Seminario FisMat

El objetivo de este seminario es de reunir, de la manera la mas amplia posible, investigadores y estudiantes de la comunidad chilena e internacional alrededor de las diversas temáticas de física matemática. Profesores, investigadores jóvenes, así como estudiantes, son los bienvenidos como expositores.

Los miércoles, a las 14:30 hrs, 
Organización:  Giuseppe De NittisGregorio Moreno, Amal Taarabt

 


2024-05-15
14:00hrs.
Massimo Moscolari. Politecnico Di Milano - Italy
Equality of magnetization and edge current for fermionic systems at positive temperature
Sala 1 - Facultad de Matemáticas
Abstract:

I will first show that for general 2d random ergodic one-body magnetic Schrödinger operators the bulk magnetization equals the total edge current at any temperature. Moreover, the celebrated bulk-edge correspondence between quantum transport indices will be obtained as a corollary of our result by imposing a gap condition and by taking a "zero temperature" limit. After that, I will show how to extend the equality of bulk magnetization and total edge current to lattice fermion systems with finite-range interactions satisfying local indistinguishability of the Gibbs state, a condition known to hold for sufficiently high temperatures. In the interacting framework, an important intermediate result is a new version of Bloch's theorem for two-dimensional systems, stating that persistent currents vanish in the bulk.

The talk is based on joint works with Horia Cornean, Jonas Lampart, Stefan Teufel and Tom Wessel.

2024-04-24
14:00hrs.
Olivier Charles Albert Sarbach. Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo
On the linear stability of nonrelativistic boson stars
Sala 1 - Facultad de Matemáticas
Abstract:
In recent years there has been much interest in boson star solutions and their application to model the core of galactic halos in the context of scalar field dark matter. In first approximation, these objects can be described as spherically symmetric static solutions of the Schrödinger-Poisson or related systems. Including in this simple model there exists an extended class of solutions, depending on whether or not the field possesses internal degrees of freedom, whether or not it is self-gravitating etc. In this talk I will provide a brief review on the properties of these solutions and analyze their stability with respect to linear spherical and nonspherical perturbations.

Based on joint work with E. Chávez-Nambo, A. Roque and A. Diez-Tejedor.
2024-04-04
16:00hrs.
-. -
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2024-03-21
16:00hrs.
Jakub Czartowski. Jagiellonian University, Krakow, Poland
Trade-off relations for operation entropy of complementary quantum channels
Sala 1 - Facultad de Matemáticas
Abstract:
Completely Positive Trace Preserving (CPTP) maps are connected to the notion of quantum channels, which provide the largest possible set of allowed operations in the theory of quantum open systems. Every such map is connected via a canonical Naimark extension to a unitary operation on a bipartite system and, in turn, to a complementary map defined as its action to the second, auxiliary, subsystem. IN this talk we will discuss a notion of map entropy connected to the CPTP maps and their complementary counterparts, the relation between the two quantities and demonstrate the bounds that need to be satisfied by these quantities. The talk will conclude with several related open problems.
 
2023-12-14
16:15hrs.
Neil Mañibo. Bielefeld University
Continuous diffraction in mathematical quasicrystals
Sala 1 - Facultad de Matemáticas
Abstract:
Quasicrystals are materials which lack a crystalline-like lattice structure, but still exhibit long-range translational order. In this talk, we will walk through the mathematical theory of
diffraction for models of quasicrystals. We will restrict to those arising from substitutions on finite alphabets/inflation rules on finitely many tiles (up to translation), which induce a hierarchical structure compatible with renormalisation techniques in spectral theory. In particular, we will discuss
(i) a Diophantine-type condition needed
 for the presence of (non-trivial) Bragg peaks,
(ii) a criterion using
 Lyapunov exponents that confirms the absence of a non-trivial absolutely continuous component.
Time permitting, we will mention further 
directions for models based on substitutions on compact alphabets. This is based on joint works with Michael Baake, Franz Gaehler, and Uwe Grimm.
2023-12-07
16:15hrs.
Sven Bachmann. The University of British Columbia, Canada
An cohomological index for loops of invertible states
Sala 1 -Facultad de Matemáticas
Abstract:
 
