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  1. Mathematics, Computer Science and Engineering
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  4. Seminar Series 2019-20
About City

Seminar Series 2019-20

DateSpeaker Titles and abstracts
1st October 2019 Peter Millington (Nottingham) Symmetry breaking in non-Hermitian, PT-symmetric quantum field theories

We consider the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories.  We begin by revisiting the derivation of Noether’s theorem and find that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant.  After describing the implications of this conclusion for gauge invariance, we consider the spontaneous breakdown of global and local symmetries, and illustrate how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out.  We conclude by commenting on the potential avenues for model building in fundamental physics from the non-Hermitian deformation of the Standard Model of particle physics.
8th October 2019 Marko Medenjak (ENS) The isolated Heisenberg magnet as a quantum time crystal

Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.
15th October 2019 Fabian Ruhle (CERN) Machine Learning and Complexity of String Vacua

I will start with an introduction to the fields of machine learning and computational complexity. Subsequently, I will discuss the complexity of problems encountered in searches for solutions to string theory’s physical and mathematical consistency conditions. Finally, I will illustrate how reinforcement learning, a branch of machine learning, can be used to tackle these types of problems. I will present an example in the context of Type II string theory, where the consistency conditions are a set of coupled, non-linear Diophantine equations. I will demonstrate that the machine learning algorithm discovers solution strategies that have previously been employed by humans, but also discovers new, previously unknown strategies.
22nd October 2019 Bernd Braunecker (St. Andrews) Non-Markovian dynamics of a spin in a fermionic bath: quantum correlations, backaction and non-thermodynamic cooling

I will present a systematic analytical approach for calculating the dynamics of a spin system in contact with a bath of fermions [1]. The approach is set up such that the full time dynamics is captured by including all quantum coherent memory effects leading to non-Markovian dynamics. I will show on the example of the free induction decay how the full time range can be obtained analytically through a systematic study of the pole structure of the memory kernel of the density matrix, based on the Nakajima-Zwanzig master equation in the weak coupling limit. The result is an analytic expression showing how a quantum correlation dominated dynamics at short times evolves smoothly into the conventional exponential thermal decay at long times. I will conclude with the proposal of a quantum thermodynamic scheme to employ the temperature insensitivity of the non-Markovian decay to transport heat out of the electron system and thus, by repeated re-initialisation of a cluster of spins, to efficiently cool the electrons at very low temperatures.

[1] S. Matern, D. Loss, J. Klinovaja and B. Braunecker, Phys. Rev. B,
Phys. Rev. B 100, 134308 (2019), arXiv:1905.11422.
5th November 2019 Klaus Ritzberger (Royal Holloway) What can Index Theory Do for Game Theorists?

The concept of the fixed point index has been productively applied to a number of fields in economics. This presentation reviews the applications in game theory, with an emphasis on the equilibrium refinement debate. This is because the index has successfully served as a refinement concept for Nash equilibrium, as well as an identification of a necessary condition for asymptotic stability in evolutionary dynamics. Indeed, the index can also be used to relate the evolutionary approach to game theory with the rationalistic one. And quite a number of results developed for game theory extend to analogous results on general equilibrium theory. Finally, a few recent extensions of the logic of index theory in games are discussed.
12th November 2019 Misha Feigin (Glasgow) Generalized Calogero-Moser-Sutherland systems

Calogero-Moser-Sutherland (CMS) system describes pairwise interaction of particles on a circle. It is a celebrated example of an integrable system partly due to its deep connections to geometry and algebra. For example, radial parts of Laplace-Beltrami operators on symmetric spaces give generalized quantum CMS systems related with root systems of Weyl groups with special values of coupling parameters. Algebraically,  interesting cases are quantum systems with integer coupling parameters; in these cases generalised CMS operators admit special Baker-Akhiezer eigenfunctions. After reviewing some facts about generalized CMS systems I’ll introduce new integrable example of a two-dimensional CMS type system closely related to but different from G_2 case. This is based on joint work with M. Vrabec.
19th November 2019 Jean Alexandre (King's) Spontaneous Symmetry Breaking or not?

