On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

Localization criteria and bethe lattices

The problem of electron localization in static, cellularly disordered, tight-binding Bethe lattices is considered. Predictions of a localization criterion due to Economou and Cohen are developed for mobility edges and critical percolation concentrations, and compared with known exact results. The status of the criterion is critically discussed and several general limitations are illustrated. It is concluded that in some respects the criterion is coarsely representative for a range of real lattices but largely for fortuitous reasons.     

The generalized partial transposition criterion for separability of multipartite quantum states

We present a generalized partial transposition separability criterion for the density matrix of a multipartite quantum system. This criterion comprises as special cases the famous Peres–Horodecki criterion and the recent realignment criterion in [O. Rudolph, quant-ph/0202121] and [K. Chen, L.A. Wu, quant-ph/0205017]. It involves only straightforward matrix manipulations and is easy to apply. A quantitative measure of entanglement based on this criterion is also obtained.     

On complete sets of polarization observables

A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent T-matrix elements of a reaction of the type a + b → c + d + … As an illustrative example, this criterion is applied to the longitudinal observables of deuteron electrodisintegration.     

Asymptotic solutions of Fokker-Planck equations for nonlinear irreversible processes and generalized Onsager-Machlup theory

Fokker-Planck equations for nonlinear processes are solved asymptotically in the limit k→0 where k is the Boltzmann constant. It is shown that the leading asymptotic solutions for conditional (two-gate) distribution functions simply correspond to generalizations of the Onsager-Machlup theory to nonlinear processes. The asumptotic solution method used in the paper is similar to the well-known W.K.B. method in quantum mechanics. A stability criterion of nonlinear irreversible processes is also considered and compared with the Glansdorff-Prigogine stability criterion.     

One-Shot Decoupling

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. One-shot decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.     

Jeans' gravitational instability of a thermally conducting plasma

The gravitational instability of an infinitely extending homogenous plasma endowed with several physical mechanisms, namely Hall currents, finite conductivity, ion viscosity and thermal conductivity is considered. The main result is that the various parameters play different physical roles in the perturbed problem. Jeans' criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q=1, q being the nonextensive parameter.     

Scalar,electromagnetic, and gravitational fields interaction: Particlelike solutions

Particlelike static spherically symmetric solutions to massless scalar and electromagnetic field equations combined with gravitational field equations are considered. Two criteria for particlelike solutions are formulated: the strong one (solutions are required to be singularity free) and the weak one (singularities are admitted but the total energy and material field energy should be finite). Exact solutions for the following physical systems are considered with their own gravitational field: (i) linear scalar (minimally coupled or conformal) plus electromagnetic field; (ii) the same fields with a bare mass source in the form of charged incoherent matter distributions; (iii) nonlinear electromagnetic field with an arbitrary dependence on the invariant F_αβF^αβ; and (iv) directly interacting scalar and electromagnetic fields. Case (i) solutions are not particlelike (except those with horizons, in which static regions formally satisfy the weak criterion). For systems (ii), examples of nonsingular models are constructed, in particular, a model for a particle-antiparticle pair of a Wheeler-handle type, without scalar field and explicit electric charges. Besides, a number of limitations upon nonsingular model parameters is indicated. Systems (iii) are proved to violate the strong criterion for any type of nonlinearity but can satisfy the weak criterion (e.g., the Born-Infeld nonlinearity). For systems (iv) some particlelike solutions by the weak criterion are constructed and a regularizing role of gravitation is demonstrated. Finally, an example of a field system satisfying the strong criterion is given.     

Renormalization group naturalness of GUT Higgs potentials

We analyze the symmetry-breaking patterns of grand unified theories from the point of view of a recently proposed criterion of renormalization-group naturalness. We perform the analysis on simple non-SUSY SU(5) and SO(10) and SUSY SU(5) GUTs. We find that the naturalness criterion can favor spontaneous symmetry breaking in the direction of the smallest of the maximal little groups. Some differences between theories with and without supersymmetry are also emphasized.     

Numerical analysis of the azimuthal periodicity in the two lowest order modes of microstructured fibres applied to the precise determination of the cutoff wavelength

The azimuthal far-field analysis technique (AFFAT) is one of the only two methods reported to date, able to measure the cutoff wavelength λ_c in microstructured fibres (MOFs). The measurement is operated through a parameter D which is related to the modulation of the power crossing a rotating slit at the output of the tested fibre. In standard fibres, the criterion of the CEI/IEC 793-1-C7A normalised method (i.e., 2.25% of the output power carried by the second mode) is expressed by the unchanged −16.4 dB value of D(λ_c). In this paper, we show that this criterion is expressed in MOFs by a value of D which strongly depends on the geometrical parameters of the fibre and on the launching conditions at the input. However, we demonstrate that, with a slightly relaxed criterion corresponding to 10% of the output power carried by the second mode at λ_c, D remains close to −10 dB whatever the considered MOF. Thus, this constitutes a universal decision criterion allowing to determine λ_c in any classical MOF, by means of the AFFAT, with a very limited uncertainty.     

Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with Van Hove singularities

A criterion for ferromagnetism in two-dimensional systems with the Fermi level near Van Hove singularities (VHSs) is analyzed. In the quasistatic approximation applied to a spin-fermion model, it is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between the electronic and spin degrees of freedom is sufficiently large (I > I _c). The critical interaction I _c is much greater than its value determined from the Stoner criterion; hence, the latter criterion is not an adequate criterion for ferromagnetism in the presence of Van Hove singularities in the electronic spectrum. By combining the quasistatic approximation with the method of equations of motion, the electronic self-energy is obtained in the first order in the inverse number of spin components.     

