics Seminar | Amanda Young, U. of Arizona, Tucson | "A gapped family of two-dimensional AKLT models" | Jadwin 343
Tue, Apr 23, 2019, 4:30 pm4:30 pm

The one-dimensional AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki conjectured that the two-dimensional version of their model on the hexagonal lattice also  exhibits a spectral gap. In this talk, we introduce a family of…

Math Physics Seminar | Ramis Movassagh, IBM Research | "Highly entangled spin chains: Exactly solvable counter-examples to the area law" | Jadwin 343
Tue, Apr 9, 2019, 4:30 pm4:30 pm

In recent years, there has been a surge of activities in proposing "exactly solvable" quantum spin chains with surprising high amount of ground state entanglement--exponentially more than critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the…

Math Physics Seminar | Jacob Shapiro, Columbia U. | "The topology of strongly-disordered chiral chains" | Jadwin Hall 343
Tue, Dec 4, 2018, 4:30 pm4:30 pm

Abstract:    We show how in the strongly-disordered, gapless regime, the topological properties of chiral chains (class AIII 1D in the Kitaev table) can be read off from the Lyapunov spectrum of the system at zero energy, and prove that these objects are topologically stable in the strongly-disordered gapless regime.

(Based on joint…

Math Physics Seminar | Ian Jauslin, Princeton | "Field electron emission and the Fowler-Nordheim equation" | Jadwin 343
Tue, Nov 13, 2018, 4:30 pm4:30 pm

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…

Math Physics Seminar | Michael Kiessling, Rutgers | "Do particles and anti-particles really annihilate each other?" | 343 Jadwin Hall
Tue, Sep 18, 2018, 4:30 pm4:30 pm

 In this talk I present theoretical evidence, based on non-perturbative semi-classical quantization techniques, that what appears as the annihilation of Positronium (Ps) may in reality be just another electromagnetic transition from the hydrogenic pseudo-ground state of Ps to a true quantum-mechanical ground state near zero energy,  caused by…

Joint Math Physics & Probability Seminar | Simone Warzel, TU, Munich | "Localization-delocalization transitions in random matrix models" | 214 Fine Hall
Wed, May 9, 2018, 3:00 pm3:00 pm

Abstract:  Hermitian random matrix models are known to exhibit phase transitions  regarding both their local eigenvalue statistics and in the eigenvectors’ localisation properties. The poster child of such is the Rosenzweig-Porter model, which is based on the interpolation between a random diagonal matrix and GOE.  Interestingly, this model has…

Math Physics Seminar | Chris Fronsdal, UCLA | "A classic Mistake and what it tells us" | Jadwin 343
Tue, Apr 17, 2018, 4:30 pm4:30 pm


Rayleigh's stability analysis of cylindrical Couette flow, of 1916, is in contradiction with observation, but it is still widely quoted and no one seems to know what   the reason is that it fails. I shall identify the mistake as one that is endemic in the literature.  Briefly, the argument depends on the Navier-Stokes…

Math Physics Seminar | Ian Jauslin, IAS | "Crystalline ordering and large-fugacity expansion for hard-core lattice particle systems" | 343 Jadwin Hall
Tue, Feb 6, 2018, 4:30 pm4:30 pm


I will present a class of hard-core lattice particle systems which exhibit a crystalline phase at high densities. The key ingredient of the proof is to show that the Gaunt-Fisher high-fugacity expansion is convergent for such models, which we acomplish using methods from Pirogov-Sinai theory…

Math Physics Seminar | Jacob Shapiro, ETH | "Bulk-Edge Duality and Complete Localization for Chiral Chains'' Jadwin 343
Tue, Dec 5, 2017, 4:30 pm4:30 pm


We study one dimensional insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with…

Math Physics Seminar, Herbert Spohn, TU-Munich, "Hydrodynamics of integrable classical and quantum systems" Jadwin 343
Tue, Nov 7, 2017, 4:30 pm4:30 pm

Abstract:  Discussed is the Euler-type hydrodynamics for one-dimensional integrable quantum systems, as the Lieb-Liniger delta Bose gas and the XXZ chain. Of particular interest are domain wall initial states. We will use classical hard rods as an illustration of the underlying structure.

Math Physics Seminar, Eric Carlen, Rutgers, "Quantum Markov Semigroups with detailed balance as gradient flow for relative entropy and entropy production inequalities" Jadwin 343
Tue, Oct 24, 2017, 4:30 pm4:30 pm


Semigroups of completely positive trace preserving maps satisfying a certain detailed balance condition are gradient flow driven by dissipation of the quantum relative entropy with respect to a non-commutative analog of the 2-Wasserstein metric on the space of probability densities on Euclidean…

Math Physics Seminar, John Imbrie, U. of Virginia, "Rare Region Effects and Many-Body Localization" Jadwin 343
Tue, Oct 17, 2017, 4:30 pm4:30 pm

Abstract:  Certain strongly disordered many-body quantum systems are incapable of reaching thermal equilibrium. The nature of this so-called many-body localized (MBL) phase has recently been an active area of research. The phenomenon can be understood through perturbative approximations, but rare regions with weak disorder (Griffiths regions)…

Math Physics Seminar, Yinon Spinka, Tel Aviv U., "Macroscopic loops in the loop O(n) model" Jadwin 343
Tue, Oct 10, 2017, 4:30 pm4:30 pm


A loop configuration on the hexagonal (honeycomb) lattice is a finite subgraph of the lattice in which every vertex has degree 0 or 2, so that every connected component is isomorphic to a cycle. The loop O(n) model on the hexagonal lattice is a random loop configuration, with the energy of of a loop configuration taken to…

Math Physics Seminar, Yuval Peres, Microsoft Research, "Gravitational allocation to uniform points on the sphere " Jadwin 343
Tue, Oct 3, 2017, 4:30 pm5:30 pm


Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them ?    "Fairly" means that each region has the same area.   It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins…

Math Physics Seminar, Vincent Vargas, ENS, "Ward and Belavin-Polyakov-Zamolodchikov (BPZ) identities for Liouville quantum field theory on the Riemann
Tue, Nov 15, 2016, 4:30 pm5:30 pm
The foundations of modern conformal field theory (CFT) were introduced in a 1984 seminal paper by Belavin, Polyakov and Zamolodchikov (BPZ). Though the CFT formalism is widespread in the physics literature, it remains a challenge for mathematicians to make sense out of it. Liouville CFT (or quantum field theory), introduced by Polyakov in his…
Math Physics Seminar, Eviatar Procaccia, Texas A & M, "Can one hear the shape of a random walk?"
Tue, Oct 25, 2016, 4:30 pm5:30 pm
We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to…
Math Physics Seminar, Vieri Mastropietro, U. of Milano, "Localization of interacting fermions with quasi-random disorder"
Tue, Oct 18, 2016, 4:30 pm5:30 pm
We consider interacting electrons in a one dimensional lattice with an incommensurate Aubry-Andre' potential in the regime when the single-particle eigenstates are localized. We rigorously establish persistence of ground state localization in presence of weak many-body interaction.The proof uses a quantum many body extension of methods adopted…