The `topological' classification of states of quantum lattice systems is a well-defined mathematical endeavour which started with the discovery of the quantum Hall effect. In this talk, I will discuss the topology of a simple class, the so-called invertible states, which I will define. It is by definition a connected set, and we shall explore its further topological properties. Specifically, I will be interested in what can be identified with its fundamental group; Physically, this is about classifying cycles of physical processes, or pumps. I will present a classification of such loops of invertible states that have a local symmetry, which can be proved to be complete. This is joint work with Wojciech De Roeck, Martin Fraas and Tijl Jappens.
2023-11-16
16:15hrs.
Heinz Siedentop. Lmu - Munich
The Engel-Dreizler Functional: An Asymptotically Correct Description of Heavy Atoms By a Density Functional
Sala 1 - Facultad de Matemáticas
2023-11-02
16:15hrs.
Luis Morales. Facultad de Física - UC
Real spectrum induced by photon-assisted tunneling in an ac-driven system with controlled gain and loss
Sala 1 - Facultad de Matemáticas
Abstract:
Photon-assisted tunneling (PAT) is a quantum phenomenon that arises from the interaction between particles with photons in the presence of an ac field. This interaction enables particles to tunnel through barriers with the assistance of photons, resulting in resonant transport. For open quantum systems with controlled gain and loss, the implementation of PAT can significantly improve the control of the border between real and complex spectra, which could lead to highly sensitive sensors. In this talk, I will discuss the effect of the PAT phenomenon on the real spectrum for an ac driven system that is non-Hermitian and fulfills the parity-time (PT) symmetry. In particular, I will show that PAT can resonantly extend stable regions with real spectrum. To this end, I will discuss phase diagrams with regions of real Floquet quasienergies created by the application of the ac drive. I will also show analytical estimations of the critical gain-loss parameter for the different resonance values of the driving frequency.
2023-10-26
16:15hrs.
José Armando Martinez Perez. Unam
Análisis casi periódico para la evolución de estados
Sala 1 - Facultad de Matemáticas
Abstract:
En 1925 Harald Bohr introdujo las funciones casi periódicas como una extensión de las funciones periódicas. Entre las extensiones que le siguieron, fue la extensión de Abram S. Besicovitch que permitió definir un espacio de Hilbert y, asimismo, extender el análisis armónico. A este análisis es al cual nos referimos como análisis casi periódico.
En esta plática expondremos brevemente las funciones casi peripodicas de Harald Bohr y en el sentido de Besicovitch, asimismo, hablaremos de las series tipo Fourier asociadas a estas funciones. Nuestro principal interés es exponer una aplicación a la mecánica cuántica no relativista. Para ello, partiendo de un Hamiltoniano con espectro discreto, mostraremos cómo la evolución de estados, a pesar de no ser periódicos aún podemos caracterizarlos con el análisis casi periódico. Parte de esta charla es fruto de reuniones y trabajos conjuntos con los profesores Gabino Torres Vega (CINVESTAV), y por otra parte, con el profesor Rafael del Rio (IIMAS, UNAM). 
2023-10-19
16:15hrs.
Carlos Román . Facultad de Matemáticas - UC
Domain branching in micromagnetism
Sala 1 - Facultad de Matemáticas
Abstract:
Nonconvex variational problems regularized by higher order terms have been used to describe many physical systems, including, for example, martensitic phase transformation, micromagnetics, and the Ginzburg--Landau model of nucleation. These problems exhibit microstructure formation, as the coefficient of the higher order term tends to zero.  They can be naturally embedded in a whole family of problems of the form: minimize E(u)= S(u)+N(u)
over an admissible class of functions u taking only two values, say -1 and 1, with a nonlocal interaction N favoring small-scale phase oscillations, while the interfacial energy S penalizes them. 
In this talk I will report on recent joint work with Tobias Ried, in which we establish self-similarity, in a statistical sense through local energy bounds, of minimizers of an energy functional that naturally arises when analyzing the behavior of uniaxial ferromagnets using the Landau-Lifschitz model.
2023-10-05
16:15hrs.
Joris de Moor. Universidad Erlangen-Nürnberg
Footprint of a topological phase transition on the density of states
Sala 1 - Facultad de Matemáticas
Abstract:

For a one-dimensional random discrete Schrödinger operator, the energies at which all transfer matrices commute and have their spectrum off the unit circle are called critical hyperbolic. Disorder driven topological phase transitions in such models are characterized by a vanishing Lyapunov exponent at the critical energy. It is shown that the density of states away from a transition has pseudogap with an explicitly computable Hölder exponent, while it has a logarithmic divergence (Dyson spike) at the transition points. The proof is based on renewal theory for the Prüfer phase dynamics and the optional stopping theorem for suitably constructed comparison martingales.

2023-09-21
16:15hrs.
Grupo de Trabajo. Facultad de Física - UC
Grupo de Trabajo
Sala 1 - Facultad de Matemáticas
2023-09-07
16:15hrs.
Dardo Goyeneche. Facultad de Física - UC
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2023-08-24
16.15hrs.
Dardo Goyeneche. Instituto de Física - UC
No localidad cuántica y exceso de matrices
Sala 1 - Facultad de Matemáticas
Abstract:
 En la presente charla se dará una introducción a la no-localidad cuántica y su relación con un problema puramente matemático formulado en la década de los 70', es decir, el exceso de una matriz.
2023-06-29
16:15hrs.
Christian Sadel. Facultad de Matemáticas
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2023-06-22
16:15hrs.
Christian Sadel. Facultad de Matemáticas - UC
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2023-06-15
16:15hrs.
Gregorio Moreno - Christian Sadel. Facultad de Matemáticas - UC
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2023-06-08
16:15hrs.
Gregorio Moreno. Facultad de Matemáticas - UC
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2023-06-01
16:15hrs.
Dieter Mitsche . Instituto de Ingeniería Matemática y Computacional - UC
Tail bounds for detection times in mobile hyperbolic graphs
Sala 1 - Facultad de Matemáticas
Abstract:
Motivated by Krioukov et al.'s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a dynamic model of hyperbolic graphs in which vertices are allowed to move according to a Brownian motion maintaining the distribution of vertices in hyperbolic space invariant. For different parameters of the speed of angular and radial motion, we analyze tail bounds for detection times of a fixed target and obtain a complete picture, for very different regimes, of how and when the target is detected: as a function of the time passed, we characterize the subset of the hyperbolic space where particles typically detecting the target are initially located.
We overcome several substantial technical difficulties not present in Euclidean space, and provide a complete picture on tail bounds. On the way, we obtain also new results for the time more general continuous processes with drift and reflecting barrier spent in certain regions, and we also obtain improved bounds for independent sums of Pareto random variables. 
Joint work with Marcos Kiwi and Amitai Linker.
2023-05-25
16:15hrs.
Guiseppe de Nittis . Facultad de Matemáticas - UC
Grupo de Estudio
Sala 1 - Facultad de Matemáticas