Lie-Poincaré transformations and a reduction criterion in Landau theory

In the Landau theory of phase transitions one considers an effective potential Φ whose symmetry group G and degree d depend on the system under consideration; generally speaking, Φ is the most general G-invariant polynomial of degree d. When such a Φ turns out to be too complicate for a direct analysis, it is essential to be able to drop unessential terms, i.e., to apply a simplifying criterion. Criteria based on singularity theory exist and have a rigorous foundation, but are often very difficult to apply in practice. Here we consider a simplifying criterion (as stated by Gufan) and rigorously justify it on the basis of classical Lie-Poincaré theory as far as one deals with fixed values of the control parameter(s) in the Landau potential; when one considers a range of values, in particular near a phase transition, the criterion has to be accordingly partially modified, as we discuss. We consider some specific cases of group G as examples, and study in detail the application to the Sergienko-Gufan-Urazhdin model for highly piezoelectric perovskites.     

Percolation on Infinite Graphs and Isoperimetric Inequalities

We consider the Bernoulli bond percolation process (with parameter p) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric inequality if the graph has a bi-infinite geodesic, or two isoperimetric inequalities if the graph has not a bi-infinite geodesic. This new criterion extends previous criteria and brings together a large class of amenable graphs (such as regular lattices) and non-amenable graphs (such trees). We also study the finite connectivity in graphs satisfying the new general criterion and show that graphs in this class with a bi-infinite geodesic always have finite connectivity functions with exponential decay when p is sufficiently close to one. On the other hand, we show that there are graphs in the same class with no bi-infinite geodesic for which the finite connectivity decays sub-exponentially (down to polynomially) in the highly supercritical phase even for p arbitrarily close to one.     

Transmission capacity of erbium-doped fiber amplifiers as a criterion for quality of erbium-doped optical fibers

A new criterion—transmission capacity in the unsaturated gain regime—is proposed for comparing the quality of glasses for erbium-doped fiber amplifiers, considered as an element of an optical communication system. It is shown that, according to the criterion for the highest transmission capacity, amplifiers based on alumino-phosphate-silicate and zinc-sodium-germanate-silicate fibers are preferred for systems with separate C and L bands, respectively. In broadband systems, the highest transmission capacity is observed in amplifiers based on tellurite fibers.     

Two-dimensional site-bond percolation as an example of a self-averaging system

The Harris-Aharony criterion for a static model predicts that if a specific heat exponent α>0, then this model does not exhibit self-averaging. In the two-dimensional percolation model, the index α= ?1/2. This means that, in accordance with the Harris-Aharony criterion, the model can exhibit self-averaging properties. We study numerically the relative variances R _M and R _χ for the probability M of a site belonging to the “infinite” (maximum) cluster and for the mean finite-cluster size χ. It was shown that two-dimensional site-bond percolation on the square lattice, where the bonds play the role of the impurity and the sites play the role of the statistical ensemble over which the averaging is performed, exhibits self-averaging properties.     

On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.     

Concrete Representation and Separability Criteria for Symmetric Quantum State

Using the typical generators of the special unitary groups S U(2), the concrete representation of symmetric quantum state is established, then the relations satisfied by those coefficients in the representation are presented. Based on the representation of density matrix, the PPT criterion and CCNR criterion are proved to be equivalent on judging the separability of symmetric quantum states. Moreover, it is showed that the matrix Γ _ρ of symmetric quantum state only has five efficient entries, thus the calculation of ∥Γ _ρ ∥ is simplified. Finally, the quantitative expressions of real symmetric quantum state under the ∥Γ _ρ ∥ separability criterion are obtained.     

Group structure optimalization for cell-spin transformations in multi-dimensional interaction spaces

A criterion of minimal deviation from exact semi-group properties is applied to a second-order cumulant expansion of a linear renormalization transformation for the two-dimensional Ising model with three interactions.Mechanisms that influence the validity of group structure and the selectivity of the criterion, such as the way in which the Hamiltonian is divided into a free part H₀ and a perturbation V, are examined in detail.For the critical exponent y_H, related to the optimal value for the free parameter of the transformation, a great improvement is found over previous calculations with only one interaction.     

Stability criterion for projective synchronization in three-dimensional chaotic systems

Projective synchronization, in which the state vectors synchronize up to a scaling factor, has recently been observed in coupled partially linear chaotic systems (Lorenz system) under certain conditions. In this Letter, we present a stability criterion that guarantees the occurrence of the projective synchronization in three-dimensional systems. By applying the criterion to two typical partially linear systems (Lorenz and disk dynamo), it shows that only some parameters play the key role in influencing the stability. Projective synchronization only happens when σ>−1 for the Lorenz and μ>0 for the disk dynamo.     

A theoretical treatment of the line-intensity jump in a decaying argon-arc plasma

The line-intensity jump in decaying argon arcs has been investigated theoretically. The population density at the peak of the jump is in Saha-Boltzmann equilibrium. Using the Saha-Boltzmann relation, the influence of the change in electron density is clarified. As a criterion above which the change in electron density does not influence the amplitude of the jump, τ_N/τ_T ≧ 10₃ is derived, where τ_N and τ_T are, respectively, the density and temperature relaxation times for the electrons. This criterion is not satisfied in most arcs. An improved method is presented for the determination of the gas temperature in stationary arcs.