Landau Institute for Theoretical Physics

With the high-temperature superconductors a qualitatively new regime in the phenomenology of type-II superconductivity can be accessed. The key elements governing the statistical mechanics and the dynamics of the vortex system are (dynamic) thermal and quantum fluctuations and (static) quenched disorder. The importance of these three sources of disorder can be quantified by the Ginzburg number $Gi=\frac{{(\frac{{T}_{c}}{{H}_{c}^{2}}\ensuremath{\varepsilon}{\ensuremath{\xi}}^{3})}^{2}}{2}$, the quantum resistance $Qu=(\frac{{e}^{2}}{\ensuremath{\hbar}})(\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\varepsilon}\ensuremath{\xi}})$, and the critical current-density ratio $\frac{{j}_{c}}{{j}_{o}}$, with ${j}_{c}$ and ${j}_{o}$ denoting the depinning and depairing current densities, respectively (${\ensuremath{\rho}}_{n}$ is the normal-state resistivity and ${\ensuremath{\varepsilon}}^{2}=\frac{m}{M}<1$ denotes the anisotropy parameter). The material parameters of the oxides conspire to produce a large Ginzburg number $\mathrm{Gi}\ensuremath{\sim}{10}^{\ensuremath{-}2}$ and a large quantum resistance $\mathrm{Qu}\ensuremath{\sim}{10}^{\ensuremath{-}1}$, values which are by orders of magnitude larger than in conventional superconductors, leading to interesting effects such as the melting of the vortex lattice, the creation of new vortex-liquid phases, and the appearance of macroscopic quantum phenomena. Introducing quenched disorder into the system turns the Abrikosov lattice into a vortex glass, whereas the vortex liquid remains a liquid. The terms "glass" and "liquid" are defined in a dynamic sense, with a sublinear response $\ensuremath{\rho}={\frac{\ensuremath{\partial}E}{\ensuremath{\partial}j}|}_{j\ensuremath{\rightarrow}0}$ characterizing the truly superconducting vortex glass and a finite resistivity $\ensuremath{\rho}(j\ensuremath{\rightarrow}0)>0$ being the signature of the liquid phase. The smallness of $\frac{{j}_{c}}{{j}_{o}}$ allows one to discuss the influence of quenched disorder in terms of the weak collective pinning theory. Supplementing the traditional theory of weak collective pinning to take into account thermal and quantum fluctuations, as well as the new scaling concepts for elastic media subject to a random potential, this modern version of the weak collective pinning theory consistently accounts for a large number of novel phenomena, such as the broad resistive transition, thermally assisted flux flow, giant and quantum creep, and the glassiness of the solid state. The strong layering of the oxides introduces additional new features into the thermodynamic phase diagram, such as a layer decoupling transition, and modifies the mechanism of pinning and creep in various ways. The presence of strong (correlated) disorder in the form of twin boundaries or columnar defects not only is technologically relevant but also provides the framework for the physical realization of novel thermodynamic phases such as the Bose glass. On a macroscopic scale the vortex system exhibits self-organized criticality, with both the spatial and the temporal scale accessible to experimental investigations.

Oscillatory effects in a strong magnetic field B and magnetic susceptibility are investigated, as applied to 2D systems, in which the twofold spin degeneracy is lifted by the spin-orbit-interaction Hamiltonian HSO= alpha ( sigma *k). nu . The term HSO is shown to change greatly the usual patterns of B-1-periodic oscillations; some oscillations are strongly suppressed due to the diminishing of the gaps between adjacent levels, and new oscillations appear due to intersections of levels.

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

Abstract There are fundamental relations between three vast areas of physics: particle physics, cosmology, and condensed matter physics. The fundamental links between the first two areas — in other words, between micro- and macro-worlds — have been well established. There is a unified system of laws governing the scales from subatomic particles to the cosmos and this principle is widely exploited in the description of the physics of the early universe. This book aims to establish and define the connection of these two fields with condensed matter physics. According to the modern view, elementary particles (electrons, neutrinos, quarks, etc.) are excitations of a more fundamental medium called the quantum vacuum. This is the new ‘aether’ of the 21st century. Electromagnetism, gravity, and the fields transferring weak and strong interactions all represent different types of the collective motion of the quantum vacuum. Among the existing condensed matter systems, a quantum liquid called superfluid 3He-A most closely represents the quantum vacuum. Its quasiparticles are very similar to the elementary particles, while the collective modes are analogues of photons and gravitons. The fundamental laws of physics, such as the laws of relativity (Lorentz invariance) and gauge invariance, arise when the temperature of the quantum liquid decreases.

