Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Renormalized boson expansion for the 2νββ decay

Two neutrino double beta (2) Gamow-Teller transitions, and , are treated with a many-body Hamiltonian involving a Bonn-type realistic two-body interaction. The states involved in these transitions are described by a pnRQRPA approach. Transition operators are expanded in first order in terms of renormalized bosons. For illustration the formalism is applied to the case Kr.     

A\overline {Poincar\acute{e}} gauge theory of gravity

We develop a gauge theory of gravity on the basis of the principal fiber bundle over the four-dimensional space-timeM with the covering groupP¯ ₀ of the proper orthochronous Poincaré group. The field components are constructed with the connection coefficients , and with a Higgs-type field. A Lorentz metricg is introduced with , which are then identified with the components of duals of the Vierbein fields. Associated with there is a spinor structure onM. For Lagrangian densityL, which is a function of , ,, matter field , and oftheir first derivatives, we give the conditions imposed by the requirement of the gauge invariance. The Lagrangian densityL is restricted to be of the formL =L ^tot (, T ^klm ,R ^klmn , _k , ), in whichT ^klm ,R ^klmn are the field strengths of , , respectively. Identities and conservation laws following from the gauge invariance are given. Particularly noteworthy is the fact that the energy momentum conservation law follows from theinternal translational invariance. The field equation of is automatically satisfied, if those of and of are both satisfied. The possible existence of matter fields with intrinsic energy momentum is pointed out. When is a field with vanishing intrinsic energy momentum, the present theory practically agrees with the conventional Poincaré gauge theory of gravity, except for the seemingly trivial terms in the expression of the spin-angular momentum density. A condition leading to a Riemann-Cartan space-time is given. The field holds a key position in the formulation.     

Random media and eigenvalues of the Laplacian

Let be a fixed number >1. We remove [m ]-balls of centersw ₁, ..., with the same radius /m from a bounded domain inR ³. We consider the asymptotic behaviour of thek ^th eigenvalue of the Laplacian in under the Dirichlet condition as a random variable on a probability space , whenm.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Transverse Thermoelectricity in a Tilted Metallic Multilayer Structure

Thermoelectricity is investigated in a material designed to show anisotropic transport properties: Copper/constantan/copper multilayer structures were prepared by sintering of a compressed stack of alternating foils of these materials and are described by effective in-plane properties and for the Seebeck-coefficient and the thermal conductivity along the layers, and out-of-plane-properties and along the stack axis. Samples in form of thin slabs prepared by cutting the stack obliquely to the stack axis showed thermoelectric fields transverse to temperature gradients across the slab due to off-diagonal elements in the Seebeck-tensor, and may be used as devices for detection of laser radiation.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

Yet another formulation of the Dirac equation

The 2-by-2 Pauli matrix algebra is used to write the 1-by-4 Dirac field in anequivalent 2-by-2 matrix . The current 4-vectors and *_µ are then compared and the latter is shown to not be easily interpretable as a probability density, and also tocontain .     

Complex Hyperspherical Equations, Nodal-Partitioning, and First-Excited-State Theorems in ℝ n

Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z _q+()Y ⁽ⁿ⁾ , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.     

Local properties of equilibrium states and the particle spectrum in quantum field theory

It is shown that in a quantum field theory describing free, scalar particles with masses m _i , i there exist locally normal equilibrium states with finite energy density for all temperature >0 if and only if . This result lends support to the conjecture that the nuclearity criterion proposed by Buchholz and Wichmann is sensitive to the thermodynamical properties of field-theoretic models.     

Nonlinear superposition for Liouville's equation in three spatial dimensions

We derive in 3+0 dimensions exact solutions of Liouville's equation ²=exp , by applying the Bäcklund transformation technique in conjunction with the principle of nonlinear superposition. The procedure, which is later extended to 3+1 dimensions, yield, as a byproduct, particular solutions of ² and ² =exp (² +² ).     

Influence of saturable absorber on critical phenomenon analogies in single mode laser driven by external coherent field

The influence of the existence of absorbing atoms in a laser cavity on the critical exponents of abrupt transitions between steady states in the system of single mode onephoton laser driven by an external coherent field is discussed. An isolated threshold when ,and a kind of threshold when, where is the pump parameter of the absorbing atoms, is obtained. The asymptotic forms of the families of potential functions for the system near these threshold are also found. The well-known scaling hypothesis in the general homogeneous function form is shown to be a characteristic of these asymptotic families. Four threshold exponents, , , and and four threshold amplitudes,B, D, andA, near each of these thresholds, are obtained. The threshold exponents near each threshold obey the scaling laws of critical phenomena, while the corresponding amplitudes obey the definite relations between exponents and amplitudes.     

A spectral characterization of KMS states

Let be a state on aC*-dynamical system . For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O.     

Higher spin BRS cohomology of supersymmetric chiral matter inD=4

We examine the BRS cohomology of chiral matter inN=1,D=4 supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators _{(a, b)} are products of the elementary chiral superfieldsS and and the derivative operatorsD , and . Such superfields _{(a, b)} can be chosen to have a symmetrized undotted indices _i and b symmetrized dotted indices . The result derived here is that each composite superfield _(a,b) is subject to potential supersymmetry anomalies ifa–b is an odd number, which means that _(a,b) is a fermionic superfield.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Eigenvalue Asymptotics for the Schrödinger Operator with a δ-Interaction on a Punctured Surface

Given n2, we put r=min . Let be a compact, C ^r -smooth surface in ⁿ which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L ²( ⁿ ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

Screening Effect Due to Heavy Lower Tails in One-Dimensional Parabolic Anderson Model

We consider the large-time behavior of the solution to the parabolic Anderson problem _tu=u+u with initial data u(0, ·)=1 and non-positive finite i.i.d. potentials . Unlike in dimensions d2, the almost-sure decay rate of u(t, 0) as t is not determined solely by the upper tails of (0); too heavy lower tails of (0) accelerate the decay. The interpretation is that sites x with large negative (x) hamper the mass flow and hence screen off the influence of more favorable regions of the potential. The phenomenon is unique to d=1. The result answers an open question from our previous study [BK00] of this model in general dimension.     

Photophysical Behavior of β-Carboline-3-Carboxylic Acid N-Methylamide

The solvent and temperature effect of fluorescence and phosphorescence and its polarization characteristics for -carboline-3-carboxylic acid N-methylamide were studied. From the results obtained it is concluded that the first excited singlet state changes from the * type in a polar solvent (EPA) to the n* type in a nonpolar solvent (MC) and that the lowest singlet excited states (* type and n* type) interact by vibronic coupling. In the nonpolar solvent (MC) the lowest singlet excited states are very close in energy and consequently the vibronic coupling is stronger. It has been found that the 0–0 band of the phosphorescence emission in EPA is polarized out of plane, using the excitations corresponding to absorptions into the first and second excited * singlet states. This fact and the order of lifetime measured indicate an emitting triplet that is *. The origin of this polarization is very likely mixing as a result of spin–orbit coupling. However, the vibrational structures and changing polarization outside the 0–0 band indicate that second-order effects involving spin–orbit coupling and vibronic interactions are important and the mixing scheme appears to be and . The proximity effect can qualitatively explain the absence of phosphorescence and the stronger vibronic interaction between the n* and the * states of -carboline-3-carboxylic acid .N-methylamide in a hydrocarbon solvent (MC).