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Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field(using zoom) (Boltzmannstr. 3, 85748 Garching)

In this talk I will present a variational formula for the thermodynamic limit of the free energy of the Sherrington-Kirkpatrick (SK) spin-glass model with transverse field, a quantum generalization of the classical SK model. Through its path integral representation, the quantum SK model can be translated to a classical vector-spin model with the spins taking values in the space of $ \{ -1, 1 \} $-valued cadlag paths. I will explain how to approximate the model by a sequence of classical finite-dimensional vector-spin models which enables us to use results of Panchenko to describe the free energy in the thermodynamic limit. The talk is based on joint work with Arka Adhikari.

Nowcasting and Forecasting using COVID-19 data(using Zoom, see http://go.tum.de/410163 for more details) (Parkring 11, 85748 Garching)

We analyse the temporal and regional structure in COVID-19 infections, making use of the openly available data on registered cases in Germany published by the Robert Koch Institute (RKI) on a daily basis. We demonstrate the necessity to apply nowcasting to cope with delayed reporting. Delayed reporting occurs because local health authorities report infections with delay due to delayed test results, delayed reporting chains or other issues not controllable by the RKI. A reporting delay also occurs for fatal cases, where the decease occurs after the infection (unless post-mortem tests are applied). The talk gives a general discussion on nowcasting and applies this in two settings. First, we derive an estimate for the number of present-day infections that will, at a later date, prove to be fatal. Our district-level modelling approach allows to disentangle spatial variation into a global pattern for Germany, district-specific long-term effects and short-term dynamics, taking the demographic composition of the local population into account. Joint work with Marc Schneble, Giacomo De Nicola & Ursula Berger The second applications combines nowcasting with forecasting of infection numbers. This leads to a fore-nowcast, which is motivated methodologically. The method is suitable for all data which are reported with delay and we demonstrate the usability on COVID-19 infections.

Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians(using zoom) (Boltzmannstr. 3, 85748 Garching)

We introduce a framework for constructing a quantum error correcting code from {\it any} classical error correcting code. This includes CSS codes and goes beyond the stabilizer formalism to allow quantum codes to be constructed from classical codes that are not necessarily linear or self-orthogonal. We give an algorithm that explicitly constructs quantum codes with linear distance and constant rate from classical codes with a linear distance and rate. As illustrations for small size codes, we obtain Steane's $7-$qubit code uniquely from Hamming's [7,4,3] code, and obtain other error detecting quantum codes from other explicit classical codes of length 4 and 6. Motivated by quantum LDPC codes and the use of physics to protect quantum information, we introduce a new 2-local frustration free quantum spin chain Hamiltonian whose ground space we analytically characterize completely. By mapping classical codewords to basis states of the ground space, we utilize our framework to demonstrate that the ground space contains explicit quantum codes with linear distance. This side-steps the Bravyi-Terhal no-go theorem because our work allows for more general quantum codes beyond the stabilizer and/or linear codes. We hesitate to call this an example of {\it subspace} quantum LDPC code with linear distance.

Herd immunity, population structure and the second wave of an epidemic(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

The classical herd-immunity level is defined as the fraction of a population that has to be immune to an infectious disease in order for a large outbreak of the disease to be impossible, assuming (often implicitly) that the immunized people are a uniform subset of the population.I will discuss the impact on herd immunity if the immunity is obtained through an outbreak of an infectious disease in a heterogeneous population. The leading example is a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemic outbreaks or waves in the same population structured by a random network. Individuals infected during the first outbreak are (partially) immune for the second one. The first outbreak is analysed through a bond percolation model, while the second wave is approximated by a three-type branching process in which the types of individuals depend on their position in the percolation clusters used for the first outbreak. This branching process approximation enables us to calculate a threshold parameter and the probability the second outbreak is large. This work is based on joined work with Tom Britton and Frank Ball and on ongoing work with Frank Ball, Abid Ali Lashari and David Sirl.

Oberseminar : Nonlinear fluctuating hydrodynamics for anharmonic particle chains on mesoscopic scalesPasscode 101816 (https://tum-conf.zoom.us/j/96536097137 , 0 (using zoom))

The statistical physics description of classical particle chains on mesoscopic scales has surprising connections to a nonlinear extension of fluctuating hydrodynamics elevated to a stochastic PDE, which is then identified as the famous Kardar-Parisi-Zhang (KPZ) equation. Specifically, the framework starts from a microscopic (Fermi-Pasta-Ulam type) model of interacting particles in one dimension, and then uses the microscopic conservation laws to arrive at a stochastic description on a mesoscopic scale. Intuitively, one assumes that local regions of the system are close to thermal equilibrium. The stochastic description predicts dynamical correlation functions in the long-time limit, which are of large interest since they determine (heat) transport properties, for example. We find good agreement between the prediction and microscopic molecular dynamics simulations. Furthermore, the framework reveals how the Tracy-Widom distribution emerges from the microscopic dynamics with carefully prepared domain-wall initial conditions. Finally, the hydrodynamic description has recently been generalized to integrable models with an "infinite" number of conservation laws; we will present recent work on the Toda lattice as representative instance.

