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.
Neil Mañibo. Bielefeld University Continuous diffraction in mathematical quasicrystals Sala 1 - Facultad de Matemáticas Abstract: Quasicrystals are materials which lack a crystalline-likelattice 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 arisingfrom substitutions on finite alphabets/inflation ruleson finitely many tiles (up to translation), which induce a hierarchicalstructure compatible with renormalisation techniques in spectral theory.In particular, we will discuss (i) a Diophantine-type condition neededfor the presence of (non-trivial) Bragg peaks, (ii) a criterion usingLyapunov exponents that confirms the absence of a non-trivial absolutelycontinuous 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
2023-05-18 16:15hrs.
Cesar Arias. Facultad de Matemáticas - UC Volumes, Surfaces, and Holography Sala 1 - Facultad de Matemáticas Abstract: We review the usage of conformal geometry techniques in the resolution of the renormalized volume problem for asymptotically hyperbolic spaces, and the potential application of these ideas in the context of holography for anti-de Sitter space-time.
2023-05-11 16:15hrs.
Andres Fernando Reyes Lega. Departamento de Física, Universidad de los Andes (Bogotá) Geometric Phases for Quasi-Free Fermions at Finite Temperature Sala 1 - Facultad de Matemáticas Abstract:
In this talk I will discuss a Z2 index associated to quadratic gapped Hamiltonians that describe fermionic systems in the context of self-dual CAR C*-algebras. Concrete examples will be used in order to illustrate the physical relevance of this invariant. I will also present preliminary results of an attempt to extend this invariant to the finite temperature case, which is based on a generalization of the geometric phase to mixed states.
2023-04-20 16:15hrs.
Per Sundell. Universidad Andres Bello Higher spin gravity and noncommutative geometry Sala 1 - Facultad de Matemáticas Abstract:
We expose the origin of Vasiliev's higher spin gravity in noncommutative geometry using the Alexandrov-Kontsevich-Schwarz-Zaborosky formalism for Batalin-Vilkovisky quantization of topological field theories, which is amenable to Atiyah's functorial approach to quantum field theory. The emerging framework exhibits two types of dualities: At the first-quantized level, nonlinear quantum-mechanical systems including anyons are connected to classical higher-spin gravity moduli spaces including particles, fuzzy black holes and various conical defects; at the second-quantized level, different operator algebras attached to various defects of topological parent models are connected through overlap conditions obeyed by entangled vacuum states encoding generalized holographic correspondences.
The talk aims to introduce basic concepts to an audience with some familiarity with analytical and quantum mechanics as well as classical and quantum relativistic field theory.
2023-04-13 16:15hrs.
Marcelo Loewe. Universidad San Sebastián Fermiones (electrones) en Electrodinámica Cuántica (QED) en presencia de un campo magnético externo con fluctuaciones espaciales Sala 1 - Facultad de Matemáticas Abstract:
Consideramos los efectos de un campo magnético de fondo, con fluctuaciones espaciales (campo ruidoso), sobre el propagador fermiónico en QED, como una aproximación a las inhomogeneidades espaciales que podrían surgir naturalmente en ciertos escenarios físicos como colisiones relativistas de iones pesados o en el plasma de quarks y gluones, en etapas tempranas del universo. Consideramos un campo magnético clásico finito y uniforme en promedio, $\bra\bf B(x)\ket=\bf B$, sujeto a fluctuaciones espaciales de ruido blanco con una auto-correlación de magnitud $\Delta_B$ . Mediante el marco provisto por el propagador de Schwinger para el campo magnético promedio, usamos el formalismo de réplicas para estudiar los efectos del campo magnético ruidoso a través de parámetros de renormalización de cuasi-partículas. De este modo obtenemos una carga efectiva y un índice de refracción efectivo que dependen no solamente de la escala de energía, como ocurre usualmente, sino también de la magnitud del ruido $\Delta_B$ y del campo promedio B.