2026, series of seminars on April 7, 14, and 21
Seminar 1 April 7, 15.00, Physics seminar room
Mikhail Kurilov and Pavel Ostrovsky
Density of scattering resonances in a disordered system, arXiv:2512.18717
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width related to the decay time of this eigenstate. We develop a general approach to study the distribution function of these resonance widths based on the nonlinear sigma model. We derive an integral representation of the distribution function that works equally well for systems of any symmetry and for any type of coupling to the measuring device. From this integral representation we find explicit analytic expressions for the distribution function in the case of disordered metallic grains. We also compare the analytic results to large-scale numerical simulations and observe their perfect agreement.
Andrei Levin and Pavel Ostrovsky
Effect of superconductivity on non-uniform magnetization in disordered Superconductor-Ferromagnet junctions, arXiv:2512.08044
We study proximity effect in a tunnel junction between a bulk superconductor and a thin disordered ferromagnetic layer on its surface. Cooper pairs penetrating from the superconductor into the ferromagnet tend to destabilize its uniform magnetic order. Competition of this effect and intrinsic magnetic stiffness of the ferromagnet leads to a second-order phase transition between uniform and non-uniform magnetic states. Using semiclassical Usadel equations, we derive Landau functional for this transition and construct complete phase diagram of the system.
Seminar 2 April 14, 16.00, Physics seminar room
Elizaveta Safonova
Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach, SciPost Phys. 18 (2025) 010 and 20 (2026) 003
Using an extension of Efetov’s supersymmetric formalism, we analytically investigate spectral properties of Lévy and Lévy–Rosenzweig–Porter random matrix ensembles with strongly non-Gaussian, power-law distributed off-diagonal elements. Employing a functional Hubbard–Stratonovich transformation, we compute the mean spectral density ρ(E) in the large-matrix limit and show that it depends sensitively on the control parameter governing the transition between ergodic and fractal (non-ergodic extended) phases, thus serving as an order parameter. We also derive the global density-of-states correlation function R(ω) in the non-ergodic extended phase across all relevant frequency ranges. At low frequencies it exhibits GUE-type oscillations damped at the Thouless scale ETh=ΔΓ/2π, while at high frequencies it matches cavity-approach results.
Vera Mikheeva
Anomalous Hall effect in rhombohedral graphene, arXiv:2510.20804
Motivated by recent experiments on rhombohedral multilayer graphene and the discovery of the anomalous Hall effect in its spontaneous spin-valley polarized state, we theoretically investigate the Hall conductivity of this system. We consider two distinct regimes of disorder: weak dense impurities and sparse strong scatterers. Our analysis accounts for all key physical mechanisms contributing to the Hall effect. We include effects arising from the internal geometry of the energy bands as well as various types of asymmetric scattering processes, including complex interference effects between impurities. To describe the influence of strong impurities, we further incorporate non-Gaussian scattering mechanisms. Finally, we supplement our analytical results for the isotropic model with numerical calculations that account for the specific shape of the energy bands (trigonal warping), which is essential for understanding the low-energy properties of rhombohedral graphene.
Seminar 3 April 21, 15.00, Physics seminar room
Pavel Orlov
Circuits Built from Pairwise Difference Conserving Gates: From Loop
Symmetries to Localization Transitions, arXiv:2509.22368, arXiv:2510.18992
We introduce a class of dynamical models built from local “pairwise difference conserving” (PDC) gates, which can be defined on arbitrary graphs for both classical and quantum spins. These gates generate an extensive set of conserved loop charges associated with closed paths on the graph, leading to strong fragmentation of the state space into many disconnected dynamical sectors. As an example, we study a classical cellular automaton on a square lattice that exhibits a localization–delocalization transition in information spreading controlled by these charges. The transition is continuous and shows critical behavior similar to second-order phase transitions. Our results identify PDC circuits as a simple framework for studying constrained dynamics, emergent conservation laws, and fragmentation phenomena in both classical and quantum systems.
Gregor Humar
Constrained dynamics of false vacuum decay in one- and two-dimensional tilted Ising models, Nature Phys. 21 (2025), 386–392
False vacuum decay, describing the transition from a metastable state to a true vacuum configuration, is a fundamental non-perturbative phenomenon in quantum field theory and non-equilibrium statistical mechanics, yet remains difficult to study experimentally. Using programmable quantum annealers and numerical simulations we investigate false vacuum decay in tilted Ising models in one and two dimensions. In one-dimensional quantum annealer experiments we directly observe the quantized nucleation of true-vacuum bubbles and develop an effective description that captures their formation and interactions [1]. Extending to two dimensions, we identify a regime where true-vacuum bubbles spread resonantly as the energy gain from the true vacuum compensates the cost of domain-wall creation. This mechanism produces fractal-like growth with a ballistically propagating wavefront that remains robust against disorder and dissipation. Further analysis of the wavefront broadening reveals scaling behaviour consistent with KPZ-type dynamics. These results establish a framework for studying false vacuum decay in large quantum systems.