### Exceptional points in classical spin dynamics

Building on the remarkable recent progress in understanding the parity-time-symmetric dynamics in spin systems, we use the topological properties of exceptional points (EPs) to implement chiral non-reciprocal transmission of a spin through a material with non-uniform magnetization, like helical magnet. We consider an exemplary system, spin-torque-driven single spin described by a time-dependent non-Hermitian Hamiltonian. We show that encircling individual EPs in a parameter space results in non-reciprocal spin dynamics and find the range of optimal protocol parameters for high-efficiency operation of asymmetric spin filter device based on this effect.

### Parity-time symmetry breaking in spin chains

We investigate nonequilibrium phase transitions in classical Heisenberg spin chains associated with spontaneous breaking of PT symmetry under the action of Slonczewski spin-transfer torque (STT). We reveal STT-driven PT symmetry-breaking phase transition between the regimes of precessional and exponentially damped spin dynamics. The physical interpretation of imaginary magnetic field as describing the action of nonconservative forces opens the possibility

of direct observations of Lee-Yang zeros in nonequilibrium physical systems.

### Fluctuation spectroscopy: From Rayleigh-Jeans waves to Abrikosov vortex clusters

We review the physics of superconducting fluctuations, commencing from a qualitative description of thermodynamic fluctuations close to the critical temperature and quantum fluctuations at zero temperature in the vicinity of the second critical field. The analysis of the latter allows us to present fluctuation formation as a fragmentation of the Abrikosov lattice. This review highlights a series of experimental findings followed by microscopic description and numerical analysis of the effects of fluctuations on numerous properties of superconductors in the entire phase diagram and beyond the superconducting phase.

### Scaling universality at the dynamic vortex Mott transition

We report the critical behavior of a system of superconducting vortices as it experiences the dynamic Mott insulator-to-metal transition, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory for the phase transition based on the parity reflection-time reversal (*PT*) symmetry-breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and, hence, the transition of the thermal universality class.

### Linear dynamics of classical spin as Möbius transformation

We have shown that non-conservative dynamics of a linear spin system has a simple interpretation in terms of Möbius transformations of the complex plane. The parity-time symmetry-breaking phase transition is identified as a transition between elliptic and hyperbolic (via parabolic) classes of Möbius transformations.

*Nature Scientific Reports 7, 1168 (2017)*

### Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions

We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.

*Nature Scientific Reports 7, 44044 (2017)*

### Parity-time symmetry breaking in magnetic systems

In this work we show that non-equilibrium dynamics of a single classical spin (monodomain ferromagnet), usually described by the Landau-Lifshitz-Slonczewski equation, can be derived using the generalized non-Hermitian Hamiltonian formalism. This is the first application of this novel approach to magnetic systems. The anti-Hermitian part of the proposed spin Hamiltonian is responsible for non-conservative forces (Gilbert damping and Slonczewski spin-transfer torque). Parity-time (*PT*) symmetry-breaking phase transition was predicted and verified numerically.

### Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems

We describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P) and time-reversal (T ) operations. The dynamic Mott transition is identified as a PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdown and describe the resulting critical behavior of transport characteristics. The obtained critical exponent is in an excellent agreement with experimental findings.

### Effect of fluctuations on the NMR relaxation beyond the Abrikosov vortex state

In this work we investigate the important role of the Maki-Thompson quantum process of electron `self-pairing' on self-intersecting trajectories involving spin-flip processes. This effect increases NMR relaxation rate in two-dimensional superconductors above the critical temperature. Due to the competing effect of suppression of particle density of states, different scenarios of NMR rate dependence on temperature and magnetic field become possible.

### Resonant tunneling of fluctuation Cooper pairs

Here we predict a novel fluctuation phenomenon: resonant tunneling of superconducting fluctuations across a Superconductor-Insulator-Superconductor junction above superconducting critical temperature. This new effect provides the first direct tool of measuring lifetime of fluctuation Cooper pairs and marks a radical departure from the conventional view of superconducting fluctuations as blurring and rounding phenomenon.

*Nature Scientific Reports 5, 8315 (2015)*

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