Thursday 6.2.2020, 14:15h in Kuščerjev seminar, Jadranska 19. This talk covers the mathematical foundation of the Mittag-Leffler functions, fractional integrals and derivatives, and many recent novel definitions of generalized operators which appear to have many applications nowadays. We pay special attention to the analysis of the complete monotonicity of the Mittag-Leffler function which is a very important prerequisite for its application in modeling different anomalous dynamics processes. We will give a number of definitions and useful properties of different fractional…

Tuesday 3.3.2020, 13:15h in Kuščerjev seminar, Jadranska 19. The Luttinger model with finite-range interactions is an exactly solvable model in 1+1 dimensions somewhere between conformal and Bethe-ansatz integrable ones. I will show how exact analytical results can be computed for the time evolution of this non-local Luttinger model following an inhomogeneous quench from initial states defined by smooth temperature and chemical-potential profiles. These results demonstrate that the finite-range interactions give rise to dispersive effects that are not present in the…

Thursday 5.3.2020, 11:15h in Kuščerjev seminar, Jadranska 19. Hydrodynamics is a theory of the collective properties of fluids and gases that can also be successfully applied to the description of the dynamics of quark-gluon plasma. It is an effective field theory formulated in terms of an infinite-order gradient expansion. For any collective physical mode, hydrodynamics will predict a dispersion relation that expresses this mode’s frequency in terms of an infinite series in powers of momentum. By using the theory of…

Rule 54 reversible cellular automaton (RCA54) is a 1-dim lattice model of solitons that move with fixed velocities and undergo nontrivial scattering. In the past years, numerous exact results have been found, ranging from the exact non-equilibrium steady state and exact large deviation treatment of the boundary driven setup to the matrix product form of time evolution of local observables. In the talk I will discuss recent progress. In particular I will present the matrix product form of multi-time correlation…

We define and study an integrable G-invariant dynamics of a field subject to a nonlinear constraint on a 1+1 dimensional discrete space-time lattice. The model allows for efficient numerical simulations, which suggest superdiffusion and Kardar-Parisi-Zhang physics in the entire family of models (arXiv:2003.05957). Further, I will present some recent results on extending the model onto other symmetric spaces and more general symmetry groups. Lastly I will discuss a recent surprising observation of conic sections in the correlation tensor of (non)-integrable…

We examine novel links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras, we identify quantum groups associated to set-theoretic solutions coming from braces and we also derive new classes of symmetries for the corresponding periodic transfer matrices. * Anastasia Doikou, Heriot-Watt University, Edinburgh The seminar will be online via Zoom (ID: 917 7027 2241, Password: 820642).

I will discuss how to use Bethe Ansatz techniques for studying the properties of certain systems experiencing loss. First of all, I will describe the general approach to obtain the Liouvillian spectrum of a wide range of experimentally relevant models. This includes any integrable model with particle number conservation experiencing the single particle bulk loss throughout the system. Following the general discussion, I will address different aspects of the XXZ spin chain driven at the single boundary. In particular, I will consider the scaling of Liouvillian gap, the…

The assumption that quantum systems relax to a stationary (time-independent) state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. However, real-world phenomena, from life to weather patterns are persistently non-stationary. We will discuss simple algebraic conditions that lead to a quantum many-body system…