Christian Sadel

Georgi Raikov. Pontificia Universidad Católica de Chile
Title: Threshold singularities of the spectral shift function for geometric perturbations of a magnetic Hamiltonian
Place: Pontificia Universidad Católica de Chile, Facultad de Matemáticas (campus San Joaquin), Sala 2
Abstract:
I will consider the 3D Schrödinger operator H0 with constant magnetic field, and its perturbations $H_+$ (resp., $H_-\,$ ) obtained from $H_0$ by imposing Dirichlet (resp., Neumann) conditions on an appropriate surface. I will introduce the Krein spectral shift function for the operator pairs $(H_0;H_+)$ and $(H_0;H_-)$ , and will discuss its singularities at the Landau levels which play the role of thresholds in the spectrum of the unperturbed operator $H_0$ .
The talk is based on a joint work with V. Bruneau (Bordeaux).
http://www.mat.uc.cl/~graikov/seminar.html

seminar FisMat

FisMat Seminar, April 24, 15:45

April 19, 2019June 4, 2019 Christian Sadel

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
Abstract:
We consider a quantum graph as a model of graphene in magnetic fields 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

Announcement

Position in Mathematical Physics at the Institute of Physics at PUC Chile

April 9, 2019June 6, 2019 Christian Sadel

The Institute of Physics at Pontificia Universidad Católica de Chile invites applications for a tenure-track faculty position in Mathematical Physics at the Assistant Professor level, to start as early as August 2019. A Ph.D. degree in Physics (or closely related areas) is required and postdoctoral experience is highly desirable. We are looking for candidates having the potential of interaction with the established research areas in Mathematical Physics at the institute such as Analysis, PDE, Quantum Physics, and Non-linear Physics.
The successful candidate is expected to establish a leading research program as well as to teach in Spanish at the undergraduate and graduate levels.
Applications must include two recommendation letters, curriculum vitae, list of publications, and statements of past and proposed research and teaching interests. The two recommendation letters must be sent separately to the application’s e-mail address. All the documents should be sent by email before April 30, 2019 to the Head of the Search Committee at concurso2019@fis.puc.cl

seminar FisMat

FisMat Seminar, April 17, 15:45

April 8, 2019June 4, 2019 Christian Sadel

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
Abstract:
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.