Quantum-state engineering, i.e., active control over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. With concepts developed in atomic and molecular physics and in the context of NMR, the field has been stimulated further by the perspectives of quantum computation and communication. Low-capacitance Josephson tunneling junctions offer a promising way to realize quantum bits (qubits) for quantum information processing. The article reviews the properties of these devices and the practical and fundamental obstacles to their use. Two kinds of device have been proposed, based on either charge or phase (flux) degrees of freedom. Single- and two-qubit quantum manipulations can be controlled by gate voltages in one case and by magnetic fields in the other case. Both kinds of device can be fabricated with present technology. In flux qubit devices, an important milestone, the observation of superpositions of different flux states in the system eigenstates, has been achieved. The Josephson charge qubit has even demonstrated coherent superpositions of states readable in the time domain. There are two major problems that must be solved before these devices can be used for quantum information processing. One must have a long phase coherence time, which requires that external sources of dephasing be minimized. The review discusses relevant parameters and provides estimates of the decoherence time. Another problem is in the readout of the final state of the system. This issue is illustrated with a possible realization by a single-electron transistor capacitively coupled to the Josephson device, but general properties of measuring devices are also discussed. Finally, the review describes how the basic physical manipulations on an ideal device can be combined to perform useful operations.

The theory of reheating of the Universe after inflation is developed. We have found that typically at the first stage of reheating the classical inflation field $\ensuremath{\varphi}$ rapidly decays into $\ensuremath{\varphi}$ particles or into other bosons due to a broad parametric resonance. Then these bosons decay into other particles, which eventually become thermalized. Complete reheating is possible only in those theories where a single particle $\ensuremath{\varphi}$ can decay into other particles. This imposes strong constraints on the structure of inflationary models, and implies that the inflation field can be a dark matter candidate.

This review considers unusual effects in superconductor-ferromagnet structures, in particular, the triplet component of the condensate generated in those systems. This component is odd in frequency and even in momentum, which makes it insensitive to nonmagnetic impurities. If the exchange field is not homogeneous in the system, the triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. Some other effects considered here and caused by the proximity effect are enhancement of the Josephson current due to the presence of the ferromagnet, induction of a magnetic moment in superconductors resulting in a screening of the magnetic moment, and formation of periodic magnetic structures due to the influence of the superconductor. Finally, theoretical predictions are compared with existing experiments.

We introduce a new cosmological diagnostic pair {r, s} called the Statefinder. The Statefinder is a geometrical diagnostic and allows us to characterize the properties of dark energy in a model-independent manner. The Statefinder is dimensionless and is constructed from the scale factor of the Universe and its time derivatives only. The parameter r forms the next step in the hierarchy of geometrical cosmological parameters after the Hubble parameter H and the deceleration parameter q, while a is a linear combination of q and r chosen in such a way that it does not depend upon the dark energy density. The Statefinder pair {r, s} is algebraically related to the equation of state of dark energy and its first time derivative. The Statefinder pair is calculated for a number of existing models of dark energy having both constant and variable w. For the case of a cosmological constant, the Statefinder acquires a particularly simple form. We demonstrate that the Statefinder diagnostic can effectively differentiate between different forms of dark energy. We also show that the mean Statefinder pair can be determined to very high accuracy from a SNAP-type experiment.

We resolve renormalization problems, indicated in Ref. 1 and find explicit formulae for the spectrum of anomalous dimensions in 2d—quantum gravity. Comparison with combinatorial approximation of random surfaces and its numerical analyses shows complete agreement with all known facts.

(1970). Oscillatory approach to a singular point in the relativistic cosmology. Advances in Physics: Vol. 19, No. 80, pp. 525-573.

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe.

Abstract Theoretical studies of the motion of an electron in a disordered system have led to a number of remarkable results especially those concerned with localization and with the importance of dimensionality. The theoretical approaches previously used run into some severe technical difficulties. This article sets out the bases of the recently introduced supersymmetry method which has already, as the article shows, provided unified derivations of the major results in this subject, free of the technical problems. The method reduces the systems it treats to field-theoretical models involving both bosons and fermions.

Reflectance and transmittance of graphene in the optical region are analyzed as a function of frequency, temperature, and carrier density. We show that the optical graphene properties are determined by the direct interband electron transitions. The real part of the dynamic conductivity in doped graphene at low temperatures takes the universal constant value, whereas the imaginary part is logarithmically divergent at the threshold of interband transitions.

