Modification of the superconducting order parameter Δ(k) by long-range interactions

It is demonstrated that the inclusion of long-range intersite interactions qualitatively modifies the dependence of a superconducting gap on quasimomentum for both s-and d-symmetry types. In particular, the order parameter of a superconducting phase with $d_{x^2 - y^2 } $ the symmetry type depends on two amplitudes and has the form Δ(k)=Δ₁(cosk _x ?cosk _y )+Δ₂(cos2k _x ?cos2k _y ). In this case, the theoretical dependence of the critical temperature on the degree of doping agrees with the experimental dependence.     

Adiabatic theorem in axiomatic quantum field theory

It is shown that Møller matricesS _± and scattering matrixS in axiomatic field theory can be expressed through their adiabatic analogs. In particular, it is proved under certain conditions that \(S_ - = \mathop {s\lim }\limits_{\alpha \to 0} S_\alpha (0,\infty )W_\alpha \) whereW _α is a trivial phase factor [i.e. a unitary operator of the form exp i / α ∝r(k)a ⁺ (k)a(k)dk]. Corresponding results in Hamiltonian approach are discussed.     

Gravitational supervertices in n=1, 4D superstrings

The gravitational supermultiplet for target space-time supersymmetry of four-dimensional heterotic strings is obtained. By an explicit construction of supervertex operators it is shown that the underlying superspace geometry corresponds to the “new-minimal” formulation of N = 1, 4D supergravity. The relation between R-symmetry in target space and the U(1) symmetry of the world-sheet N = 2 superconformal algebra is outlined.     

Stochastic bifurcation in FitzHugh-Nagumo ensembles subjected to additive and/or multiplicative noises

We have studied the dynamical properties of finite N-unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. In the AMM, original 2N-dimensional stochastic equations are transformed to eight-dimensional deterministic ones, and the dynamics is described in terms of averages and fluctuations of local and global variables. The stochastic bifurcation is discussed by a linear stability analysis of the deterministic AMM equations. The bifurcation transition diagram of multiplicative noise is rather different from that of additive noise: the former has the wider oscillating region than the latter. The synchronization in globally-coupled FN ensembles is also investigated. Results of the AMM are in good agreement with those of direct simulations (DSs).     

On the uniqueness of the smooth zero mass limit for invariant amplitudes

The behavior of the invariant amplitudes for processes involving massive vector mesons is investigated in the limit as the mass goes to zero. The constraints of gauge invariance impose a definite structure on the amplitudes at k² = 0, and the question of the uniqueness of this structure is examined. It is shown that if the limit is smooth, the consequent relations between the massive and massless helicity amplitudes are unique, provided only that any additional dynamical assumptions are made consistently. Some of the implications of this result are discussed, with particular reference to the unambiguous covariant formulation of vector meson dominance for scattering amplitudes.     

Light scattering from E-symmetry amplitudon in the incommensurate phase of quartz

Low frequency depolarized Raman spectra of quartz were investigated in the incommensurate phase near the α-β transition at T_c = 573°C. A weak mode, but underdamped in the temperature region close to the commensurate α phase, was observed at about 8 cm^-1 with an intensity proportional to the square of the order parameter. The mode is assigned as the E-symmetry amplitudon which has been predicted to exist in the “3-k state” of the incommensurate phase, in addition to a totally symmetric A-amplitudon.     

On the large order expansion for the anharmonic oscillators

Using functional approaches, we investigate the large-K behaviour of theK ^th coefficientE _k in the perturbation expansion for the ground-state energyE(g) of the generalized anharmonic oscillatorX ^2N with internalO(_n)-symmetry. We establish the equivalence between the pure functional approach and the method of Collins-Soper at any order in 1 /K. For that purpose, we first develop an algebraic treatment of perturbation series and prove a theorem on Borelsummable functions. Finally, we compute analytically the 1 /K and 1 /K ² corrections to the leading term forN=2.     

