This book brings together reviews by internationally renowed experts on quantum optics and photonics. It describes novel experiments at the limit of single photons, and presents advances in this emerging research area. It also includes reprints and historical descriptions of some of the first pioneering experiments at a single-photon level and nonlinear optics, performed before the inception of lasers and modern light detectors, often with the human eye serving as a single-photon detector. The book comprises 19 chapters, 10 of which describe modern quantum photonics results, including single-photon sources,  direct measurement of the photon's spatial wave function, nonlinear interactions and non-classical light, nanophotonics for room-temperature single-photon sources, time-multiplexed methods for optical quantum information processing, the role of photon statistics in visual perception, light-by-light coherent control using metamaterials, nonlinear nanoplasmonics, nonlinear polarization optics, and ultrafast nonlinear optics in the mid-infrared.

This volume collects the referred papers based on plenary, invited, and oral talks, as well on the posters presented at the Third International Conference on Computer Simulations in Physics and beyond (CSP2018), which took place September 24-27, 2018 in Moscow. The Conference continues the tradition started by an inaugural conference in 2015. It took place on the campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics in Strogino, was jointly organized by the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics and Science Center in Chernogolovka.

The Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample.

We hope that this volume will interest readers, and we are already looking forward to the next conference in the series.

Moscow, Russia

November, 2018

CSP2018 Conference Chair and Volume Editor

Lev Shchur

Computer simulations are nowadays a rmly established third pillar of modern natural sciences, complementing experimentation and paper-and-pencil theoret- ical studies. Simulations, experiments in silico, prove indispensable in diverse areas of research in physics and other natural sciences. This volume collects papers based on presentations delivered at the Sec- ond International Conference on Computer Simulations in Physics and beyond (CSP2017), which took place October 9-12, 2017 in Moscow. The Conference, which continues a biannual tradition started by an innaugural conference in 2015, took place on campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics, was jointly organized by the National Research University Higher School of Economics, the Landau Insitute for Theoretical Physics and Science Center in Chernogolovka. As the name implies, the Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample. We hope that this volume will interest a wide range of readers, and we are already looking forward for the next conference in this biannual series.

This book highlights selected topics of standard and modern theory of accretion onto black holes and magnetized neutron stars. The structure of stationary standard discs and non-stationary viscous processes in accretion discs are discussed to the highest degree of accuracy analytic theory can provide, including relativistic effects in flat and warped discs around black holes. A special chapter is dedicated to a new theory of subsonic settling accretion onto a rotating magnetized neutron star. The book also describes supercritical accretion in quasars and its manifestation in lensing events. Several chapters cover the underlying physics of viscosity in astrophysical discs with some important aspects of turbulent viscosity generation. The book is aimed at specialists as well as graduate students interested in the field of theoretical astrophysics.

The present book gathers chapters from colleagues of A. Ezersky from Russia, especially those from Nizhny Novgorod Institute of Applied Physics of the Russian Academy of Science and from France, with whom he has been collaborating on experimental and theoretical developments. The book is subdivided into two parts. Part I contains eight chapters related to nonlinear water waves and Part II addresses in five chapters, patterns dynamics in nonequilibrium media. The contributions of Alexander B. Ezersky were valuable from both the experimental and the theoretical points of view. We thank all the authors for their contributions and the Springer Editor for having kindly accepted the edition of this book in memory of our colleague and friend, Prof. Alexander Borisovich Ezersky.

The materials of The International Scientific – Practical Conference is presented below.

The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies.

It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

These notes have appeared as a result of a one-term course in superfluidity and superconductivity given by the author to fourth-year undergraduate students and first-year graduate students of the Department of Physics, Moscow State University of Education. The goal was not to give a detailed picture of these two macroscopic quantum phenomena with an extensive coverage of the experimental background and all the modern developments, but rather to show how the knowledge of undergraduate quantum mechanics and statistical physics could be used to discuss the basic concepts and simple problems, and draw parallels between superconductivity and superfluidity.

Superconductivity and superfluidity are two phenomena where quantum mechanics, typically constrained to the microscopic realm, shows itself on the macroscopic level. Conceptually and mathematically, these phenomena are related very closely, and some results obtained for one can, with a few modifications, be immediately carried over to the other. However, the student of these notes should be aware of important differences between superconductivity and superfluidity that stem mainly from two facts: (1) electrons in a superconductor carry a charge, therefore one has to take into account interaction with electromagnetic radiation; (2) electrons move in a lattice, therefore phonons play a role not only a mediators of attractive interaction between pairs of electrons, but also as scatterers of charge carriers.

