Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

Dense stellar matter in asymptotically free gauge theories: I. The high density limit

In asymptotically free gauge theories perturbation theory may be used to obtain the behavior of dense stellar matter. The criteria for the determination of ?_crit, the minimum density above which perturbation theory is valid, are presented. The asymptotic form for the quark-gluon thermodynamic potential is given.     

The dispersion force of physical adsorption: II. Nonlocal theory

We present a nonlocal theory of the dispersion force of physisorption for non-polar atoms or molecules. The calculation uses linear response theory and the surface impedance method. The results generalize those presented previously, which relied on a local theory of the dielectric response. Also included in the treatment is the role of diffuseness of the interface between substrate and vacuum. Adatom dipole and quadrupole fluctuations are treated. Several diverse contributions to the potential are thus calculated, giving rise to a substantial modification of the conventional expression V ? -C₃(z-z₀)^?3, especially at small separation z.     

A mode coupling theory of higher order time correlation functions

Kawasaki's mode coupling theory [Ann. Phys. 61 (1970) 1] is used to compute time correlation functions of the form 〈A_k0(t₀) … A_kn(t_n)〉, where A_k(t) represents some slowly varying quantity. The Gaussian and Bare Vertex approximations are made, thus yielding extremely simple expressions for these higher order correlation functions. These do not contain any bare transport coefficients and suggest relatively simple tests by which the theory could be checked. Examples relating to light scattering in nonequilibrium systems and the hydrodynamics of simple fluids are presented.     

On the theory of the second optical harmonic in nonlinear crystals with a regular domain structure

The theory of the second-harmonic generation in crystals with a regular domain structure (RDS) is developed in the approximation of the fixed intensity of the fundamental radiation. An analytical expression for the second-harmonic intensity is derived. The results are compared with the data obtained in the fixed-field approximation and the numerical solution. The maximum number of layers n _max at which the theory remains valid is determined. Numerical estimates of n _max are presented for the frequency doubling of an ultrashort light pulse in the LiNbO₃ RDS crystal.     

Ground-state phase diagrams of Ising metamagnet in a mixed longitudinal and transverse magnetic field

The ground-state magnetic properties of a two-sublattice Ising metamagnet in a mixed longitudinal and transverse magnetic field are studied within the effective-field theory. A parameter j₂=J₂/J₁ is introduced, which reflects the strength ratio of spin coupling between adjacent planes and in each plane. In addition to the second-order transition lines, the first-order transition lines are also presented, since the ground-state energy can be calculated numerically. The ground-state phase diagrams in h_x–h_z are presented. The results show that when j₂<0 the phase transition of the system is always first-order for h_x<2.751, and when −1000?j₂<0 it is always second-order for h_x>4.36. For the given h_x (0<h_x<14.71), the longitudinal critical magnetic field increases as j₂ decreases. The reentrant phenomenon occurs in the range of j₂<−11.89, h_x>14.71. There is no fourth-order critical point in the phase diagrams given by using EFT as found by using mean field theory (MFT).     

Theory of laser-induced gas ionization

The mechanism of laser-induced gas ionization is analyzed in the context of the theories presently available, namely multiphoton and cascade theory, and their predictions are shown to be in serious divergence from experimentation. A novel hypothesis is then formulated which considers the classical photon energy expression ε=hν as the limit of a general expression ε=hν/[1?β_ν f(I)],f(I) being a function of light intensity and β_ν a coefficient such that β_ν f(I) significantly differs from zero only for high-intensity laser light. Starting from the new formulation of the photon energy expression, a theory is developed for the laser ionization phenomenon and a few simple relations are found. The successful use of these relations in the verification of the experimental results suggests that the new photon energy expression has a real physical meaning rather than an empirical significance, and some considerations on the physical meaning are presented.     

Classical theory of a space-time sheet

By embedding the space-time V₄ in a higher-dimensional space M_N we can formulate a theory of gravity in which the true dynamical variables are the coordinates η^a(x) (a = 1,2,…, N) of V₄ with respect to M_N. Before constrained by the variational principle, which gives the equations of the four-surface V₄, all the coordinates η^a are independent. This enables the canonical formulation of the theory (without additional constraints except for the initial and boundary conditions on η^a and ones due to the reparametrization invariance) which is presented here. When expressed in terms of the metric tensor g_μ$\text{v}$ of the space-time four-surface V₄ the theory reduces to the Einstein general relativity.     

Relationships in Raman intensity theories,in particular the Mayants-Averbukh theory

