On heat fluctuations near a critical point

The spatial dependence of the heat fluctuations is examined from a thermodynamic potential for the probability of fluctuations. The corresponding correlation length is seen to diverge near the critical point.     

Scaling theory of transient phenomena near the instability point

A general scaling theory of transient phenomena is formulated near the instability point for the moments of the relevant intensive macrovariable, for the generating function, and for the probability distribution function. This scaling theory is based on a generalized scale transformation of time. The whole range of time is divided into three regions, namely the initial, scaling, and final regions. The connection procedure between the initial region and the scaling region is studied in detail. This scaling treatment has overcome the difficulty of divergence of the variance for a large time which was encountered in the -expansion, and this scaling theory yields correct values of moments to order unity for an infinite time. Some instructive examples are discussed for the purpose of clarifying the concepts of the scaling theory.     

Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point

We consider an anisotropic gap superconductor in the vicinity of the disorder-driven quantum critical point. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action, which is a critical theory with the dynamic critical exponent, z=2. This allows us to use the parquet method to calculate the nonperturbative effect of quantum superconducting fluctuations on thermodynamics. We derive a general expression for the fluctuation magnetic susceptibility, which exhibits a crossover from the logarithmic dependence, chi proportional, variantlndeltan, valid beyond the Ginzburg region to chi proportional, variantln(1/5)deltan valid in the immediate vicinity of the transition (where deltan is the deviation from the critical disorder concentration). These nonperturbative results may describe the quantum critical behavior of overdoped high-temperature cuprates, disordered p-wave superconductors, and conventional superconducting films with magnetic impurities.     

Scaling theory of relaxation and fluctuation near the instability point

The idea of generalized scale transformation of time is introduced to evaluate asymptotically the relaxation and fluctuation in non-equilibrium systems. This scaling theory is demonstrated to be very powerful in discussing the relaxation just from the instability point.     

On the theory of a detuned single mode laser near threshold

A theory of a detuned single mode laser near threshold is given using the Fokker-Planck equation technique. The Fokker-Planck equation is solved by an eigenfunction expansion. The eigenfunctions and the corresponding eigenvalues are determined by a nonhermitian operator and are calculated numerically in the threshold region. The dependence of the linewidth from the detuning is shown. In the intensity distribution the detuning enters only via a change of the scaling parameter. For the linewidth, however, an additional broadening is found. Finally it is shown that in certain cases the correlation function must not be approximated by a single exponential term.     

On the dielectric theory of a crystalline slab of point molecules

We discuss the dielectric response of a crystalline slab of point molecules to an incident plane electromagnetic wave. The slab is assumed to be made up of non-polar, polarizable molecules (a) lying at points of a simple cubic lattice and (b) interacting only via the electromagnetic field. Expressions for the dispersion relations, polarisation and electric fields and the transmission coefficient are derived. Conditions under which a point dielectric equation of state holds are obtained. This simple system exhibits three resonances near the transverse optic frequency.     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

On the mechanics of a mass point in the general theory of relativity

An investigation is made into the equations of motion for mass points of comparable masses, the energy-momentum tensor of which is a linear function of the-function, in connection with the principle of equivalence. If some conditions are fulfilled the equations of motion for mass points subject to a supplementary non-gravitational force effect can be transformed to equations of motion for free motion of mass points in a certain equivalent gravitional field. The equivalent field, in agreement with the local validity of the principle of equivalence, is defined merely along the trajectories of the mass points. , - -, . , , , . , , .

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On the theory of point defect recombination in crystals

A new approach to the diffusion-limited reaction kinetics for particles migrating by random walks on discrete lattice sites and reacting when two particles occupy the same site is extended to a more general case of a large reaction radius and applied to the problem of the recombination rate of point defects in cubic lattices. Numerical calculations correctly reproduce the analytic expressions in the limit cases considered in previous work and in the general case represent a stepwise dependence of the reaction rate on the recombination radius.     

Investigation of rotating He II near the lambda point by means of the Ginzburg-Landau-Abrikosov theory

Equations describing the spatial distribution of the order parameter and the rotational velocities are derived on the basis of the thermodynamic potential of rotating He II near the point. It is shown that the given approach is analogous to the Ginzburg-Landau-Abrikosov theory (superconductors).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 75–81, May, 1984.The author is grateful to V. L. Ginzburg and A. A. Sboyanin for their interest in the work and for sending a copy of the article [13], and also to L. P. Pitaevskii for a critique.     

Regularizing a vortex sheet near a separation point

Current methods for computing vortex sheet separation use a regularization parameter which is discontinuous from the body to the vortex sheet. We propose two methods for reducing the errors associated with the discontinuity and improving convergence with respect to the regularization parameter. The “velocity smoothing” method is the simpler of the two, and removes the discontinuity in regularization from one of the two equations where it occurs. The “tapered smoothing” method removes the discontinuity from both equations. In a model problem, both methods are found to converge much more rapidly (with exponents 3/2 and 2 versus 1/2 for the standard method) as the regularization parameter tends to zero. Unsteady algorithms are proposed for evolving the free sheet using the two methods, and are tested in a benchmark problem. Accuracy is significantly improved for similar computational expense.     

Topological crossovers near a quantum critical point

We study the temperature evolution of the single-particle spectrum ε-(p) and quasiparticle momentum distribution n(p) of homogeneous strongly correlated Fermi systems beyond a point where the necessary condition for stability of the Landau state is violated, and the Fermi surface becomes multi-connected by virtue of a topological crossover. Attention is focused on the different non-Fermi-liquid temperature regimes experienced by a phase exhibiting a single additional hole pocket compared with the conventional Landau state. A critical experiment is proposed to elucidate the origin of NFL behavior in dense films of liquid ³He.     

On the field theory expansion of superstring five point amplitudes

A simple recursive expansion algorithm for the integrals of tree level superstring five point amplitudes in a flat background is given which reduces the expansion to simple symbol(ic) manipulations. This approach can be used for instance to prove the expansion is maximally transcendental to all orders and to verify several conjectures made in recent literature to high order. Closed string amplitudes follow from these open string results by the KLT relations. To obtain insight into these results in particular the maximal R-symmetry violating amplitudes (MRV) in type IIB superstring theory are studied. The obtained expansion of the open string amplitudes reduces the analysis for MRV amplitudes to the classification of completely symmetric polynomials of the external legs, up to momentum conservation. Using Molien?s theorem as a counting tool this problem is solved by constructing an explicit nine element basis for this class. This theorem may be of wider interest: as is illustrated at higher points it can be used to calculate dimensions of polynomials of external momenta invariant under any finite group for in principle any number of legs, up to momentum conservation.     

Diffusion-broadened line shape near a turning point

The absorption spectrum of a gas with a large Doppler width and soft collisions between particles is studied. The particles are assumed to have a nonlinear dependence of the resonance frequency on velocity. The shape of the narrow peak in the spectrum resulting from an extremum of this dependence is calculated analytically for the first time. In the absence of collisions it has a characteristic asymmetric shape. Collisions are shown to broaden the line and change its shape. The profile of the probe-field spectrum is obtained for a three-level system with the strong field at an adjacent transition. The components of the Autler-Townes doublet are found to spread and repel each other because of collisions. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 27–32 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.