The thermodynamics of a system containingn identical black holes and black-body radiation

The problem ofn identical black holes in a box separated by partitions is considered. Each black hole is in thermal equilibrium with black-body radiation. The separating partitions are removed and the possible final states of the combined system are investigated. Limits on the amount of gravitational wave energy that can be produced are calculated, and it is shown that forn large enough, as large a fraction of the initial energy as is desired may be extracted as gravitational waves.     

Maslov distribution and formulas for the entropy

The Maslov distribution for a system of identical particles is used. The entropy and some other thermodynamical characteristics of this system are found for diverse fractal dimensions. A general formula for the entropy is established, which shows that the entropy is proportional to the derivative of the system energy with respect to the temperature. It is shown that a parastatistical parameter b, which is introduced formally, is related to the temperature of the system indeed. The nature of the phase transition in the system is studied in the two-dimensional case.     

Monte Carlo evaluation of trial wavefunctions for the fractional quantized Hall effect: Spherical geometry

Monte Carlo methods have been employed to evaluate trial wave-functions for quantized Hall states and excitations using up to 92 electrons on a sphere. Results are presented for the energy of quasiparticle and quasihole excitations at filling factorv=1/3. These are consistent with extrapolations of exact small system calculations and earlier Monte Carlo results. A trial wavefunction for neutral excitations atv=1/m (m odd integer) is proposed. Results for its excitation energy in the long wavelength limit, atv=1/3, are consistent with those based on the single mode approximation. We have also studied a trial wavefunction representing a quasiparticle excitation involving an electron with reversed spin. Results are presented for the effects on excitation energies of the finite extent of the electron wave function perpendicular to the surface. We have also evaluated the energy of a microscopic trial wave-function for the ground state atv=2/5.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Wave mechanics and the tunnel effect

It is shown that the nonconservation of energy to the extent given by the uncertainty relation can be interpreted also as the storing of inner energyQ by a wave mechanical system. The latter formalism is, apart from its terminology, identical with the accepted one.     

Highly efficient beamline and spectrometer for inelastic soft X‐ray scattering at high resolution

The design, construction and commissioning of a beamline and spectrometer for inelastic soft X‐ray scattering at high resolution in a highly efficient system are presented. Based on the energy‐compensation principle of grating dispersion, the design of the monochromator–spectrometer system greatly enhances the efficiency of measurement of inelastic soft X‐rays scattering. Comprising two bendable gratings, the set‐up effectively diminishes the defocus and coma aberrations. At commissioning, this system showed results of spin‐flip, d–d and charge‐transfer excitations of NiO. These results are consistent with published results but exhibit improved spectral resolution and increased efficiency of measurement. The best energy resolution of the set‐up in terms of full width at half‐maximum is 108 meV at an incident photon energy tuned about the Ni L₃‐edge.     

Twist of growing bacterial colonies

Twist observed in growing bacterial colonies at the macrolevel is explained in terms of the self-assembly (self-organization) of film-forming protein clusters, since the in vitro and in vivo behavior and symmetry properties of protein in an open thermodynamically nonequilibrium system are identical. The self-assembly of elastic protein films in the course of condensation in the protein-water system obeys the laws of the elasticity theory. As the viscosity of the system grows, the transition of the protein from the liquid-crystal to the solid phase occurs. This transition has a nonlinear dynamics, which also shows up at the macrolevel. Opposite vorticities (twist) appear in the system. Such a modification of protein has been named protos. It is hypothesized that the formation of an elastic nonequilibrium protos film is consistent with the behavior and orientation of elastic forces and magnetic fields in the presence of unlike electric charges.     