Brief surveys are given of the Mayants-Averbukh Raman intensity theory, and of the polar tensor Raman intensity theory recently presented by Bogaard and Haines. It was found that these intensity theories in essence are equivalent. In addition, the appearances of the symmetry invariant parameter matrices F_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries of bond n. These matrices, and a single bond coordinate system, can be used as a convenient alternative to the Mayants-Averbukh treatment of bonds which have some kind of symmetry with respect to the midpoint of the bond. A modification of the Mayants-Averbukh treatment is also suggested. The rotational mode equations of the Mayants-Averbukh theory have been investigated to elecudate the constraints which they impose on Raman intensity theories based on the bond polarizability model. It was found that the valenceoptical theory is in conformity with the rotational modes only if all electrooptical parameters $\text{?α}{}_{\mathrm{ii}}{}^{\mathrm{(n)}}\text{?γ}{}_{\mathrm{p}}$ are neglected, where α_ii⁽ⁿ⁾ (i = 1, 2, 3) are the diagonal components of the polarizability α⁽ⁿ⁾ of bond n, and γ_p is the pth internal angular coordinate. Furthermore, the valence-optical theory was found to be strictly applicable only for cylindrical bond symmetry, C_mv (m ≥ 4). A generalized valence-optical Raman intensity theory, allowing also for non-zero off-diagonal components α_ij⁽ⁿ⁾, was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic polarizability equation was useful for suggesting a unique interpretation of a set of f parameters (elements of F_n⁰) in terms of components of the anisotropic part of a symmetric bond polarizability.     

Charge distributions and correlations in fragmentation models for soft hadron collisions

Theλφ ⁴ theory in 3+1 dimensions is often claimed to be trivial; that is, either free or inconsistent. Here, the theory is studied in a simple variational approach, which confirms that for any positiveλ _Bare the theory is indeed sick. However, proper renormalization actually requiresλ _Bare to be negative infinitesimal. This apparently leads to a viable, non-trivial theory.     

Theory of the period-doubling phenomenon of one-dimensional mappings based on the parameter dependence

A theory is presented of the period-doubling phenomenon of one-dimensional mappings of the form x_n+1 = F(x_n, r), which is different from that of Feigenbaum mainly in that it is based on the r dependence of various quantities rather than on their x dependence. Consequently, it enables us to evaluate, for example, the Lyapunov numbers of periodic orbits as a function of r as well as the Feigenbaum ratio. It is shown that the results of our theory are in good agreement with those of numerical simulations.     

2s Hyperfine splitting in light hydrogen-like atoms: Theory and experiment

Since the combination D ₂₁ = 8f _HFS(2s)-f _HFS(1s) of hyperfine intervals in hydrogen and light two-body hydrogen-like atomic systems weakly depends on the nuclear structure, comparison between theory and experiment can be sensitive to high order QED corrections. New theoretical and experimental results are presented. Calculations have been performed for the hydrogen and deuterium atoms and for the helium-3 ion. Experiments on the 2s hyperfine splitting (responsible for the dominant contribution to the error in D ₂₁) have been conducted for hydrogen and deuterium. The theory and experiment are in good agreement, and their accuracy is comparable to that attained in verifying the QED theory of the hyperfine splitting in leptonic atoms (muonium and positronium).     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field

In this paper, a Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field is presented. For orbital doublet ²E, which is an orbital degenerate state in the cubic field and is a near-degenerate state in the tetragonal field, we obtain the cubic invariant form and the tetragonal invariant form of the Spin-Hamiltonian. In case of near-degeneracy (tetragonal splitting is very small) two additional g-factors are introduced to investigate Zeeman-splitting for tetragonal field. The two additional g-factors g_2z and g_2xy describe the magnetic interest between A_1g and B_1g states for a parallel magnetic field with z-axis and a perpendicular magnetic field with z-axis, respectively. The theory is based on the time-reversal invariant and the point-group symmetry invariant. The theoretical method can also be used for other orbital degenerate states ^2S+1Γ including and Γ=T₁ or T₂ and can be used for other point-group symmetry.     

Electronic structure and positron annihilation in alkali metals: Isolation of ionic core contribution and valence high-momentum components

Momentum densities of annihilation pairs from valence as well as from ionic core electrons in alkali metals are calculated ab initio and compared with the experimental results. It is shown that the valence high-momentum components constitute a great deal (23–34% in Na-Cs and probably even more in Li) of the Gaussian part of the angular correlation curves. The average core enhancement factor γ_c ranges from 1.5 (Li) to 7.1 (Cs) and may be well expressed by a logarithmic function of ionic core polarizability. The presented values of γ_c are much higher than the core enhancement factors in the high-momentum (?15 mrad) region which, according to the recent theory of Bonderup, Andersen and Lowy, should not be very different from unity.     

An algebraic framework for the supersymmetry theory

In the absence of a rigorous mathematical definition (or proof of existence and consistency) of the “g-dimensional space” whose points are labelled by the four (commutative) Minkowski coordinates x_n and four anticommuting coordinates θ_n, a clearly consistent algebraic scheme is presented in the frame of which the concepts used in the theory of the supersymmetry have a well established mathematical meaning.     

Simultaneous Q-switching and mode-locking in the CW Nd: YAG laser

The theory of transient mode-locking for an active modulator in a laser with a homogeneously broadened line is presented. The theory is applied to simultaneously Q-switched and mode-locked Nd:YAG lasers and good agreement between theory and experiment is obtained. The main conclusion is that under usual Q-switched operating conditions the mode-locking process does not have sufficient time to build up to steady-state conditions. We also present a method to overcome this problem by allowing the laser to prelase before the Q-switch is opened. Mode-locked pulses whose width approaches the steady-state value are obtained. The transient mode-locking theory presented here also applies to actively mode-locking TEA CO₂ lasers and to other types of simultaneously pulsed and mode-locked lasers.