seminar FisMat

FisMat Seminar, June 5, 15:45

Speaker: Horia Cornean. Aalborg University

Title: A Beals criterion for magnetic pseudo-differential operators proved with magnetic Gabor frames

Place: Pontificia Universidad Católica, Facultad de Matemáticas, Campus San Joaquin, Sala 5

First, we give a new proof for the Beals commutator criterion for non-magnetic Weyl pseudo-differential operators based on classical Gabor tight frames. Second, by introducing a modified ‘magnetic’ Gabor tight frame, we naturally derive the magnetic analogue of the Beals criterion originally considered by Iftimie-Mantoiu-Purice. This is joint work with Bernard Helffer (Nantes) and Radu Purice (Bucharest).

seminar FisMat

FisMat Seminar, May 29, 15:45

Speaker: Andrés Fernando Reyes Lega. Universidad de los Andes (Colombia)

Title: Emergent Gauge Symmetries, Quantum Operations and Anomalies

Place: Pontificia Universidad Católica, Facultad de Matemáticas (campus San Joaquin), Sala 5

The Gelfand-Naimark-Segal (GNS) construction is a fundamental tool for the study of the representation theory of operator algebras. It also plays a prominent role in the algebraic approach to quantum field theory. In this talk I will discuss some examples of applications of the algebraic approach to quantum physics to systems with a finite number of degrees of freedom. I will illustrate how the GNS construction naturally leads to interesting connections between gauge symmetries, anomalies and quantum-information concepts like entanglement entropy and quantum operations.

seminar FisMat

FisMat Seminar, May 15, 15:45

Massimo Moscolari. Aalborg University
Title: Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau Hamiltonians
Place: Pontificia Universidad Católica, Facultad de Matemáticas (Campus San Joaquin), Sala 5
In 1978 Wannier discovered a Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic field flux with integer slope. I will show how to extend this relation to a gap labelling theorem for any 2D Bloch-Landau Hamiltonian operator and to certain non-covariant systems having slowly varying magnetic fields. The integer slope will be interpreted as the Chern character of the projection onto the space of occupied states. The talk is based on a joint work with H. Cornean and D. Monaco.

seminar FisMat

FisMat Seminar, April 24, 15:45

Svetlana Jitomirskaya. University of California, Irvine
Title: Cantor spectrum of a model of graphene in magnetic field
Place: Pontificia Universidad Católica de Chile, Facultad de Matemáticas (Campus San Joaquin), Sala 5
We consider a quantum graph as a model of graphene in magnetic fi elds and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux  through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero and Hausdorff dimension bounded by 1/2.

Based on joint works with S. Becker, R. Han, and also I. Krasovsky

seminar FisMat

FisMat Seminar, April 17, 15:45

Walter de Siqueira Pedra. University of São Paulo
Title: Thermodynamical Stability and Dynamics of Lattice Fermions with Mean-Field Interactions
Place: Pontificia Universidad Católica, Facultad Matemáticas (Campus San Joaquin) Sala 5
For lattice fermions we study the thermodynamic limit of the time evolution of observables when the corresponding finite-volume Hamiltonians contain mean-field terms (like, e.g., the BCS model). It is well-known that, in general, this limit does not exist in the sense of the norm of observables, but may exist in the strong operator topology associated to a well-chosen representation of the algebra of observables. We proved that this is always the case for any cyclic representation associated to an invariant minimizer of the free energy density, if the Hamiltonians are invariant under translations. Our proof uses previous results on the structure of states minimizing the free energy density of mean-field models along with Lieb-Robinson bounds for the corresponding families of finite-volume time evolutions. This is a joint work with Jean-Bernard Bru, Sébastien Breteaux and Rafael Miada.