Juan Carlos Arroyave Blanco (IMPA): Universality of NESS for KPZ
Abstract: We analyze the open $\textbf{WASEP}$($\alpha$), where each site can host up to $\alpha$ particles, coupled to boundary reservoirs fixing the densities $\rho_- = \beta$ and $\rho_+ = \gamma$. Under a suitable reference measure and hydrodynamic scaling, we show, via the relative entropy method, that the macroscopic density profile satisfies the inviscid Burgers-type equation: $\partial_x^2 u - v \partial_x u^2 = 0$. At the diffusive time scale, the associated density fluctuation field is tight, and its trajectories concentrate on energy solutions of the stochastic Burgers equation (SBE): $d\mathscr{Y}_t = \alpha \Delta_{\mathrm{Dir}} \mathscr{Y}_t \, dt + \frac{v\alpha}{2} \nabla_{\mathrm{Dir}}(u \mathscr{Y}_t) \, dt + v \nabla_{\mathrm{Dir}} (\mathscr{Y}_t^2) \, dt + \sqrt{2\chi(\rho)} \nabla_{\mathrm{Dir}} \, d\mathscr{W}_t$, where $\chi(\rho) = \rho(\alpha - \rho)$ and $\mathscr{W}_t$ denotes space-time white noise. This establishes WASEP($\alpha$) as a microscopic foundation for the universality of the SBE in non-equilibrium open systems.
Ubaldo Cavazos Olivas (University of Warsaw): Ionic polaron and bipolaron in a Bose gas
Abstract: Ultracold quantum many-body systems constitute an interesting research playground due to their wide range of applications, from precision measurements to transport phenomena in the field of condensed matter. One particular example are hybrid systems of atoms and ions, which are rapidly developing [1] and at ultralow temperature provide an ideal environment for the emergence of polarons. Namely, a quantum bath composed of bosonic atoms weakly coupled to an ion can be properly described by means of Bogoliubov theory. Nevertheless, this approach is no longer valid as soon as the strong coupling regime is taken into account, leading to an instability with an infinite number of bosons collapsing into the ion. Ion-atom systems feature long-range interactions which drive the system to form a many-body bound state with high density and large atom number [2]. In order to explore this physics and circumvent the bosons unstable behavior, based on [3], a variational approach is adopted. Employing a regularized potential that retains the correct long-distance behavior, we study the properties of interest in the formation of ionic Bose polaron and bipolaron, such as their energy, the number of bosons that takes part in the cloud formation, and the induced interactions which are tunable by the potential parameters.
References:
[1] Tomza, M. et al. Cold hybrid ion-atom systems. Rev. Mod. Phys. 91, 035001(2019).
[2] Astrakharchik, G.E., Ardila, L.A.P., Schmidt, R. et al. Ionic polaron in a Bose-Einstein condensate. Commun Phys 4, 94 (2021).
[3] Schmidt, R. and Enss, T. Self-stabilized Bose polarons. SciPost Phys. 13, 054 (2022).
Adrien Escoubet (Université de Lille): Experimental Measurement of the Dynamical Structure Factor in a Normal Dispersion Fiber Recirculating Loop
Abstract: The search for universality classes aims to group together many systems that exhibit identical asymptotic behaviors, regardless of their underlying microscopic mechanisms. In this context, Kardar, Parisi, and Zhang (KPZ) introduced their famous equation in 1986 to describe the growth of an interface between two phases [1]. This nonlinear stochastic equation was later found to be connected to the description of various systems within its universality class, such as the Eden model [2] and the free energy distribution in random polymers [3]. In 2004, Prähofer and Spohn developed a discrete growth model that allowed the theoretical determination of the dynamic exponent, which characterizes the evolution of the system’s characteristic length scale over time, yielding z=3/2 [4]. A recent study on a Bose-Einstein condensate with repulsive interatomic interactions hints at the defocusing nonlinear Schrödinger equation (dNLSE) belonging, in the regime of small modulation amplitudes, to the KPZ universality class [5]. The theoretical justifications are based in particular on the Madelung transformation, which maps the dNLSE to the stochastic Burgers equation, itself part of this universality class. The numerical results of the study recover the value of the dynamic exponent z through the computation of the dynamic structure factor, defined as the Fourier transform of spatio-temporal correlations. This is however only a numerical signature, and the conclusions are still up for debate. We develop a nonlinear optical experiment described by the KPZ universality class in a system governed by the dNLSE. The first numerical results show the reproducibility of simulations with parameters suitable for implementation in an optical system. A recirculating fiber loop allows full observation of spatio-temporal dynamics, enabling comparison with the model. We address the issues of spectral resolution and signal-to-noise ratio, which are the main obstacles to experimentally estimating the dynamic structure factor.
References:
[1] - M. Kardar, G. Parisi & Y. Zhang, Physical Review Letters, 56, 889-892 (1986).
[2] - M. Eden, Dynamics of fractal surfaces, 4, 598 (1961).
[3] - G. Amir, I. Corwin & J. Quastel, Communications on pure and applied mathematics, 64, 466-537 (2011).
[4] - M. Prähofer & H. Spohn, Journal of Statistical Physics, 115, 255-279 (2004).
[5] - M. Kulkarni & A. Lamacraft, Physical Review A, 88, 021603 (2013).
Siddhant Mal (University of Michigan): Coherent Magneto-Conductance Oscillations in Amorphous Topological Insulator Nano-wires
Abstract: Recent experiments on amorphous materials have established the existence of surface states similar to those of crystalline three-dimensional topological insulators (TIs). Amorphous topological insulators are also independently of interest for thermo-electric and other properties. To develop an understanding of transport in these systems, we carry out quantum transport calculations for a tight-binding model of an amorphous nano-wire pierced by an axial magnetic flux, then compare the results to known features in the case of crystalline models with disorder. Our calculations complement previous studies in the crystalline case that studied the surface or used a Green's function method. We find that the periodicity of the conductance signal with varying magnetic flux is comparable to the crystalline case, with maxima occurring at odd multiples of magnetic flux quanta. However, the expected amplitude of the oscillation decreases with increasing amorphousness, as defined and described in the main text. We characterize this deviation from the crystalline case by taking ensemble averages of the conductance signatures for various wires with measurements simulated at finite temperatures. This striking transport phenomenon offers a metric to characterize amorphous TIs and stimulate further experiments on this class of materials.
Eduardo Pimenta (Federal University of Bahia): A functional Central Limit Theorem and weak Berry-Esseen Estimates for Non-homogeneous Random Walks
Abstract: In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative estimates in the vague topology at any fixed time. As important applications, we deduce functional central limit theorems for random walks on the positive integers with boundary conditions, which converge to Brownian motions on the positive half-line with boundary conditions at zero.
Enrique Rozas Garcia (University of Gothenburg): Universal Fragmentation in Annihilation Reactions with Constrained Kinetics
Abstract: In reaction-diffusion models of annihilation relations, the late-time evolution to a final empty state is independent of the initial state of the system. This universal behaviour may be attributed to the diffusive dynamics allowing the complete exploration of the space of available states. In this poster, I discuss a reaction model where the exploration is hindered by constraining the dynamics to preserve the centre of mass. With such constraints, the system does not evolve into an empty state but rather freezes into fragmented particle clusters. The late-time dynamics and final density are universal, and I discuss exact results for the final density in the large-reaction rate limit. This setup constitutes a minimal model for the fragmentation of a one-dimensional lattice into independent particle clusters.
