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15-26 Apr 2024 Les Houches School of Physics (France)
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Program > Invited Seminars
Abstracts Guillaume Barraquand Title: Non-equilibrium steady-state of the open KPZ equation Abstract: It is well-known that the Brownian motion is a stationary measure for the one dimensional KPZ equation on R. This means that if we start from a Brownian motion at time 0, the solution of the KPZ equation at time t remains a Brownian motion, up to a global height shift. For the KPZ equation on a bounded domain like [0,L], however, the stationary process is no longer Brownian in general. Its precise description was obtained only recently. In this talk, I will review recent progress on this question, and discuss connections with Liouville quantum mechanics and Gibbsian line ensembles.
Jacqueline Bloch Title: Kardar Parisi Zhang scaling in the coherence of polariton condensates Abstract: Cavity polaritons are hybrid light-matter quasiparticles emerging from the strong coupling between photons confined in cavities and electronic excitations named excitons confined in quantum wells. Cavity polaritons present rich physical properties emerging from this mixed nature. From their photonic component, they exhibit a light effective mass and large coherence areas (micron scale) together with a coupling to the bath of electromagnetic modes outside the cavity (driven dissipative nature). From their excitonic component, polaritons interact with each other and thus present a significant Kerr non-linearity. Semiconductor microcavities, in which cavity polaritons can be generated, appear as a powerful platform to explore the physics of quantum fluids in a driven dissipative context [1]. For instance, Bose Einstein condensation can be triggered with the characteristic onset of macroscopic coherence but with distinct physical properties related to their out of equilibrium regime. Indeed in 2015, it was discovered the phase dynamics of driven dissipative polariton condensates obeys the celebrated Kardar Parisi Zhang (KPA) equation [2]. This means that the spatio-temporal coherence decay should reveal universal KPZ scalings. Interestingly, since the phase is a compact variable, periodically defined between 0 and 2pi, the physics is enriched with the possible emergence of vortices. Actually even in 1D, where usually vortices are excluded, spatio-temporel vortices have been predicted to play a role [6] so that a rich phase diagram is predicted [2-5]. In the present talk, after a general introduction to cavity polaritons, I will explain how we could generate extended 1D polariton condensates and probe their first order coherence. We demonstrate that the spatio-temporal decay of the first order coherence presents universal scaling laws characteristic for the KPZ universality class in 1D [8]. The influence of vortices in these experiments will be discussed as well as the extension of this work to 2D [9]. This work highlights the profound difference between driven-dissipative out of equilibrium condensates and their equilibrium counterparts. We anticipate that this physics should also be relevant in extended vertical cavity lasers. References: [1] I. Carusotto and C Ciuti, Rev. Mod. Phys. 85, 299 (2013) [2] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986) [3] E. Altman, et al., Phys. Rev. X 5, 011017 (2015). [4] K. Ji, et al., Phys. Rev. B 91, 045301 (2015). [5] L. He, et al., Phys. Rev. B 92, 155307 (2015) [6] L. He et al, Phys. Rev. Lett. 118, 085301 (2017). [7] F. Vercesi et al., Phys. Rev. Research 5, 043062 (2023) [8] Q. Fontaine et al, Nature 608, 687 (2022) [9] K. Deligiannis et al., Phys. Rev. Research 4, 043207 (2022). Léonie Canet Title: The non-perturbative side of the KPZ equation Abstract: In this talk, I will discuss the non-perturbative aspect of the KPZ equation, and show how it can be described using functional and non-perturbative renormalisation group (FRG) [1]. First, in all dimensions d>1, the KPZ rough phase is controlled by a genuinely strong-coupling fixed point, ie it cannot be accessed at any order of the perturbation theory performed around vanishing non-linearity. One needs a non-perturbative method, such as the FRG, to capture it and compute the associated universal statistical properties [2]. I will explain the general setting of the FRG and the results which can be obtained for the KPZ equation in d>1. Second, even in d=1, the non-perturbative nature of the KPZ equation arises. Although the KPZ equation is exactly solvable in this dimension, and its statistical properties are known to an exquisite degree, recent numerical simulations [3] unveiled a new scaling, with a dynamical exponent z=1 different from the KPZ one z=3/2. I will show that this scaling is controlled by a fixed point which had been missed so far and which corresponds to an infinite effective coupling. This fixed point can be accessed using the FRG, and it yields z=1 [4]. The FRG also allows for the calculation of the correlation function at this fixed point. I will discuss the associated scaling function, providing both an analytical asymptotic form and the complete numerical solution, which accurately matches the result from the numerical simulations. References: [1] N. Dupuis et al, Phys. Rep. 910, 1 (2021). [2] L. Canet, H. Chaté, B. Delamotte, N. Wschebor, PRL 104, 150601 (2010). [3] Cartes, Tirapegui, Pandit, Brachet, Phil. Trans. Roy. Soc. A 380, 20120090 (2022). [4] Vercesi, Fontaine, Brachet, Canet, PRL 131, 247101 (2023).
Iacopo Carusotto Title: Quantum fluids of light as a platform for non-equilibrium statistical mechanics Abstract: In this talk I will give a short introduction to the field of quantum fluids of light as a promising platform to investigate non-equilibrium statistical mechanics effects. Milestones experiments will be reviewed and open challenges will be sketched. A brief summary of the different experimental realizations will also be given. Giorgio Parisi Title: Random considerations on the KPZ equation, the "P" of KPZ
Gregory Schehr Title: Large deviations for the KPZ equation in 1+1 dimension Abstract: It is now well known that the typical fluctuations of the KPZ height field in 1+1 dimension (say in the droplet geometry) are described, at short time, by a Gaussian and, at large time, by the Tracy-Widom distribution corresponding to the Gaussian Unitary Ensemble of Random Matrix Theory. In this talk, I will instead discuss the atypical fluctuations for the KPZ equation, which are described by large deviation forms. These questions have attracted a growing interest during the last decade, both in the physics and in the maths literature. If time permits, I will then present the implications of these results for one-dimensional trapped fermions at finite temperature.
Herbert Spohn Title: KPZ equation with two components Abstract: Discussed are older results on models when the flux Jacobian is non-degenerate, which are based on nonlinear fluctuating hydrodynamics. Current research elucidates the intriguing scaling behavior when the flux Jacobian is degenerate.
Marzena Szymanska Title: Driven-dissipative superfluids: a compact Kardar-Parisi-Zhang dynamics of the phase Abstract: Driven-dissipative quantum fluids can differ substantially from their equilibrium counterparts. The long-wavelength phase dynamics of a polariton/photon condensate has been shown to obey Kardar-Parisi-Zhang (KPZ) equation. Since the phase is a compact variable, vortices in 2D and phase slips in 1D can proliferate destroying the KPZ scaling. The interplay between KPZ physics and topological defects is currently subject of great interest, especially in polariton context. In this talk, I will review our work on the topic [1,2,3]. Véronique Terras Title: The open XXZ spin chain Abstract: The open XXZ spin chain is an integrable model. It can be mapped on an open ASEP model. The model can be exactly solved by Algebraic Bethe Ansatz when the boundary fields are longitudinal, i.e. oriented along the direction of anisotropy, and by Separation of Variables for more general boundary fields. We review here the solution of this model by these different integrability techniques. If time permits, the problem of the computation of the correlation functions will also be briefly discussed. David Wei Title: Quantum gas microscopy of spin superdiffusion in Heisenberg chains
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