Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

An upper bound on the critical temperature for a continuous system with short-range interaction

A classical gas with short-range interaction in the grand canonical ensemble is studied. Ifp(, z) denotes the thermodynamic pressure at inverse temperature and activityz, then it follows from the Mayer expansion thatp(, z) is infinitely differentiable provided andz are sufficiently small. Here it is shown that there exists ₀>0 such thatp(, z) is infinitely differentiable if< ₀ andz>0. One can interpret this result as saying that ( ₀)^–1 is an upper bound on the critical temperature for the system.     

Relationship between field shift and phase constant change in two-dimensional three-layered dielectric or hollow waveguides due to uniform bends

It is shown theoretically that the field shift x and phase constant change in two-dimensional three-layered dielectric or hollow waveguides bent uniformly with large bending radiusR are related by x = 2R/ ₀, where ₀ is the axial phase constant. The relationship predicts that the field distributions of the TE₀ or TM₀ mode shift toward the outward direction of bending, whereas those of other TE _n or TM _n (n=1,2,...) modes shift inward in a hollow waveguide. Characteristic features in dielectric waveguides are also described.     

Random surfaces with two-sided constraints: An application of the theory of dominant ground states

We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints _x m/2. The main result is that for ₀, where ₀ does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two.     

The Critical Attractive Random Polymer in Dimension One

A polymer chain with attractive and repulsive forces between the building blocks is modeled by attaching a weight e ^– for every self-intersection and e ^/(2d) for every self-contact to the probability of an n-step simple random walk on ^d , where , >0 are parameters. It is known that for d=1 and > the chain collapses down to finitely many sites, while for d=1 and < it spreads out ballistically. Here we study for d=1 the critical case = corresponding to the collapse transition and show that the end-to-end distance runs on the scale _n = (log n)^–1/4. We describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size _n times a constant. Moreover, we derive the asymptotics of the partition function.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

Fluorescence of horse liver alcohol dehydrogenase using one- and two-photon excitation

We examined the steady-state and time-resolved emission of liver alcohol dehydrogenase resulting from one-photon and two-photon excitation. Previous studies with one-photon excitation revealed that the two nonidentical tryptophan residues display different emission spectra and decay times. The use of two-photon excitation resulted in similar emission spectra, multiexponential intensity decays, time-resolved emission spectra, and anisotropy decays as was observed for one-photon excitation. These results suggest that both nonidentical tryptophan residues are excited to a similar extent for one- and two-photon excitation. However, the limiting anisotropy (r ₀) with two-photon excitation from 585 to 610 nm is below 0.1 and appears distinct from that observed previously forN-acetyl-l-tryptophanamide.Abbreviations LADH liver alcohol dehydrogenase - -NAD⁺ -nicotinamide adenine dinucleotide - OPE one-photon excitation - OPIF one-photon induced fluorescence - TPE two-photon excitation - TCSPC time-correlated single photon counting - TPIF two-photon induced fluorescence     

A Boltzmann map for quantum oscillators

We define a map on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points ofx. The map is the composition of a doubly stochastic map T^* and the quasifree reductionQ. Under mixing conditions onT, iterates of take any initial state to the Gibbs state, provided that the oscillator frequencies are mutually rational. We give an example of a system with three degrees of freedom with energies ₁, ₂, and ₃ mutually irrational, but obeying a relation n₁₁+n₂₂=n₃₃,n _i . The iterated Boltzmann map converges from an initial statep to independent Gibbs states of the three oscillators at betas (inverse temperatures) ₁,₂, ₃ obeying the equation n₁₁₁+n₂₂₂=n₃₃₃. The equilibrium state can be rewritten as a grand canonical state. We show that for two, three, or four fermions we can get the usual rate equations as a special case.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

The [, , ]-Langevin equation describes the time evolution of a real stationary process withT-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [, , ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics.     

Phases of the number-theoretic spin chain

We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition functionZ()=(–1)/() at the inverse temperature _cr=2.     

Some remarks on pathologies of renormalization-group transformations for the Ising model

The results recently obtained by van Enter, Fernandez, and Sokal on non-Gibbsianness of the measurev =T _{b ,h} arising from the application of a single decimation transformationT _b , with spacingb, to the Gibbs measure _,h , of the Ising model, for suitably chosen large inverse temperature and nonzero external fieldh, are critically analyzed. In particular, we show that if, keeping fixed the same values of, h, andb, one iterates a sufficiently large number of timesn the transformationT _b , one obtains a new measurev = (T _b )_n,h which is Gibbsian and moreover very weakly coupled.     