Although these are notes on superfluidity and superconductivity, and there are a few cross-references, the two subjects can be studied independently with, perhaps, a little extra work by the student to fill in the gaps resulting from such study. The material of Chapter 1 introduces the method of second quantisation that is commonly used to discuss systems with many interacting particles. It is then applied in Chaper 2 to treat the uniform weakly interacting Bose gas within the approach by N. Bogoliubov, and in Chapter 4 to formulate the theory of the uniform superconducting state put forth by J. Bardeen, L. Cooper and R. Schrieffer. Chapter 3 presents the theory proposed independently by E. Gross and L. Pitaevskii of a non-uniform weakly interacting Bose gas, with a discussion of vortices, rotation of the condensate, and the Bogoliubov equations. In Chapter 5 we discuss the Ginzburd-Landau theory of a non-uniform superconductor near the critical temperature and apply it to a few simple problems such as the surface energy of the boundary between a normal metal and a superconductor, critical current and critical magnetic field, and vortices.

In this paper we present the studies of an ultrametric mathematical model for protein operation and give them physical interpretations that extend the conventional view of ensymatic activity regulation. The model is based on a representation of a multidimentional rugged energy landscapes by a hierarchy of nested basins of local minima and an approximation of protein dynamics with an ultrametric random walk. In contrast to an ordinary random walk, the ultrametric random walk is more suitable for describing of multiscale conformational dynamics and it is consistent with the kinetic features of ligand binding. Using our ultrametric model we show different ways to regulate enzymatic activity.

Superconducting properties of metallic nanowires can be entirely different from those of bulk superconductors because of the dominating role played by thermal and quantum fluctuations of the order parameter. For superconducting channels with diameters below ∼ 50 nm fluctuations of the phase of the complex order parameter - the phase slippage  -  lead to non-zero resistance below the critical temperature.  Fluctuations of the modulus of the complex order parameter broaden the gap edge of the quasiparticle energy spectrum and modify the density of states. In extreme case of very narrow channels imbedded in high-impedance environment  (which fix the charge and, hence, enable strong fluctuations of the quantum-conjugated variable, the phase) the superconductor can be driven to insulating state  – the Coulomb blockade. We review recent experimental activities in the field demonstrating rather unusual phenomena.

The materials of The International Scientific – Practical Conference is presented below. The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies.

It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

The textbook is meant for students continuing to study English (levels B1-B2 according to the European Framework) and majoring in science. The exercises and tasks are aimed at developing speaking, writing and reading skills on the basis of authentic texts on the achievements of scientists rewarded the Nobel Prize in the years 2000-2014

Adequate assessment of individual functional motor potentials is important for developing appropriate rehabilitation strategies in ischemic stroke [1]. Microstructural changes in corticospinal tract (CST) and corpus callosum (CC) were repeatedly correlated to post-stroke outcome [2, 3]. However, relationship between them and functional recovery remains unclear. Here we investigated relationship between integrity of CST and CC assessed with diffusion tensor imaging (DTI) and brain functional state assessed with navigated transcranial magnetic stimulation (nTMS) in chronic ischemic supratentorial stroke.

In this volume we have collected papers based on the presentations given at the International Conference on Computer Simulations in Physics and beyond (CSP2015), held in Moscow, September 6-10, 2015. We hope that this volume will be helpful and scientifically interesting for readers.

The Conference was organized for the first time with the common efforts of the Moscow Institute for Electronics and Mathematics (MIEM) of the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics, and the Science Center in Chernogolovka. The name of the Conference emphasizes the multidisciplinary nature of computational physics. Its methods are applied to the broad range of current research in science and society. The choice of venue was motivated by the multidisciplinary character of the MIEM. It is a former independent university, which has recently become the part of the National Research University Higher School of Economics.