Two models of disorder in two dimensions are discussed. The first is a localization theory that treats noninteracting particles by perturbation theory in the weak scattering limit. A weak magnetic field is found to have strong effects on the previously predicted logarithmic rise in resistivity at low temperatures. No logarithmic divergence is found for the Hall constant. A second model treats the disorder scattering by conventional diagramatic technique but includes the effects of interactions. In a short communication it has previously been reported that the resistivity and Hall constant both show a logarithmic increase at low temperatures. The details of the calculation are reported here, together with an extension to thin wires which shows a ${T}^{\ensuremath{-}\frac{1}{2}}$ divergence in the resistivity.

Abstract Recently it has been shown that many traditional models used for a description of dilute magnetic alloys are completely integrable and may be solved exactly without any approximation. In this article we summarize the results which have been obtained in this way. The main part of the article is devoted to the consistent and detailed account of the Bethe-Ansatz technique for the s-d exchange (Kondo) model with arbitrary impurity spin, s-d model with anisotropic exchange, degenerate exchange model and for the canonical Anderson model. The thermodynamic properties of a magnetic impurity in a non-magnetic metal host obtained by the Bethe method are considered in detail. Mainly attention is paid to the analysis of singularities associated with the formation of a localized moment, Kondo effect and mixedvalence phenomenon, which can be treated analytically. In the introductory part of the article we discuss the applicability of the models which we study in the paper to the real alloys and consider some modern experimental data which give the evidence of the many-body effects in dilute magnetic alloys. A brief review of some theoretical results which have been obtained using alternative approaches is given. We think that these results illustrate some features of the exact solution. This review was completed in June 1982.

The nature of flux-creep phenomena in the case of collective pinning by weak disorder is discussed. The Anderson concept of flux bundle is explored and developed. The dependence of the bundle activation barrier, U, on current j is studied and is shown to be of power-law type: U(j)\ensuremath{\propto}${\mathrm{j}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$. The values of exponent \ensuremath{\alpha} for the different regimes of collective creep are found.

We analyze the features of the graphene mono- and multilayer reflectance in the far-infrared region as a function of frequency, temperature, and carrier density taking the intraband conductance and the interband electron absorption into account. The dispersion of plasmon mode of the multilayers is calculated using Maxwell's equations with the influence of retardation included. At low temperatures and high electron densities, the reflectance of multilayers as a function of frequency has the sharp downfall and the subsequent deep well due to the threshold of electron interband absorption and plasmon excitations.

The coming few years are likely to witness a dramatic increase in high-quality supernova data as current surveys add more high-redshift supernovae to their inventory and as newer and deeper supernova experiments become operational. Given the current variety in dark energy models and the expected improvement in observational data, an accurate and versatile diagnostic of dark energy is the need of the hour. This paper examines the statefinder diagnostic in the light of the proposed SuperNova Acceleration Probe (SNAP) satellite, which is expected to observe about 2000 supernovae per year. We show that the statefinder is versatile enough to differentiate between dark energy models as varied as the cosmological constant on one hand, and quintessence, the Chaplygin gas and braneworld models, on the other. Using SNAP data, the statefinder can distinguish a cosmological constant (w=−1) from quintessence models with w≥−0.9 and Chaplygin gas models with κ≤ 15 at the 3σ level if the value of Ωm is known exactly. The statefinder gives reasonable results even when the value of Ωm is known to only ∼20 per cent accuracy. In this case, marginalizing over Ωm and assuming a fiducial Λ-cold dark matter (LCDM) model allows us to rule out quintessence with w≥−0.85 and the Chaplygin gas with κ≤ 7 (both at 3σ). These constraints can be made even tighter if we use the statefinders in conjunction with the deceleration parameter. The statefinder is very sensitive to the total pressure exerted by all forms of matter and radiation in the Universe. It can therefore differentiate between dark energy models at moderately high redshifts of z≲ 10.

The present acceleration of the Universe strongly indicated by recent observational data can be modeled in the scope of a scalar-tensor theory of gravity. We show that it is possible to determine the structure of this theory along with the present density of dustlike matter from two observable cosmological functions: the luminosity distance and the linear density perturbation in the dustlike matter component as functions of redshift. Explicit results are presented in the first order in the small inverse Brans-Dicke parameter omega(-1).

The behavior of a weakly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). The existence of the de Sitter-invariant equilibrium quantum state of the scalar field in the presence of the interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculating an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in the equilibrium state, correlation time, and spatial physical correlation radius are presented. The latter does not depend on time, which implies that the characteristic size of domains with positive and negative values of the scalar field remains the same on average in the equilibrium state in spite of the expansion of the t=const hypersurface of the de Sitter space-time.