# 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 15:45 hrs, sala 5 de la Facultad de Matemáticas.

Organización: Olivier Bourget, Giuseppe De Nittis, Christian Sadel, Edgardo Stockmeyer, Rafael Tiedra de Aldecoa.
2018-09-12
15:45 hrs.
Akito Suzuki. Shinshu University
Tba
Sala 5
2018-08-22
15:45 hrs.
Emanuela Radici. Università Degli Studi Dell'aquila
Tba
Sala 5
2018-06-27
15:45 hrs.
Tba
Sala 5
2018-06-20
15:45 hrs.
Esteban Castillo. Pontificia Universidad Católica de Chile
Non Commutative Geometry for Particle Physics
Sala 5
Abstract:

In this talk we discuss the construction of the Standard Model for particle physics on the basis of the noncommutative geometric approach. We display the ideas developed by Connes and coworkers in the last two decades.

2018-06-13
15:45 hrs.
Rolando Rebolledo. Pontificia Universidad Católica de Chile
The Generalised Quantum Harmonic Oscillator and its Decoherence-Free Sub-Algebra
Sala 5
Abstract:
We consider the de finition of the generalised Quantum Harmonic Oscillator (QHO) introduced by Bath and Parthasarathy in [2]. It is well-known (see [1]) that all QMS suffers decoherence in its evolution. Loosely speaking, one says that "the quantum evolution becomes classical", this means that after some time, the dynamics concentrates on a commutative sub-algebra of observables. In [3] we characterized decoherence-free subalgebras where the evolution preserves its quantum structure. In general, these sub-algebras are trivial, nevertheless some physical systems do contain non trivial decoherence sub-algebras. More precisely, the decoherence-free subalgebra is the biggest (non commutative) where the semigroup act as a group of endomorphisms. The conference will show that the generalised QHO has a non trivial decoherence-free subalgebra.

[1] Ph. Blanchard and R. Olkiewicz, Decoherence induced transition from quantum to classical dynamics. Rev. Math. Phys. 15 (2003), no. 3, 217-243.

[2] B.V.R. Bhat and K.R. Parthasarathy, Generalized harmonic oscillators in quantum probability, Sem. Probab. XXV (1991) 39-51.

[3] A. Dhahri, F. Fagnola and R. Rebolledo, The Decoherence-free Subalgebra of a Quantum Markov Semigroup with Unbounded Generator. Infi n. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 3, 413-433.

[4] F. Fagnola and R. Rebolledo, Entropy Production for Quantum Markov Semigroups, Commun. Math. Phys. 335 (2015), 547-570.
2018-06-06
15:45 hrs.
Edgardo Stockmeyer. Pontificia Universidad Católica de Chile
Asymptotic Dynamics for Certain 2-D Magnetic Quantum Systems
Sala 5
Abstract:

In this talk I will present new results concerning the long time localisation in space (dynamical localisation) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form $H=H_0+W$, where $H_0$ has dense point spectrum and rotational symmetry and $W$ is a perturbation that breaks the symmetry. (Joint with: I. Anapolitanos, E. Cárdenas, D. Hundertmark, and S. Wugalter)

2018-05-30
15:45 hrs.
Mircea Petrache. Pontificia Universidad Católica de Chile
Crystallization Principles for The Simplest Many Body Systems in 2 Dimensions
Sala 5
Abstract:
Consider the following fundamental crystallization question: if a point configuration (x_1,..,x_N) is a ground state for the energy E_f given as the sum of pairwise energies f(|x_i-x_j|), what principles force the configuration to approximate a particular lattice in 2-dimensions, asymptotically for very large N? The two possible settings are (a) the one in which we fix the particle density as a constraint for the minimization, or (b) the one in which we fix a natural scale via the shape of f itself, i.e. we look at one-well potentials f. In both cases, we want to find the relevant and tractable properties of the potential f which allow to treat the minimization amongst lattice and some non-lattice configurations. I will recall important known results for the two situations (a), (b), and present some new results and counterexamples, obtained in collaboration with L. Betermin.
2018-05-23
15:45 hrs.
Mauro Spera. Università Cattolica del Sacro Cuore
Remarks on Landau Levels, Braid Groups and Laughlin Wave Functions
Sala 5
Abstract:
In this talk, after discussing ([1]) the holomorphic geometric quantization of a charged particle on a plane subject to a constant magnetic field perpendicular to the latter (see also [2]), we shall outline the geometric approach to unitary Riemann surface braid group representations via stable holomorphic bundles on Jacobians developed in [3] and the ensuing construction of generalized Laughlin wave functions.
[1] A. Galasso and M. Spera: Remarks on the geometric quantization of Landau levels, Int. J. Geom. Meth. Mod. Phys. 13 (10) (2016), 1650122 (19 pages).
[2] J. Klauder and E. Onofri: Landau levels and geometric quantization, Int. J. Modern Phys. A 4 (1989) 3939–3949.
[3] M. Spera: On the geometry of some unitary Riemann surface braid groups representations and Laughlin-type wave functions, J. Geom. Phys. 94 (2015), 120-140.
2018-05-16
15:45 hrs.
Kevin Morand. Universidad Técnica Federico Santa María Valparaíso
Three Approaches To Non-Riemannian Geometries
Sala 5
Abstract:
Recent years have seen a surge of interest regarding non-Riemannian geometries, the most prominent examples thereof being Newton-Cartan and Carroll geometries. We review these two dual geometries and related aspects from three perspectives:

1) Intrinsic à la Cartan

2) Ambient à la Eisenhart

3) Algebraic à la Cartan (again)
2018-05-09
15:45 hrs.
Martin Chuaqui. Pontificia Universidad Católica de Chile
La Derivada Schwarziana de Ahlfors y Ceros de Soluciones de Ecuaciones Lineales
Sala 5
Abstract:
Expondremos la definición y propiedades de la derivada Schwarziana de Ahlfors, junto a un resumen de resultados conocidos y problemas abiertos. Se discutira el concepto de parametrizacion de Möbius de curvas de largo infinito, para terminar con un teorema sobre los ceros de soluciones de ecuaciones lineales en la recta real.
2018-05-02
15:45 hrs.
María Isabel Cortez. Universidad de Santiago de Chile
Propiedades Espectrales de los Sistemas Minimales de Cantor
Sala 5
Abstract:
Ejemplos de sistemas minimales de Cantor son los subshifts de substitución y algunas extensiones simbólicas de las rotaciones sobre el círculo. En esta charla veremos algunas propiedades que caracterizan a los valores propios de estos sistemas, así como su relación con el grupo de dimensión, invariante algebraico asociado a estos sistemas. Algunas de estas propiedades se pueden extender a los sistemas dinámicos generados por las traslaciones de un tiling en R^d.
2018-04-24
15:45 hrs.
Richard Froese. University of British Columbia
Resonances Lost and Found
Sala 5
Abstract:
We compute the large $L$ asymptotics of the resonances for one dimensional Schrödinger operators $H_L=V_1(x)+\mu(L)V_2(x−L)$, where $V_1$ and $V_2$ are compactly supported and $\mu(L)\sim e^{-cL}$ for $c\ge0$. These are compared to the Schrödinger dynamics of $H_L$. This is joint work with Ira Herbst.
2018-04-18
15:45 hrs.
Amal Taarabt. Pontificia Universidad Católica de Chile
On The Current-Current Correlation Measure for Random Schrödinger Operators
Sala 5
Abstract:
We review various properties of random Schrödinger operators and recall formulations of conductivity and current-current correlation measure. In this talk we will present a panoramic view and recent results on localized regime. We will focus in particular on the diagonal behaviour problem of the ccc-measure and explain how it is related to the localization length. This is a work in progress with J. Bellissard and G. De Nittis.
2018-04-11
15:45 hrs.
Carlos Román. Leipzig University & Max Planck Institute for Mathematics in The Sciences
On The 3D Ginzburg-Landau Model of Superconductivity
Sala 5
Abstract:
The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature is the presence of vortices (similar to those in fluid mechanics, but quantized), which appear above a certain value of the applied magnetic field called the first critical fi eld. We are interested in the regime of small ε, where ε>0 is the inverse of the Ginzburg-Landau parameter (a material constant). In this regime, the vortices are at main order codimension 2 topological singularities.
In this talk I will present a quantitative 3D vortex approximation construction for the Ginzburg-Landau energy, which provides an approximation of vortex lines coupled to a lower bound for the energy, optimal to leading order, analogous to the 2D ones, and valid for the first time at the ε-level. I will then apply these results to describe the behavior of global minimizers for the 3D Ginzburg-Landau functional below and near the first critical fi eld. I will also provide an ε-quantitative product-type lower bound for the study of Ginzburg-Landau dynamics.
2018-04-04
15:45 hrs.
Rafael Tiedra de Aldecoa. Pontificia Universidad Católica de Chile
Quantum Time Delay for Unitary Propagators
Sala 5
Abstract:
We give the definition of quantum time delay in terms of sojourn times for unitary propagators in a two-Hilbert spaces setting. We prove that this time delay defined in terms of sojourn times (time-dependent definition) exists and coincides with the expectation value of a unitary analogue of the Eisenbud-Wigner time delay operator (time-independent definition). Our proofs rely on a new summation formula relating localisation operators to time operators and on various tools from functional analysis such as Mackey's imprimititvity theorem, Trotter-Kato Formula and commutator methods for unitary operators. Joint work with Diomba Sambou (PUC).