The development of terahertz imaging instruments for security systems is on the cutting edge of terahertz technology. We are developing a THz imaging system based on a superconducting integrated receiver (SIR). An SIR is a new type of heterodyne receiver based on an SIS mixer integrated with a flux-flow oscillator (FFO) and a harmonic mixer which is used for phase-locking the FFO. Employing an SIR in an imaging system means building an entirely new instrument with many advantages compared to traditional systems. In this project we propose a prototype THz imaging system using an 1 pixel SIR and 2D scanner. At a local oscillator frequency of 500 GHz the best noise equivalent temperature difference (NETD) of the SIR is 10 mK at an integration time of 1 s and a detection bandwidth of 4 GHz. The scanner consists of two rotating flat mirrors placed in front of the antenna consisting of a spherical primary reflector and an aspherical secondary reflector. The diameter of the primary reflector is 0.3 m. The operating frequency of the imaging system is 600 GHz, the frame rate is 0.1 FPS, the scanning area is 0.5 × 0.5 m2, the image resolution is 50 × 50 pixels, the distance from an object to the scanner was 3 m. We have obtained THz images with a spatial resolution of 8 mm and a NETD of less than 2 K.

IVEC was originally created in 2000 by merging the U.S. Power Tubes Conferences and the European Space Agency TWTA Workshops. Now a fully international conference, IVEC is held every other year in the U.S., and in Europe and Asia alternately every fourth year. After the successful and enjoyable meeting in Paris, France in May, IVEC 2014 will return to its beautiful U.S. location in the city of Monterey.

These proceedings have been written in an attempt to communicate the major purpose of the NATO Advanced ResearchWorkshop (ARW), 2013, that is, to bring to light the possibilities of performance, based on the actual level, of the everpromising THz (terahertz) technology, a kind of Araba Fenice, not yet known tomost technical operators, especially its appeal in security applications. To achieve this, the ARWhas invited highly experienced scientists with expertise in THz science and technology and its application areas. We begin with the consideration that the risk of mass murder due to terroristic attacks is on the rise, thus posing a threat for security in the civil and military world. To counter this problem, we look at one of the most appealing, newly emerging, technologies that is based on the THz detection of explosives and other forms of threats. However, operational difficulties (both for THz sensors and sources), especially regarding size, complexity of use, overall cost, and the need of very low temperatures for sensors, strongly limit the application of this technology. To find solutions to these and related issues, we invited expert scientists to present review papers on the most advanced sensors and sources based on THz technology, especially for security system applications. The ARW has been conferred the major task of describing the most advanced technologies, in terms of identifying their operational strengths and weaknesses, forecasting the best technological solutions to overcome the actual operational limits, and suggesting to the NATO SPS (Science for Peace and Security) Division the most reliable ways to proceed for future developments. To achieve a broad evaluation of the above aspects, a questionnaire on various key points with regard to the actual performance and possible future developments in the field of THz science, technology, and applications has been discussed.

Direct numerical simulations of irregular unidirectional nonlinear wave evolution are performed within the framework of the Korteweg–de Vries equation for bimodal wave spectra model cases. The additional wave system co-existence effect on the evolution of the wave statistical characteristics and spectral shapes, and also on the attained equilibrium state is studied. The concerned problem describes, for example, the interaction between wind waves and swell in shallow seas. It is next demonstrated that a low-frequency spectral component yields more asymmetric waves with more extreme statistical properties.

Landau level splitting in a two-dimensional electron gas (2DEG) confined in an ultrapure GaN/AlGaN heterostructure grown by molecular beam epitaxy on bulk GaN is verified spectroscopically. The Landau level fan reconstructed from magneto-photoluminescence (PL) data yields an effective mass of 0.24m0 for the 2D electrons. Narrow excitonic PL line widths < 100 μeV, an atomically flat surface of the layer stack, as well as the absence of the 2DEG in the dark environment, are important ancillary experimental findings while focusing on magneto-PL investigations of the heterostructure. Simultaneously recorded Shubnikov-de Haas and magneto-PL intensity oscillations under steady UV illumination exhibit an identical frequency and allow for two independent ways of determining the 2D density.

The terahertz photoconductivity of 100 μm and 20 μm Hall bars fabricated from narrow AlAs quantum wells (QWs) of different widths is investigated in this paper. The photoresponse is dominated by collective magnetoplasmon excitations within the body of the Hall structure. We observed a radical change of the magnetoplasma spectrum measured precisely for AlAs QWs of widths ranging from 4 nm to 15 nm. We have shown that the observed behavior is a vivid manifestation of valley transition taking place in the two-dimensional electron system. Remarkably, we show that the photoresponse for AlAs QWs with a width of 6 nm features two resonances, indicating simultaneous occupa- tion of strongly anisotropic X x
y valleys and isotropic X z valley in the QW plane. Our results pave the way for realizing valley-selective layered heterostructures, with potential applications in valleytronics.