Efficient large-array k-domain parallel MRI using channel-by-channel array reduction

This article presents a method to explore the flexibility of channel reduction in k-domain parallel imaging (PI) with massive arrays to improve the computation efficiency. In PI, computation cost increases with the number of channels. For the k-domain methods requiring channel-by-channel reconstruction, this increase can be significant with massive arrays. In this article, a method for efficient k-domain PI reconstruction in large array systems is proposed. The method is based on the fact that in large arrays the channel sensitivity is localized, which allows channel reduction through channel cross correlation. The method is tested with simulated and in vivo MRI data from a 32-channel and 64-channel systems using the multicolumn multiline interpolation (MCMLI) method. Results show that the proposed algorithm can achieve similar or improved reconstruction quality with significantly reduced computation time for massive arrays with localized sensitivity.     

Fractional supersymmetric Liouville theory and the multi-cut matrix models

We point out that the non-critical version of the k-fractional superstring theory can be described by k  -cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q)$(p,q)$ minimal fractional superstring theories appear in the Zk${\mathbb{Z}}_k$-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.     

Special features in photoemission from the s-p bands of copper

Angle-resolved photoemission (ARPES) studies of the (100) face of clean copper using He I radiation reveal two distinct peaks with binding energies between 0 and 2 eV. These peaks have the opposite dispersion with emission angle and have very different widths, one peak in particular being unusually sharp. We show that both of these peaks are associated with the upper part of the s-p band and that their behaviour can be qualitatively explained by an examination of the bulk band structure for finite values of k_∥ away from the Δ-symmetry direction. We also show that rather good quantitative agreement with the experimental spectra can be obtained by performing realistic photocurrent calculations which include a proper treatment of the surface electronic structure, matrix elements and lifetime effects. Finally, the significance of a sharp peak arising from the s-p band for ARPES studies of random alloys and chemisorption systems is briefly discussed.     

Neutron star magnetism

It is shown that

1. an appreciable change of magnetic moment of a neutron star cannot occur via ohmic dissipation
2. pulsars provide evidence for large internal magnetic fields in main sequence stars. If pulsars are born from stars with masses exceeding 3 ?_⊙ the internal field must be of the order of 10³-10⁴ Gauss while if they derived from less massive urstars 10² Gauss are sufficient to give rise to a magnetic moment ofM～10³⁰ Gauss cm³.

     

Noncommutative M-branes from covariant open supermembranes

We discuss an open supermembrane in the presence of a constant three-form. The boundary conditions to ensure the κ-invariance of the action lead to possible Dirichlet branes. It is shown that a noncommutative (NC) M5-brane is possible as a boundary and the self-duality condition that the flux on the world-volume satisfies is derived from the requirement of the κ-symmetry. We also find that the open supermembrane can attach to each of infinitely many M2-branes on an M5-brane, namely a strong flux limit of the NC M5-brane.     

Exact solution of the Boltzmann equation in the relaxation approximation,existence of negative differential conductivity for certain types of energy bands and its implication for the fluctuation spectrum and the noise temperature

The Boltzmann equation for the distributionf _k of a system of charged particles obeying classical statistics in a uniform fieldF, $$\frac{{\partial f_k }}{{\partial t}} + F\frac{{\partial f_k }}{{\partial k}} = \smallint d^3 k'(W_{kk'} f_{k'} - W_{k'k} f_k ),$$ will be solved analytically for a special class of transition ratesW _kk′=const·h _k ·ν _k ·ν _k′ for any initial distribution.h _k is the Maxwell distribution andν _k >0 can be interpreted as ak-dependent relaxation frequency. The constant relaxation approximation (ν _k =ν) will be used to discuss the drift velocitiesu for all the fields and temperaturesT for certain types of band structuresE(k). Bands with lineark-dependence for largek give rise to drift velocities saturating for large fields. For bands with the periodicity of the reciprocal lattice, the zero drift-theorem has been proved. It states that $$\mathop {\lim }\limits_{F \to \infty } u (F,T) = \mathop {\lim }\limits_{T \to \infty } u (F,T) = 0$$ for all the periodic band structures. This theorem is even correct for a generalW _kk′ if certain restrictions are made. Finally, making use of the Markov character of the conditional probability (Green's function) solution of the Boltzmann equation, the velocity fluctuation spectrumS is calculated forE(k)=A(1?cosa k). It will be shown thatS(F, T, 0) remains positive for the critical field and all temperatures, and therefore the noise temperature diverges on approaching the critical field.     

