We point out that superconducting quantum computers are prospective for the simulation of the dynamics of spin models far from equilibrium, including nonadiabatic phenomena and quenches. The important advantage of these machines is that they are programmable, so that different spin models can be simulated in the same chip, as well as various initial states can be encoded into it in a controllable way. This opens an opportunity to use superconducting quantum computers in studies of fundamental problems of statistical physics such as the absence or presence of thermalization in the free evolution of a closed quantum system depending on the choice of the initial state as well as on the integrability of the model. In the present paper, we per-W. V. P. acknowledges a support from RFBR (project no. 15-02-02128). Yu. E. L. acknowledges a support from RFBR (project no. 17-02-01134) and the Program of Basic Research of HSE. arXiv:1807.10149v1 [quant-ph] 25 Jul 2018 2 A. A. Zhukov et al.formed proof-of-principle digital simulations of two spin models, which are the central spin model and the transverse-field Ising model, using 5-and 16-qubit superconducting quantum computers of the IBM Quantum Experience. We found that these devices are able to reproduce some important consequences of the symmetry of the initial state for the system's subsequent dynamics, such as the excitation blockade. However, lengths of algorithms are currently limited due to quantum gate errors. We also discuss some heuristic methods which can be used to extract valuable information from the imperfect experimental data.

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Electric and magnetic fields created by moving uniform lattice of Josephson vortices in the magnetic field parallel to the layers are calculated in the frame of exactly solvable model. At large velocities of the vortex lattice the plasma oscillations of superconducting electrons are excited by vortex motion, this results in interference features in I-V curves at low temperatures. The spectrum of electromagnetic radiation by moving vortices contains peaks related to the excitation of plasmons and to the Cherenkov radiation.

A new non-Fermi liquid state of quasi-one-dimensional conductors is suggested in which electronic system exists in a form of collection of bounded Luttinger liquids stabilized by impurities. This state is shown to be stable towards inter-chain electron hopping at low temperatures. Electronic spectrum of the system contains zero modes and collective excitations of the bounded Luttinger liquids in the segments between impurities. Zero modes give rise to randomly distributed localized electronic levels, and long-range interaction generates the Coulomb gap in the density of states at the Fermi energy. Mechanism of conductivity at low temperatures is phonon-assisted hopping via zero-mode states. At higher voltages the excitations of Luttinger liquid are involved into electron transport, and conductivity obeys power-law dependence on voltage. The results are compared with recent experimental data for NbSe 3 and TaS 3 crystals.