We discuss magnetization curves of a toy-model trigonal and tetrahedral clusters. Nonlinearity of magnetization with local minimum of differential susceptibility resembling known magnetization plateaus of triangular-lattice and pyrochlore lattice antiferromagnets is observed at intermediate temperature range J ≲ T ≲ Θ (here, J is the exchange coupling constant and Θ is a Curie–Weiss temperature). This behavior is due to increased statistical weight of the states with intermediate total spin of the cluster, which is related to the “order-by-disorder” mechanism of plateau stabilization of a macroscopic frustrated magnet.

Experimental results on the properties of a recently discovered new collective state, the magnetofermionic condensate, are summarized herein. Condensation occurs in a fermionic system, a quantum Hall insulator (filling factor ν = 2), as a result of the formation of a dense ensemble of long-lived spin cyclotron magnetoexcitons, composite bosons. At temperatures below 1 K, the exciton ensemble exhibits a sharp enhancement in its response to an external electromagnetic field due to the formation of a super-absorbing state that interacts coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level rearrange to form a new non-equilibrium radiative recombination channel. The condensate shows a sharp decrease in viscosity and the ability to spread over macroscopically large distances, on the order of a millimeter, at a speed of ≈103 cm s−1. Due to this rapid long-distance spin transfer, new opportunities in the field of spintronics have been opened up.

We describe the correspondence of the Matsuo-Cherednik type between the quantum nn -body Ruijsenaars-Schneider model and the quantum Knizhnik-Zamolodchikov equations related to supergroup GL(N|M)GL(N|M) . The spectrum of the Ruijsenaars-Schneider Hamiltonians is shown to be independent of the {\mathbb Z}_2 -grading for a fixed value of N+M , so that N+M+1 different qKZ systems of equations lead to the same n -body quantum problem. The obtained results can be viewed as a quantization of the previously described quantum-classical correspondence between the classical n -body Ruijsenaars-Schneider model and the supersymmetric GL(N|M) quantum spin chains on n sites.

We have measured the ultrafast anisotropic optical response of highly doped graphene to an intense single cycle terahertz pulse. The time profile of the terahertz-induced anisotropy signal at 800 nm has minima and maxima repeating those of the pump terahertz electric field modulus. It grows with increasing carrier density and demonstrates a specific nonlinear dependence on the electric field strength. To describe the signal, we have developed a theoretical model that is based on the energy and momentum balance equations and takes into account optical phonons of graphene and the substrate. According to the theory, the anisotropic response is caused by the displacement of the electronic momentum distribution from zero momentum induced by the pump electric field in combination with polarization dependence of the matrix elements of interband optical transitions.

The phonon and electronic properties, the Eliashberg function and the temperature dependence of resistance of electride Ca2N are investigated by the DFT-LDA (density functional theory in local density approximation) plane-wave method. The phonon dispersion, the partial phonon density of states and the atomic eigenvectors of zero-center phonons are studied. The electronic band dispersion and partial density of states conclude that Ca2N is a metal and the Ca 3p, 4s and N 2p orbitals are hybridized. For the analysis of an electron-phonon interaction and its contribution of the Eliashberg function to resistance was calculated and a temperature dependence of resistance due to electron-phonon interaction was found.

The possibility to observe a macroscopically coherent state in a gas of two-dimensional direct excitons at temperatures up to tens of Kelvin is described. The dramatic increase of the exciton lifetime allowing effective thermalization is predicted for the o -resonant cavities that strongly suppress exciton recombination. The material systems considered are single GaAs quantum wells of di erent thicknesses and a transition metal dichalcogenide monolayer, embedded in a layered medium with subwavelength period. The quantum hydrodynamic approach combined with the Bogoliubov description yield the one-body density matrix of the system. Employing the Kosterlitz-Thouless \dielectric screening" problem to account for vortices, we obtain the superfluid and the condensate densities and the critical temperature of the Berezinskii-Kosterlitz-Thouless crossover, for all geometries in consideration. Experimentally observable manyfold increase of the photoluminescence intensity from the structure as it is cooled below the critical temperature is predicted.

