The goal of this International Roadmap for Devices and Systems (IRDS) chapter is to survey, catalog, and assess the status of technologies in the areas of cryogenic electronics and quantum information processing. Application drivers are identified for sufficiently developed technologies and application needs are mapped as a function of time against projected capabilities to identify challenges requiring research and development effort. Cryogenic electronics (also referred to as low-temperature electronics or cold electronics) is defined by operation at cryogenic temperatures (below −150 °C or 123.15 K) and includes devices and circuits made from a variety of materials including insulators, conductors, semiconductors, superconductors, or topological materials. Existing and emerging applications are driving development of novel cryogenic electronic technologies. Information processing refers to the input, transmission, storage, manipulation or processing, and output of data. Information processing systems to accomplish a specific function, in general, require several different interactive layers of technology. A top-down list of these layers begins with the required application or system function, leading to system architecture, micro- or nano-architecture, circuits, devices, and materials. A fundamental unit of information (e.g., a bit) is represented by a computational state variable, for example, the position of a bead in the ancient abacus calculator or the voltage (or charge) state of a node capacitance in CMOS logic. A binary computational state variable serves as the foundation for von Neumann computational system architectures that dominated conventional computing. Quantum information processing is different in that it uses qubits, two-state quantum-mechanical systems that can be in coherent superpositions of both states at the same time, which can have computational advantages. Measurement of a qubit in a given basis causes it to collapse to one of the basis states. Technology categories covered in this report include: • Superconductor electronics (SCE) • Cryogenic semiconductor electronics (Cryo-Semi) • Quantum information processing (QIP)

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.

An analytical expression is obtained for the anomalous magnetic moment of an electron in a constant magnetic field in topologically massive two-dimensional electrodynamics. In the limiting case of a relatively weak magnetic field, asymptotic formulas are found, which specify the dependence of the anomalous magnetic moment on the Chern-Simons parameter and dynamic parameter of synchrotron radiation. The conditions are identified for the applicability of the computations of the anomalous magnetic moment of an electron, which have previously been made based on the calculation of the vertex function in two-dimensional electrodynamics with the Chern-Simons term.

Equivalent photon approximation is used to calculate fiducial cross sections for dimuon production in ultraperipheral proton—proton and lead—lead collisions. Analytical formulae taking into account experimental cuts are derived. The results are compared with the measurements reported by the ATLAS collaboration.

We present development of large active area superconducting single-photon detectors well coupled with standard 50 µm-core multi-mode fiber. The sensitive area of the SSPD is patterned using the photon-number-resolving design and occupies an area of 40×40 µm2 . Using this approach, we have obtained excellent specifications: system detection efficiency of 47% measured using a 900 nm laser and low dark count rate of 100 cps. The main advantages of the approach presented are a very short dead time of the detector of 22 ns and FWHM jitter value of about 130 ps.

The radiation of human skin in the terahertz frequency range under the influence of mental stresses has been studied in the current work. An experimental setup for observation of changes in human skin radiation, which occur under the influence of psychological stresses, by means of a superconducting integrated receiver has been developed. More than 30 volunteers participate in these studies, which allows us to verify presence of correlation between the signals from the superconducting integrated terahertz receiver and other sensors that monitor human mental stress.

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS  $\nu(E)$ above the gap, a "vertical" peculiarity of the DOS around energy equal to the bulk order parameter $\Delta_0$, and perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and coherence length. The vertical peculiarity implies infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E<\Delta_0$ and $E>\Delta_0$, so the peculiarity is asymmetric.

We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension df visits the same spot n≥3 times, at given moments t1,...,tn, and obtain a determinant expression for these probabilities in terms of a displacement-displacement covariance matrix. Except for the standard Brownian trajectories with df=2, the resulting many-body contact probabilities cannot be factorized into a product of single-loop contributions. Within a Gaussian network model of a self-interacting polymer chain, which we suggested recently [K. Polovnikov et al., Soft Matter 14, 6561 (2018)], the probabilities we calculate here can be interpreted as probabilities of multibody contacts in a fractal polymer conformation with the same fractal dimension df. This Gaussian approach, which implies a mapping from fractional Brownian motion trajectories to polymer conformations, can be used as a semiquantitative model of polymer chains in topologically stabilized conformations, e.g., in melts of unconcatenated rings or in the chromatin fiber, which is the material medium containing genetic information. The model presented here can be used, therefore, as a benchmark for interpretation of the data of many-body contacts in genomes, which we expect to be available soon in, e.g., Hi-C experiments.

The objective of this paper is to establish that algorithms, which reconstruct the coupling between solar proxies based on the properties of the Kuramoto equations, and algorithms, based on the van der Pol equations, might produce similar estimates. To this end, the inverse problem is formulated as follows: reconstruct the coupling based on the solutions of the corresponding equations. For either system of the equations we construct an algorithm solving the inverse problem and establish that there exists a range of moderate values of the correlation such that the algorithms produce practically identical coupling within the established range. The lower boundary of this range is dependent on the half-difference of the oscillators' frequencies. Then, we apply the two reconstruction algorithms to solar index ISSN and the geomagnetic index aa, which are proxies to the toroidal and poloidal magnetic fields of the Sun respectively. Their correlation belongs within the range that yields the proximity of the coupling reconstructed with all solar cycles from 11 till 23 except 20 and, possibly, 21.  Our finding relate the reconstruction of characteristics of solar activity inferred by Blanter et al [Sol. Phys. 2014, 289, 4309; Sol. Phys. 2016, 291, 1003] from the Kuramoto model to the state of the art solar dynamo theory based on the magnetohydrodynamic equations.

Here we experimentally studied dependence of a focusing grating coupler efficiency versus taper length and angle on silicon nitride platform. As a result, we obtained a dependence for the efficiency of a focusing grating coupler on the parameters of the taper length and angle.

We propose a method of measuring low concentrations of fluorescent molecules located in a small volume of a liquid solvent (about 5 μl) based on the Ebbesen effect of the extraordinary transmission (EOT) of light through a state-of-the-art plasmonic crystal formed by a nanohole array perforated in the ultra-high-quality Ag film. In the method, the EOT effect is realized at the fluorescence wavelength of the detected molecules with a low transmission of light at the absorption wavelength. This approach enables the realization of high level sensor sensitivity approaching a sensitivity level of single molecules counting sensors, owing to the suppression of the sensor substrate’s inevitable parasitic luminescence. The proposed method was successfully demonstrated by detection an ultra-low concentration of Cy-5 fluorescent markers in a dimethyl sulfoxide solution corresponding to less than 1000 molecules in the sensor detection volume.

Interactions between vortices in thin superconducting films are investigated in the crossover (intertype) regime between superconductivity types I and II. We consider two main factors responsible for this crossover: a) changes in the material characteristics of the film and b) variations of the film thickness controlling the effect of the stray magnetic fields outside superconducting sample. The analysis is done within the formalism that combines the perturbation expansion of the microscopic equations to one order beyond the Ginzburg-Landau theory with the leading contribution of the stray fields. It is shown that the latter gives rise to qualitatively different spatial profile and temperature dependence of the vortex interaction potential, as compared to bulk vortex interactions. The resulting interaction is long-range repulsive while exhibiting complex competition of attraction and repulsion at small and intermediate separations of vortices. This explains the appearance of vortex chains reported earlier for superconducting films.

We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with N fermionic particles, where N tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit formulas for limits of Dunkl operators and the Yangian generators are presented by means of fermionic fields.

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.

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.