H+D2O→HD+OD反应的微分截面:一种全维态-态量子动力学计算

用含时波包方法计算得到H+D₂O→HD+OD反应的第一个初始基态,第一对称（100）和反对称（001）伸缩振动激发态的全维态-态微分截面.计算的三个初始态的微分截面在低碰撞能量下都是很强的后向散射.随着碰撞能量的增加,微分截面越来越宽,伴随着峰的位置逐渐向小角度移动,与标题反应是一个通过抽取机理的直接反应相一致.发现（100）和（001）态不只有几乎完全相同的积分截面,还有基本相同的微分截面-在相同的总能量下和基态反应也接近.反应产生的OD只有很小一部分在v=1态上,其分布几率和基态与振动激发态的相对几率相似,从而证实了Zare等人的实验结果和局域模式图像.另外让人意想不到的是,在相同的总能量下,伸缩激发抑制了产物HD的转动激发.     

Discrete Stochastic Modeling for Epidemics in Networks

In this paper, we construct a microscopic mechanism for the epidemic processes in heterogeneous populations, which contains two basic assumptions: all edges of the network are broken and reconnected at every time step among the epidemic process; the probability of randomly chosen two half-edges to make a pair is identical. We define the stochastic epidemic process and get the epidemic distributions numerically according to the transmission probability λ. Two different phases are observed, which means the onset of phase transition, and the threshold value is very small. Under the thermodynamic limit, the process can be approximated by a deterministic dynamical system. About this deterministic system, we get the analytical threshold value, which is consistent with the numerical results of the epidemic distributions.     

The two-body problem in Rosen's bimetric theory of gravitation

This is a continuation of a previous paper, in which the field equations in successive approximations and the post-Newtonian equations of motion in Rosen's theory of gravitation were derived. In this paper the energy integral and the center of mass for an insular system with an arbitrary structure are obtained in the post-Newtonian approximation. A many-body system is considered, and in the extreme case of point bodies (particles) the center-of-mass coordinates are found to be identical with the Einsteinian ones. The two-body problem is considered. For a system of two identical neutron stars of mass 1.3M (a possible model of the Hulse-Taylor binary pulsar system) the trajectory and the perihelion precession are calculated. It is found that the expressions obtained depend on the gravitational self-energy of the stars. The relations deduced from Rosen's bimetric gravitation in the case of small velocities and weak fields are compared with those of general relativity.In partial fulfillment of the requirements for Dr.Sc. degree at the Technion-Israel Institute of Technology.     

On Møller's tetrad theory of gravitation. Gravitational radiation

In the background of Møller's theory, two energy-momentum complexest andP, are defined. From them, the losses of energy and angular momentum of a nongravitationally bound system due to the radiation of gravitational waves are evaluated. To solve the field equations some approximation procedures are used. The post-Newtonian limit is studied. When the modulus of the coupling constant of the theory is smaller than 10³ and some reasonable conditions are assumed, the results here obtained appear to be identical to those of general relativity. The work performed here would be basic when dealing with some important questions in generalizing Møller's theory.     

Break-up stage restoration in multifragmentation reactions

In the case of Xe + Sn at 32MeV/nucleon multifragmentation reaction break-up fragments are built up from the experimentally detected ones using evaluations of light-particle evaporation multiplicities which thus settle fragment internal excitation. Freeze-out characteristics are extracted from experimental kinetic energy spectra under the assumption of full decoupling between fragment formation and energy dissipated in different degrees of freedom. The thermal kinetic energy is determined uniquely while for the freeze-out volume - collective energy a multiple solution is obtained. The coherence between the solutions of the break-up restoration algorithm and the predictions of a multifragmentation model with identical definition of primary fragments is regarded as a way to select the true value. The broad kinetic energy spectrum of ³He is consistent with the break-up genesis of this isotope.     