For an even qudit dimension d≥2, we introduce a class of two-qudit states exhibiting perfect correlations/anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2 -- the upper bound attained on some two-qubit states. We show that the two-qudit Greenberger--Horne-- Zeilinger (GHZ) state with an arbitrary even d≥2 exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results are important steps towards proving in general the 3/2 upper bound on quantum violation of the original Bell inequality. The latter would imply that similarly as the Tsirelson upper bound 2√2 specifies the quantum analog of the CHSH inequality for all bipartite quantum states, the upper bound (3/2) specifies the quantum analog of the original Bell inequality for all bipartite quantum states with perfect correlations/ anticorrelations. Possible consequences for the experimental tests on violation of the original Bell inequality are briefly discussed.

We have investigated the critical temperature behavior in periodic superconductor/ ferromagnet (S/F) multilayers as a function of the ferromagnetic layer thickness $d_f$ and the interface transparency. The critical temperature $T_c(d_f)$ exhibits a damped oscillatory behavior in these systems due to an exchange field in the ferromagnetic material. In this work we have performed $T_c$ calculations using the self-consistent \textit{multimode approach}, which is considered to be exact solving method. Using this approach we have derived the conditions of 0 or $\pi$ state realization in periodic S/F multilayers. Moreover, we have presented the comparison between the single-mode and multimode approaches and established the limits of applicability of the single-mode approximation, frequently used by experimentalists.

We formulate and prove the main properties of the generalized Gell-Mann representation for traceless qudit observables and analyze via this representation violation of the CHSH inequality by a general two-qudit state. For the maximal CHSH violation by a two-qudit state with an arbitrary qudit dimension d≥2, this allows us to derive two new bounds, lower and upper, which are expressed via the spectral properties of the correlation matrix for a two-qudit state. We have not yet been able to specify a class of two-qudit states for which the new upper bound improves the general upper bound of Tsirelson. However, this is the case for each two-qubit state, where the new lower bound and the new upper bound coincide and reduce to the precise two-qubit CHSH result of Horodecki, and also, for the Greenberger--Horne--Zeilinger (GHZ) state with an arbitrary odd qudit dimension d≥2, where the new upper bound is less than the upper bound of Tsirelson. Moreover, we explicitly find the correlation matrix for the GHZ state and prove that, for this state, the new upper bound is attained for each d≥2 and this specifies the following new result: the maximal violation of the CHSH inequality by the two-qudit GHZ state is equal to √2  if a qudit dimension d≥2 is even and to ((d-1)/d)√2  if a qudit dimension d≥2 is odd.

Thin superconducting films are usually regarded as type-II superconductors even when they are made of a type-I materials. The reason is a strong influence of the stray magnetic fields outside the superconductive sample. While very thin films indeed reach this limit, there is a sufficiently large interval of film thicknesses in which the magnetic properties cannot be classified as either of the two conventional superconductivity types. We demonstrate that in this interval superconducting condensate and magnetic field reveal exotic spatial profiles that are very sensitive to system parameters, in particular, the temperature and applied field. Magnetic properties of such systems can be attributed to a special regime of intertype superconductivity. Its physical origin lies in the removal of infinite degeneracy of the superconducting state at the critical Bogomolnyi point. Here we demonstrate that qualitative characteristics of obtained condensate-field structures and the way they change with the temperature and applied field are independent of the choice of the in-plane boundary conditions for the order parameter and magnetic field.

We study a model of a spatial evolutionary game, based on the Prisoner's dilemma for two regular arrangements of players, on a square lattice and on a triangular lattice. We analyze steady state distributions of players which evolve from irregular, random initial configurations. We find significant differences between the square and triangular lattice, and we characterize the geometric structures which emerge on the triangular lattice.

We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found that a finite step of the random walk produces a bias in the hitting probability and this bias vanishes in the limit of an infinitesimal step. Therefore, it is important to know how a change in the step size of the random walk influences the performance of simulations. We propose an algorithm with the most effective procedure for the step-length-change protocol.

We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-π junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, non-vanishing supercurrent and half-integer Shapiro steps at the 0-π transition selfconsistently point to an intrinsic second harmonic term, making it possible to rule out common alternative origins of half-periodic behavior. While surprising for diffusive multimode junctions, the large second harmonic is in agreement with theory predictions for thin ferromagnetic interlayers.

