In the talk, I briefly discuss the present-day view of the magnetic field evolution of neutron stars and its main observational appearance. Then, I focus on the possibility of finding magnetars in binary systems of a different kind. Possible candidates include accreting neutron stars (in particular, ultra-luminous X-ray sources), gamma-ray sources, and fast radio bursts. I present a scenario in which the existence of a highly magnetized neutron star in a high-mass X-ray binary is possible at an age ~few million years.

We consider a harmonic chain of oscillators in the presence of a disordered magnetic field. The disorder, in general, causes localization of the normal modes, due to which a system becomes insulating. However, for this system, the localization length diverges as the normal mode frequency approaches zero. Therefore, the low-frequency modes contribute to the heat transmission and the heat current goes down as a power law with the system size. This power law is determined by the small frequency behavior…

We study localization phenomena in an SNS junction with a disordered metallic wire as its normal part. Standard description of the Josephson effect in such systems is based on the Usadel equation. However, the classical approach remains valid only while the junction is shorter than the localization length in the wire. In the opposite limit, quantum effects become important and the Usadel description is no longer valid. We develop a general theory of the Josephson effect taking into account all…

We consider black hole linear perturbation theory in a four-dimensional Schwarzschild (anti-)de Sitter background. We describe two methods that provide the quantization condition for the quasinormal mode frequencies of the perturbation field. The first consists of using the Nekrasov-Shatashvili functions, or, equivalently, the classical Virasoro conformal blocks, to obtain the connection coefficients for the differential equation encoding the spectral problem. The second method is based on a perturbative expansion of the local solutions of the differential equation, that involves multiple…

We study the out-of-time-order correlation function (OTOC) in a lattice extension of the Sachdev-Ye-Kitaev (SYK) model with quadratic perturbations. The results obtained are valid for arbitrary time scales, both shorter and longer than the Ehrenfest time. We demonstrate that the region of well-developed chaos is separated from the weakly chaotic region by the "front region", which moves ballistically across the lattice. The front velocity is calculated for various system's parameters, for the first time for SYK-like models. *Aleksey Lunkin, Landau…

Simulation of the single-particle tunneling problem by means of the Suzuki-Trotter approximation (STA) is analyzed. The target system describes a particle hopping across a chain of sites with position-dependent potential profile. The latter is assumed to be smooth and posses several local minima separated by a potential barrier, arranging a tunneling problem between the localized states in different minima. The STA error is found to manifest itself in three ways: i) perturbative energy shifts, ii) nonperturbartive renormalization of the tunneling…