2018-03-28
15:45 hrs.
Diomba Sambou. Pontificia Universidad Católica de Chile
Complex Eigenvalues for a Non-Self-Adjoint Dirac Operator
Sala 5
Abstract:
We will consider a 2d Dirac operator with constant magnetic field perturbed by non-self-adjoint potentials. It is well known that when it is perturbed by certain self-adjoint potentials, then, there is creation and accumulation of real eigenvalues near every point of its essential spectrum given by a set of degenerate isolated eigenvalues called the Landau levels. Recently, similar results have been proved for Schrödinger operators perturbed by non-self-adjoint perturbations showing the existence of complex-valued potentials generating infinitely many non-real eigenvalues accumulating at every point of [0,+∞). We will present a similar result for the 2d Dirac operator above, showing the existence of non-self-adjoint perturbations generating infinitely many non-real eigenvalues accumulating at every Landau level.
2018-03-21
15:45 hrs.
Nicolas Raymond. University of Rennes 1
Survey on The Semiclassical Magnetic Laplacian
Sala 5
Abstract:
In the first part of the talk, I will describe recent advances about the description of the discrete spectrum of the magnetic Laplacian, in the semiclassical limit. In the second part, I will describe two results in two dimensions, essentially in the case of a non-degenerate magnetic well: the Birkhoff normal forms and their applications (collaboration with S. Vu Ngoc) and the magnetic WKB constructions (collaboration with Y. Bonthonneau).
2018-03-14
15:45 hrs.
Timo Weidl. University of Stuttgart
The Edge Resonance in Elastic Media With Zero Poisson Coefficient
Sala 5
Abstract:
A two-dimensional elastic semistrip with stress-free boundary conditions and zero Poisson coefficients has an embedded eigenvalue on top of the continuous spectrum. This effect is known as edge resonance. For an infinite plate of finite thickness with a drilling hole $(R^2\setminus\Omega)\times I$ actually infinitely many edge resonances will occur. This is related to the spectral problem of perturbations of symbols with strongly degenerated minima, which also appear in BCS theory. I give an overview on some of our results in this area, which still poses a number of mathematical challenges.
2017-12-20
15:45 hrs.
Michael Loss. Georgia Institute of Technology
Entropy Decay for The Kac Master Equation
Sala 5
Abstract:
The Kac master equation models the behavior of a large number of randomly colliding particles. Due to its simplicity it allows, without too much pain, to investigate a number of issues. E.g., Mark Kac, who invented this model in 1956, used it to give a simple derivation of the spatially inhomogeneous Boltzmann equation. One important issue is the rate of approach to equilibrium, which can be analyzed in various ways, using, e.g., the gap or the entropy. Explicit entropy estimates will be discussed for a Kac type master equation modeling the interaction of a finite system with a large but finite reservoir. This is joint work with Federico Bonetto, Alissa Geisinger and Tobias Ried.
2017-12-06
15:45 hrs.
Daniel Remenik. Cmm, Universidad de Chile
The Kpz Fixed Point
Sala 5
Abstract:
I will describe the construction and main properties of the KPZ fixed point, which is the scaling invariant Markov process conjectured to arise as the universal scaling limit of all models in the KPZ universality class, and which contains all the fluctuation behavior seen in the class. The construction follows from an exact solution of the totally asymmetric exclusion process (TASEP) for arbitrary initial condition. This is joint work with K. Matetski and J. Quastel.