The doubling of the anomalous magnetic moment of electron in a very strong constant homogeneous electric field

Calculated by the author previously [8], the anomalous magnetic moment (AMM) of the electron in an intense constant electric field changes nonmonotonically as the field increases, passing through a minimum and tending to the doubled Schwinger value for very strong fields. In the present paper, it is supposed that the AMM is related by the Lande factor to the angular momentum of a virtual electron accompanied by a virtual photon. This factor changes its effective value because of the influence of the external field on the motion of the virtual electron and its self-action. With increase of the electric field strength, the virtual electron can successively occupy the excited states l = 1, j = 1/2 and l = 1, j = 3/2 in addition to the original state with the orbital angular momentum l = 0 and the total angular momentum j = 1/2. The first of these excited states decreases the AMM and the second increases and doubles it if only this state is occupied for a very strong field. The latter condition is equivalent to the alignment of the spin and the orbital angular momentum of the electron along the field, while the total angular momentum of the entire system of the virtual electron and the virtual photon remains equal to 1/2.     

On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds

We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux Y(s ₁, ..., s _k ) with k rows. The procedure is based on the construction of scalar auxiliary oscillator realizations for the symplectic sp(2k) algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.     

From phenomenological thermodynamics to the canonical ensemble

Given the generic canonical probability in phase φ=exp[β(Ψ-H)], contact is traditionally made with phenomenological thermodynamics by comparing the identity δ〈φ〉=0 with the relationTδS=δU+δW, δ indicating an arbitrary infinitesimal variation of the thermodynamic coordinates and angular brackets ensemble means. This paper is concerned with the inverse problem of finding both the generic form of the phase functionw such thatS=〈w〉 and the explicit form φ=αexp[(F-H)/kT] of the canonical distribution on the basis of the requirement that the consequences of the phenomenological laws must be safeguarded, i.e., the relations between the quantities which are their concomitants must also be satisfied by their statistical representatives. Given the generic statistical formalism and specifically thatU=〈H〉, δW=?〈δH〉, the problem is soluble, granted the following generic assumption: “the statistical representative of the entropy is the ensemble mean of a function which depends upon the phase through φ alone.”     

A mechanism for ferrimagnetism and incommensurability in one-dimensional systems

In this paper I discuss a mechanism for ferrimagnetism in 1+1 dimensions. The mechanism is related to a special class of interactions described by operators with non-zero Lorentz spin. Such operators are present in such problems as the problem of tunneling between Luttinger liquids and the problem of frustrated spin ladder. Exact solutions are presented for a representative class of models possessing a continuous isotopic symmetry. It is shown that the interactions (i) dynamically generate static oscillations with the wave vector dependent on the coupling constant, (ii) give rise to spontaneous breaking of this symmetry at T=0 accompanied by generation of the magnetic moment and appearance of gapless modes with a non-relativistic (ferromagnetic) dispersion E∼k², (iii) generate massive (roton) modes.     

Superspace geometry from D = 4, N = 1 heterotic superstrings

The presence of classical κ-supersymmetry invariance is shown to be consistent with an off-shell D = 4, N = 1 conformal supergravity background in the presence of a tensor multiplet. We derive a suitable set of constraints, via super Weyl rescaling, for a heterotic superstring in such a background. Starting from the geometry of 16-16 supergravity and gauging the R-symmetry with a composite connection, we derive a geometrical structure similar to that of new minimal supergravity.