Path integral quantisation of a scalar theory requires the one-particle irreducible effective potential to be a convex function of the background field. On the other hand, Spontaneous Symmetry Breaking  (SSB) is based on a non-convex potential, so how are these two features consistent? This talk will review convexity properties, explain in what situation one can expect either SSB or convexity to happen,  and show a semi-classical derivation of the convex effective potential. To conclude, an example where convexity could play a role will be discussed, in the context of cosmological Inflation.
6th December 2019 Ignacio Reyes (AEI) Fermionic entanglement on the torus

Concepts from quantum information theory have become increasingly important in our understanding of entanglement in QFTs. One prominent example of this is the modular Hamiltonian, which is closely related to the Unruh effect. Using complex analysis, we determine this operator for the chiral fermion at finite temperature on the circle and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality, thus bridging the gap between previously known limits. We derive the first exact results for the entropy in the different spin sectors, and comment on the analytic continuation of the Rényi entropies to the complex plane.
21st January 2020 Elli Pomoni (DESY) T_N, Toda and topological strings

In this talk we will consider the long-standing problem of obtaining the 3-point functions of 2D Toda CFT. We will propose a solution to this problem employing topological strings and the AGT relation between 4D gauge theories and 2D CFTs.
28th January 2020 Jacopo de Nardis (Ghent) Emergent diffusion and super-diffusion in quantum and classical chains.

Finding a theoretical framework to explain how phenomenological transport laws on macroscopic scales emerge from microscopic deterministic dynamics poses one of the most significant challenges of condensed matter physics. In recent years, the advent of the generalized hydrodynamics in integrable quantum systems and more recent studies of quantum chaos and its relation to transport, reinvigorated the field of nonequilibrium physics in spin chains. Numerous results were found: lower bounds to diffusion constants, exact expressions for diffusion coefficients and remarkable anomalous features of transport in quantum and classical chains, deeply related to the Kardar-Parisi-Zhang dynamical universality class.I will present an overview of such results with a particular focus on anomalous transport and its relation to non-linear hydrodynamics.
4th February 2020 Rainer Klages (QMUL)

Stochastic modeling of diffusion in dynamical systems: three examples

Consider equations of motion yielding dispersion of an ensemble of particles. For a given dynamical system an interesting problem is not only what type of diffusion is generated but also whether the resulting diffusive dynamics matches to a known stochastic process. I will discuss three examples of dynamical systems displaying different types of diffusive transport: The first model is fully deterministic but nonchaotic
by showing a whole range of normal and anomalous diffusion under variation of a single control parameter [1]. The second model is a soft Lorentz gas where a point particles moves through repulsive Fermi potentials situated on a triangular periodic lattice [2]. It is fully deterministic by displaying an intricate switching between normal and superdiffusion under variation of control parameters. The third model randomly mixes in time chaotic dynamics generating normal diffusive spreading with non-chaotic motion where all particles localize [3]. Varying a control parameter the mixed system exhibits a transition characterised by subdiffusion. In all three cases I will show successes, failures and pitfalls if one tries to reproduce the resulting diffusive dynamics by using simple stochastic models.

Joint work with all authors on the references cited below.

[1] L. Salari, L. Rondoni, C. Giberti, R. Klages, Chaos 25, 073113 (2015)
[2] R.Klages, S.S.Gallegos, J.Solanp¨a¨a, M.Sarvilahti, Phys. Rev. Lett. 122, 064102
[3] Y.Sato, R.Klages, Phys. Rev. Lett. 122, 174101 (2019)

12th February 2020 Shivaji Ratnasingham (U of North Carolina Greensboro)

An exact bifurcation diagram for a reaction diffusion equation arising in population dynamics

We analyze the positive solutions to
􏰀 −∆v=λv(1−v); x∈Ω0,

∂v +γ√λv=0; x∈∂Ω0, ∂η

where Ω0 = (0,1) or is a bounded domain in Rn; n = 2,3 with smooth boundary and |Ω0| = 1, and λ,γ are positive parameters. Such steady state equations arise in population dynamics encapsulating assumptions regarding the patch/matrix in- terfaces such as patch preference and movement behavior. In this paper, we will discuss the exact bifurcation diagram and stability properties for such a steady state model.

18th February 2020 Jose Edelstein (Santiago de Compostela) Beyond General Relativity: causality issues and geometric inflation

We will explore the consequences of imposing consistency conditions in the introduction of higher curvature corrections to the Einstein-Hilbert Lagrangian. We will discuss two separate issues. First, we will argue that causality and unitarity put some tough restrictions at tree level, pointing in the direction of a UV stringy completion. Second, we will show that it is possible to write down an action given by an infinite series in the Riemann tensor with nice properties in terms of its spectrum and cosmology, which suggests a tantalizing mechanism of geometric inflation.

The later seminars were cancelled due to Covid-19.