Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g ². The density and temperature dependence of results is occulted in the effective mass of the system.     

The Landau–Khalatnikov Relaxation Mechanism in Smectic Liquid Crystals

Journal of Experimental and Theoretical Physics - The idea proposed and implemented by Landau and Khalatnikov to describe the dispersion and absorption of sound in superfluid helium is applied to...     

Phase Conjugation by Degenerate Four-wave Mixing in Nematic Liquid Crystals

1.IntroductionOpticalphaseconjugationhasbeeninvestigatedextensivelybecauseofitswideapplicationsinimagingtechnology,phase--conjugationlasers,andopticalassociativememorysystems.Notedfortheirlargeopticalreorientationnonlinearities[IJ,nematicliquidcrystals(NLC)havebecomepromisingopticalmediaforapplicationsinthefieldofnonlinearopticsincludingnonlinearphaseconjugation.In1980,Feketectal.[2)firstrealizedphase--conjugationbydegeneratefour--wavemixing(DFWM)inNLCintheisotropicphase.Sincethen,thefie…     

On the Thermal Explosion Theory of a Heterogeneous Liquid–Liquid System

In this paper, the regularities of a thermal explosion of a heterogeneous system consisting of two immiscible liquids have been studied. Each phase is a solution of A and B reagents. Reagent B is extracted into a solution of reagent A, where the bimolecular exothermic reaction A + B → Products takes place. It has been shown that an exothermic reaction (combustion regime) continues to proceed in the system at high mass-exchange rates between phases after a thermal explosion. As a result, the maximal temperature may significantly exceed the temperature of the thermal explosion. The critical value of the Semenov parameter decreases with an increase in the mass-exchange rate between phases. In the limited range of values of the distribution coefficient of reagent B between phases, the increase of this coefficient is also accompanied by a decrease in the critical value of the Semenov parameter. The concentration of reagent B in the initial phase decreases monotonically due to its extraction into another phase. However, the equilibrium of the extraction of reagent B can shift, due to the temperature dependence of the distribution coefficient during the reaction. Thus, the time dependence of the concentration of reagent B on may be more complex and can pass through a minimum.     

Enhancement of the Nonlinear Optical Absorption of the E7 Liquid Crystal at the Nematic–Isotropic Transition

We present an experimental study of the nonlinear optical absorption of the eutectic mixture E7 at the nematic?Cisotropic phase transition by the Z-scan technique, under continuous-wave excitation at 532?nm. In the nematic region, the effective nonlinear optical coefficient ??, which vanishes in the isotropic phase, is negative for the extraordinary beam and positive for an ordinary beam. The parameter $S_\textrm{NL}$ , whose definition in terms of the nonlinear absorption coefficient follows the definition of the optical-order parameter in terms of the linear dichroic ratio, behaves like an order parameter with critical exponent 0.22 ±0.05, in good agreement with the tricritical hypothesis for the nematic?Cisotropic transition.     

On the Effect of Boundary Conditions in the Ginzburg–Landau Theory on the Results of Calculations of the Critical State of Layered Structures

The effect of boundary conditions in the Ginzburg–Landau theory on the critical state of superconducting layered structures is studied. The method is based on the numerical solution of the Ginzburg–Landau nonlinear equations describing the behavior of a superconducting plate carrying a transport current in a magnetic field, provided the absence of vortices in it. The use of the general boundary condition for the Ginzburg–Landau system of equations leads to a change in the order parameter over the thickness of thin superconducting plates. The calculated dependences of the critical current of plates on the magnetic field applied in parallel to layers are used to determine the critical current of multilayered structures. It is assumed that the mutual influence of superconducting layers occurs only through the magnetic field induced by them.     

Non-Markoffian Dynamic Evolution of Spontaneous Emission in Photonic Crystals

The spontaneous emission of a two level atom embedded in photonic crystals is investigated. The photonic crystal will lead to the feedback of the atom-emitted radiation which will influence the evolution of the atom. Because the feedback is within the time scale of a few optical periods, the Markoffian approximation could not be applied for the study of the time evolution of the atom. Due to the feedback of the reflected waves at different interfaces of the photonic crystals, the atomic evolution is quite different from the vacuum.     

Some Features of Critical Parameters Calculations of Nonhomogeneous Superconducting Films Using the Ginzburg–Landau Theory

Bulletin of the Lebedev Physics Institute - A method for calculating the critical state of inhomogeneous superconducting films using the Ginzburg–Landau (GL) theory is proposed. From the...     

Kink–Antikink Interaction in a Linear Defect of the Electroconvective Structure of a Nematic

JETP Letters - Features of the interaction of two dislocations in a new type of a singular defect appearing in a one-dimensional domain structure at electroconvection in π/2-twisted nematic...     

Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Discrete thinning of free-standing smectic films in the de Gennes “pre-smectic liquid” model

It is shown that the successive discrete thinning of free-standing smectic films (FSSFs), which is observed when the films are heated above the temperature of the smectic A-nematic bulk phase transition, has a natural explanation in terms of the de Gennes “pre-smectic liquid” model, provided that a sufficiently large external compressive force is applied to the free surfaces of the FSSF. In a real situation this force stems from the curvature of the surrounding miniscus, which plays the role of a volume reservoir. In this model a superheated FSSF is stabilized by balancing the external compressive and elastic forces. When heating takes place the bulk modulus of the pre-smectic lattice decreases, and when the superheating reaches a critical value, the FSSF is subject to a long-wavelength instability in thickness beause the external compressive and elastic forces can no longer be balanced for a fixed number of smectic layers. If a superheated FSSF possesses adequate stability against disruption, the balance of forces, which was disrupted, and hence the stability of the FSSF can be restored as a result of spontaneous thinning of the film to a thickness corresponding to a smaller number of smectic layers. In general, heating of a superheated FSSF is accompanied by a series of such thinning transitions. Near the critical points where the balance of the forces breaks down, the dislocation mechanism of spontaneous thinning, which could be responsible for the stratified nature of the progressive discrete thinning of real FSSFs, can become dangerous. Zh. éksp. Teor. Fiz. 115, 61–69 (January 1999)     

Energy–Momentum Tensor in the Relativistic Theory of Gravity

It has been shown that the following modification of the symmetric (Gilbert) total energy–momentum tensor (EMT) density \({t^{\mu v}} \to {t^{\mu v}} - \frac{{{m^2}}}{{16\pi G}}{\tilde \varphi ^{\mu v}}\) leads to incorrect results in basic energetic calculations. It is pointed out that some attempts to prove the positive definiteness of the gravitational radiation flux in the RTG are based on the nonconservative energy–momentum tensor.     

Complex Dynamics of the Cascade of Kink—Antikink Interactions in a Linear Defect of the Electroconvective Structure of a Nematic Liquid Crystal

JETP Letters - The complex dynamics of an ensemble of dislocations in a linear defect appearing in a one-dimensional electroconvective structure of a π/2-twisted nematic liquid crystal has...     

Anisotropy in Third-Order Nonlinear Optical Susceptibility of a Squarylium Dye in a Nematic Liquid Crystal

A squarylium dye is dissolved in 4-cyano-4＇-pentylbiphenyl （SCB） and oriented by sandwiching mixtures between two pieces of rubbed glass plates. The optical absorption spectra of the oriented squarylium dye-5CB layers exhibit high anisotropy. The third-order nonlinear optical responses and susceptibilities X^（3）e of squarylium dye in 5CB are measured with light polarizations parallel and perpendicular to the orientational direction by the resonant femtosecond degenerate four-wave mixing （DFWM） technique. Temporal profiles of the DFWM signal of the oriented squarylium dye-5CB layers with light polarizations parallel and perpendicular to the orientational direction are measured with a time resolution of 0.3ps （FWHM）, and are found to consist of two components, i.e., the coherent instantaneous nonlinear response and slow response due to the formation of excited molecules. A high anisotropic ratio of x^（3）e, 10.8 ：k 1.2, is observed for the oriented layers.     

Trimer–Tetramer Interwoven States in the Scaling Limit

We report here some results we have obtained on the scale dependence of tetramer energies at the unitary limit, considering the number of tetramer energy levels appearing between the ground and the excited Efimov trimers. Our numerical investigation is done by solving a renormalized set of Faddeev–Yakubovsky equations for identical bosons with zero-range interaction, requiring a four-body scale, which in principle can be independent of the trimer properties. The ratio between the three- and four-body scales is introduced by considering the two lower trimer states and corresponding associated tetramers. We conclude that at least three tetramers are possible to exist between two Efimov states by varying the relation between such scales, and considering the relation between three-body Efimov states in the unitary limit. The results for the trimer–tetramer interwoven states are shown through a correlation between tetramers attached to consecutive Efimov trimer states.     

Fermionic solutions of chiral Gross–Neveu and Bogoliubov–de Gennes systems in nonlinear Schrödinger hierarchy

The chiral Gross–Neveu model or equivalently the linearized Bogoliubov–de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz–Kaup–Newell–Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n  -th NLS hierarchy generally has n+1$n+1$ gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.     

Light-Front Quantization of the Chern–Simons–Higgs Theory in the Broken Symmetry Phase

Two-space one-time dimensional Chern–Simons–Higgs theory is quantized on the light-front in the broken (frozen) symmetry phase of the Higgs potential.     

A Thermodynamic Model of Nucleation of p-Terphenyl Crystals with Surface Energy Anisotropy at the Liquid–Air Interface

Physics of the Solid State - An analysis of the variation of Gibbs free energy ΔG upon the formation of a plane nucleus of the p-terphenyl crystal at the liquid–air interface is...     

Ultrasonic Determination of the Jahn–Teller Effect Parameters in Impurity-Containing Crystals

Journal of Experimental and Theoretical Physics - A method is developed to determine the symmetry properties of strains and the type of Jahn–Teller effect in crystals with impurity ions in a...