The Kardar-Parisi-Zhang (KPZ) equation describes an important universality class of nonequilibrium stochastic growth. There has been a surge of recent interest in the one-point probability distribution P(H,t) of height H of the evolving interface at time t in one dimension. I will show how one can use the optimal fluctuation method (OFM) to evaluate P(H,t) for different initial conditions and in different dimensions.

In one dimension the central part of the short-time height distribution is Gaussian, but the tails are non-Gaussian and strongly asymmetric. One interesting initial condition is an ensemble of Brownian interfaces, where we found a singularity of the large deviation function of the height at a critical value of |H|. This singularity results from a breakdown of mirror symmetry of the optimal path of the system, and it has the character of a second-order phase transition. At d>2 the OFM is valid, in the weak-coupling regime, at all times. Here the long-time height distribution P(H) is time-independent, and we use the OFM to determine the Gaussian body and strongly asymmetric non-Gaussian tails of P(H).

Transport in systems with many particles experiencing frequent mutual collisions (such as gases or liquids) has been studied for more than two centuries and is accurately described by the theory of hydrodynamics. It has been argued theoretically for a long time that the collective behavior of charge carriers in solids can also be treated by the hydrodynamic approach. However, despite many attempts, very little evidence of hydrodynamic electron transport has been found so far. Graphene encapsulated between hexagonal boron nitride (hBN) offers an ideal platform to study electron hydrodynamics as it hosts an ultra-clean electronic system with the electron-electron mean free path being the shortest lengths scale in the problem. In the first part of my talk we will discuss why electron hydrodynamics has not been observed before and how it manifests itself in electron transport. Furthermore, it will be shown that electrons in graphene can behave as a very viscous fluid (more viscous than honey) forming vortices of applied electron current [1]. In the second part, we will discuss the measurements of the viscosity of an electron fluid by its superballistic flow through graphene point contacts [2]. Then we will talk about the behavior of electron fluids in the presence of magnetic field where I will report the experimental measurements of the Hall viscosity in two dimensions [3]. This dissipationless transport coefficient has been widely discussed in theoretical literature on fluid mechanics, plasma physics and condensed matter physics, yet, until now, any experimental evidence has been lacking, making the phenomenon truly a unicorn. Last but not least, we will discuss how electron hydrodynamics can be used for the development of resonant terahertz photodetectors.

References: [1] D.A. Bandurin, A. Principi, G.H. Auton, E. Khestanova, K.S. Novoselov, I.V Grigorieva, L.A. Ponomarenko, A.K. Geim, and M. Polini, Science 351, 1055 (2016). [2] R.K. Kumar, D.A. Bandurin, F.M.D. Pellegrino, Y. Cao, A. Principi, H. Guo, G.H. Auton, M. Ben Shalom, L.A. Ponomarenko, G. Falkovich, I.V. Grigorieva, L.S. Levitov, M. Polini, and A.K. Geim, Nat. Phys. 13, 1182 (2017). [3] A.I. Berdyugin, S.G. Xu, F.M.D. Pellegrino, R. Krishna Kumar, A. Principi, I. Torre, M. Ben Shalom, T. Taniguchi, K. Watanabe, I.V. Grigorieva, M. Polini, A.K. Geim, and D.A. Bandurin, to appear on arxiv soon.

(семинар проводится совместно с лабораторией ФКС ВШЭ)