Stationary vine copula models for multivariate time series(using Zoom, see http://go.tum.de/410163 for more details) (Parkring 11, 85748 Garching)

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantees stationarity under a condition called translation invariance. Translation invariance is not only a necessary condition for stationarity, but also the only condition we can reasonably check in practice. In this sense, the new model class characterizes all practically relevant vine structures for modeling stationary time series. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the \emph{iid} case, go beyond what is available in the literature. The new model class is illustrated by an application to forecasting returns of a portolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation.

Homogenization of fast-slow systems with chaotic fast dynamicsVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

In my masterthesis I was interested in deterministic (ODE) systems with chaotic fast dynamics and three seperated time scales. In many applications the rapidly varying variables lie in high-dimensional space and complicate the model significantly. Homogenization is a method which is used to find reduced equations for the slowly varying variables only. My talk will be divided into three parts: In the first part we are going to discuss about a recent approach on homogenization of deterministic systems [1]; this approach uses the so called Weak Invariance Principle (a principle that generalizes the classical Central Limit Theorem) and the main dissadvantage is that it is restricted only to skew-product systems (these are systems with uncoupled fast dynamics, or in other words, with fast dynamics which envolve independently). Then in the second part we are going to move our attention towards stochastic systems; and finally, in the third and last part we are going to learn about a new approach, which is used in our recent paper [2] and is applicable to deterministic systems with coupled fast dynamics . References: [1] D. Kelly, I. Melbourne (2016) Deterministic homogenization for fast-slow systems with chaotic noise. Journal of Functional Analysis, Volume 272, Issue 10, pages 4063 – 4102. [2] M. Engel, M. A. Gkogkas, C. Kühn (2020) Homogenization of Coupled Fast-Slow Systems via Intermediate Stochastic Regularization, arxiv preprint

Oberseminar : Communication is more than information sharing: The role of status-relevant knowledgePasscode 101816 (https://tum-conf.zoom.us/j/96536097137 , 0 (using zoom))

In cheap talk games where senders’ accuracy of information depend on their background knowledge, a sender with image concerns may want to signal that she is knowledgeable despite having material incentives to lie. These image benefits may, in turn, depend on the type of knowledge and its perceived social status. Theoretically, we show that when some senders care sufficiently about their image, there is both a non-informative babbling equilibrium, and a separating equilibrium, in which the average sender’s message is informative and receivers always follow. In a laboratory experiment, we vary the social status of knowledge (1) by providing senders with multiple-choice questions on either(a) broadsheet topics (general knowledge) or (b) tabloid topics, and (2) by systematically modifying the degree of difficulty. We find truth-telling rates to be significantly higher when senders can signal high-status knowledge.

A renewal equation model for disease transmission dynamics with contact tracingVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

I will present a deterministic model for disease transmission dynamics including diagnosis of symptomatic individuals and contact tracing. The model is structured by time since infection and formulated in terms of the individual disease rates and the parameters characterising diagnosis and contact tracing processes. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. After presenting the derivation of the model, I will conclude with some applications of public health relevance, especially in the context of the ongoing COVID-19 pandemic.

Joint work with Lorenzo Pellis (University of Manchester), Nicholas H Ogden (PHAC, Public Health Agency of Canada) and Jianhong Wu (York University).

Reference: Scarabel F, Pellis L, Ogden NH, Wu J. A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control, submitted.

Percolation theory on epidemic models including long distance connections(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

TBA

The free energy of a quantum Sherrington--Kirkpatrick spin-glass model for weak disorder(using zoom) (Boltzmannstr. 3, 85748 Garching)

We extend two rigorous results of Aizenman, Lebowitz, and Ruelle in their pioneering paper of 1987 on the Sherrington--Kirkpatrick spin-glass model without external magnetic field to the quantum case with a transverse magnetic field of strength $b$. More precisely, if the Gaussian disorder is weak in the sense that its standard deviation $v>0$ is smaller than the temperature $1/\beta$, then the (random) free energy almost surely equals the annealed free energy in the macroscopic limit and there is no spin-glass phase for any $b/v \geq 0$. The macroscopic annealed free energy turns out to be non-trivial and given, for any $\beta v>0$, by the global minimum of a certain functional according to a Varadhan large-deviation principle. We prove that the so-called static approximation to the minimization problem yields the wrong $\beta b$-dependence even to lowest order in a Taylor series. Our main tool for dealing with the non-commutativity of the spin-operator components is a Feynman--Kac (path-integral) formula based on an independent collection of Poisson processes in the positive half-line with common rate $\beta b$. This is joint work with Hajo Leschke, Rainer Ruder, and Sebastian Rothlauf.