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of 0 to p transition. These CPR consist of two independent branches corresponding to 0− and p− states of the contact. We have found that depending on the transparency of the SIs tunnel barrier the decrease of the s-layer thickness leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only in discrete intervals of the phase difference j or both branches are sinusoidal but differ in the magnitude of their critical currents. We demonstrate that the difference can be as large as 10% under maintaining superconductivity in the s layer. An applicability of these phenomena for memory and logic application is discussed.

We review recent advances in the analysis of the Wang--Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang-Landau probability. Properties of the TMES can explain some features of the Wang-Landau algorithm, for example, the flatness of the histogram. We show that the Wang--Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of the Wang-Landau algorithm consists of two simulation stages: the original Wang-Landau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.

We propose a superconducting spin-triplet valve of a new type. This spin valve consists of a bilayer that involves a superconductor and an itinerant magnetic material, with the magnet showing an intrinsic non-collinear magnetic order characterized by a wave vector Q that may be aligned in a few equivalent preferred directions under control of a weak external magnetic field. Re-orienting the direction of Q allows one to controllably modify long-range spin-triplet superconducting correlations in the magnetic material, leading to spin-valve switching behavior. This new type of superconducting spin valve may be used as a magnetic memory element for cryogenic nanoelectronics. It has the following advantages in comparison with superconducting spin valves proposed earlier: (i) it contains only one magnetic layer, which may be more easily fabricated and controlled; (ii) its ground states are separated by a potential barrier, which solves the “half-select” problem of the addressed switch of such memory elements.

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients insure the possibility of the odd-frequency pairing: 1) the topological surface states, 2) the induced pair potential, and 3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac cone in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

In recent paper of Falkovich and Levitov it was shown, that geometry of separatrixes for viscous electronic flow in graphene is sensitive to boundary conditions. Here we discover theis relation in details. Also we propose, how boundary conditions could be probed experimentally, using weak magnetic field and observed features of separatrixes.

We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties -- ferromagnetic, half-metallic or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realises a $\varphi_0$ junction with sample-dependent $\varphi_0$ and critical current. Cooper pair splitting between the two arms plays a major role and leads to $2\Phi_0$ periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the three types of magnetic links.

The topic of superconductivity in strongly disordered materials has attracted a significant attention. In particular vivid debates are related to the subject of intrinsic spatial inhomogeneity responsible for non-BCS relation between the superconducting gap and the pairing potential. Here we report experimental study of electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. We find that conventional models based on phase slip concept provide reasonable fits for the shape of the R(T) transition curve. Temperature dependence of the critical current follows the text-book Ginzburg-Landau prediction for quasi-one-dimensional superconducting channel Ic~(1-T/Tc)3/2. Hence, one may conclude that the intrinsic electronic inhomogeneity either does not exist in our structures, or, if exist, does not affect their resistive state properties.

Dynamics of solitons is considered in an extended nonlinear Schrödinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, third-order dispersion (TOD) and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account TOD. The equilibrium state is stable for positive parameter of TOD and unstable for negative one. The analytical solutions are verified by comparison with numerical results

The neutrino dispersion in the magnetized medium was analyzed as a function of the neutrino spin and mass. It was shown that in a super-strong magnetic field plasma contribution to the neutrino energy greatly exceeds the analogous correction in the field-free case.

We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. Analyzing in detail the spectral density of ensembles of linear subgraphs, we discuss its ultrametric nature and show that near the spectrum boundary, the tails of the spectral density exhibit a Lifshitz singularity typical for Anderson localization. We pay attention to an intriguing connection of the spectral density to the Dedekind $\eta$-function. We conjecture that ultrametricity emerges in rare-event statistics and is inherit to generic complex sparse systems.

In order to determine the concept of space interpretation in several multiverse hypotheses, this article analyzes a number of them, which arises from some theories of modern physics. The interpretation of space in the history of philosophy and science and their interrelation with modern physical notions are presented. The research is based on the cognitive interpretation method of the contents of formalistic mathematics and physics theories, the method of comparative analysis (analysis of philosophical texts), the hermeneutical method, and the phenomenological method (analysis of representations). The author shows how the context of modern physics multiverse hypotheses contributes to new connotations in the perception of space. The research draws some conclusions about the present status of the philosophical perception of space.