Search of the chemical change of the119mSn (T1/2=293 days) radioactive decay rate

The differences in decay rates of the nuclear isomer^119mSn (T_1/2=293 days; the strongly converted M4 transition) have been measured for different chemical compounds. The experimental results show that the^119mSn nuclei in the telluride SnTe decay faster then in the metal -Sn and in the dioxide SnO₂ [the relative change / of the decay probability is +(3.6±1.4)·10^–4]. No measurable difference between the decay rates of^119mSn in -Sn and SnO₂ has been observed [(/=–(0.1±1.2)·10^–4], irrespective of the great difference in electronic structure of the tin atoms. The results cannot be explained by considering the internal conversion of the valence electrons only. It is necessary to assume that the chemical changes of the decay rate are strongly influenced by the chemical changes of the probabilities of the internal conversion of electrons of the inner shells of the atom. This conclusion is confirmed by theoretical calculations. They show that for the deep inner subshells the relative changes _nlj/_nlj of the internal conversion coefficients _nlj are much greater than the relative changes _nlj/_nlj of the electron densities near the nucleus _nlj.     

Determination of the electron phonon coupling and the superconducting gap in β-(BEDT-TTF)2X crystals (X=I3, IAuI)

We performed point-contact and tunneling measurements on the organic superconductors -(BEDT-TTF)₂I₃ and -(BEDT-TTF)₂IAuI, in the normal and superconducting states. The point-contact measurement in the normal state provides the Eliashberg function ²()F (). This function has maxima at 4 and 15 mV, as well as a sharp peak at 1 mV which seems to indicate a very soft phonon strongly coupled to the electrons. The measurements in the superconducting state provide the superconducting gap, which for the tunneling measurements has a value 2/k_B T_c4, just slightly above the BCS value.     

The energy-momentum gravitational pseudotensor and Kerr-Schild metrics

It is shown that the Landau-Lifshitz pseudotensor vanishes for any Kerr-Schild metricg =n + 2Hl l satisfying the conditionS l =0. Some solutions verifying this condition are indicated.     

On the layering transition of an SOS surface interacting with a wall. I. Equilibrium results

We consider the model of a 2D surface above a fixed wall and attracted toward it by means of a positive magnetic fieldh in the solid-on-solid (SOS) approximation when the inverse temperature is very large and the external fieldh is exponentially small in . We improve considerably previous results by Dinaburg and Mazel on the competition between the external field and the entropic repulsion with the wall, leading, in this case, to the phenomenon of layering phase transitions. In particular, we show, using the Pirogov-Sinai scheme as given by Zahradník, that there exists a unique critical valueh _k ^* () in the interval (1/4e ^–4k , 4e ^–4k ) such that, for allh(h _k+1 ^* ,h _k ^* ) and large enough, there exists a unique infinite-volume Gibbs state. The typical configurations are small perturbation of the ground state represented by a surface at heightk+1 above the wall. Moreover, for the same choice of the thermodynamic parameters, the influence of the boundary conditions of the Gibbs measure in a finite cube decays exponentially fast with the distance from the boundary. Whenh=h _k ^* () we prove instead the convergence of the cluster expansion for bothk andk+1 boundary conditions. This fact signals the presence of a phase transition. In the second paper of this series we will consider a Glauber dynamics for the above model and we will study the rate of approach to equilibrium in a large finite cube with arbitrary boundary conditions as a function of the external fieldh. Using the results proven in this paper, we will show that there is a dramatic slowing down in the approach to equilibrium when the magnetic field takes one of the critical values and the boundary conditions are free (absent).     

Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models

Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ _x,y const/¦x–y¦². For translation-invariant systems with well-defined lim _x x ² J _x =J ⁺ (possibly 0 or ) we establish: (1) There is no long-range order at inverse temperatures withJ ⁺1. (2) IfJ ⁺>q, then by sufficiently increasingJ ₁ the spontaneous magnetizationM is made positive. (3) In models with 0<J ⁺< the magnetization is discontinuous at the transition point (as originally predicted by Thouless), and obeysM( _c )1/( _c J ⁺)^1/2. (4) For Ising (q=2) models withJ ⁺<, it is noted that the correlation function decays as xy()c()/|x–y|² whenever< _c . Points 1–3 are deduced from previous percolation results by utilizing the Fortuin-Kasteleyn representation, which also yields other results of independent interest relating Potts models with different values ofq.