Decay of a negative molecular ion in a constant electric field

The problem of the shift and broadening of the electron energy levels in the field of two 3D short-range potentials (e.g., the model of a negative molecular ion) by a constant electric field F is considered. The interaction of an electron with attraction centers is taken into account in the effective range approximation. We analyze the cases when both centers maintain weakly bound s states and when the electron state in the field of one of the centers is a p state. Exact numerical results for the shift and the width of the energy levels of a quasi-molecule as functions of field F, distance R between atomic centers, and the orientation of the quasi-molecule axis relative to vector F are presented, as well as the results of analytic treatment for a number of limiting cases. The exact values of complex energies of the quasi-molecule are compared with analytic results for a weak field in the case of identical s centers [26], as well as nonequivalent s centers and s-p centers; the applicability boundaries of the weak field approximation are established. It is shown that for large values of R, the position and width of the levels in a strong field are correctly described in perturbation theory in the exchange interaction. We analyze the field-induced quasi-intersection of molecular energy levels of the system with nonequivalent atomic centers and peculiarities in the energy level widths associated with this intersection. The results make it possible to qualitatively interpret the results of numerical calculations of the probability of homo- and heteronuclear molecules being ionized by a low-frequency laser field.     

Lifshitz points in ising systems

Phase diagrams of Ising systems with competing interactions are calculated using (a) the method of Müller-Hartmann and Zittartz to determine the transition temperature via the vanishing of an interface free energy (b) a Migdal-Kadanoff bond-moving scheme and (c) Monte Carlo simulations. It is shown that in two-dimensional Ising systems a uniaxial Lifshitz point can exist at non-zero temperatures, whereas the lower critical dimensiond _l for a Lifshitz point in a system with identical competing interactions along each of its cartesian axis isd _l 2.     

Stochastic theory of nonlinear rate processes with multiple stationary states. II. Relaxation time from a metastable state

We have developed a methodology for obtaining a Fokker-Planck equation for nonlinear systems with multiple stationary states that yields the correct system size dependence, i.e., exponential growth with system size of the relaxation time from a metastable state. We show that this relaxation time depends strongly on the barrier heightU(x) between the metastable and stable states of the system. For a Fokker-Planck (FP) equation to yield the correct result for the relaxation time from a metastable state, it is therefore essential that the free energy functionU(x) of the FP equation not only correctly locate the extrema of U(x), but also have the correct magnitudeU at these extrema. This is accomplished by so choosing the coefficients of the FP equation that its stationary solution is identical to that of the master equation that defines the nonlinear system.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Multiple expansions for energy and momenta carried by gravitational waves

We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar Ψ ₄. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear momentum and angular momentum starting from the gravitational waveforms which are typically extracted from numerical simulations. An erratum to this article can be found at     

Spin fluctuation contribution to the specific heat of strongly correlated fermions

We calculate the free energy of a system of fermions at low temperatures within the Hubbard model using a slave boson representation, which generalizes the approach of Kotliar and Ruckenstein. The mean field approximation is identical to Gutzwiller's solution. The one-loop corrections provide aT ³ lnT spin fluctuation contribution to the specific heat, which reduces for weak coupling to the result of paramagnon theory first derived by Brenig et al.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Diffractive jet production in deep-inelastic e^+p collisions at HERA

A measurement is presented of dijet and 3-jet cross sections in low- diffractive deep-inelastic scattering interactions of the type , where the system X is separated by a large rapidity gap from a low-mass baryonic system Y. Data taken with the H1 detector at HERA, corresponding to an integrated luminosity of 18.0 pb, are used to measure hadron level single and double differential cross sections for and . The energy flow not attributed to jets is also investigated. The measurements are consistent with a factorising diffractive exchange with trajectory intercept close to 1.2 and tightly constrain the dominating diffractive gluon distribution. Viewed in terms of the diffractive scattering of partonic fluctuations of the photon, the data require the dominance of over states. Soft colour neutralisation models in their present form cannot simultaneously reproduce the shapes and the normalisations of the differential cross sections. Models based on 2-gluon exchange are able to reproduce the shapes of the cross sections at low values. Received: 21 December 2000 / Published online: 6 April 2001     

Ab-initio Study of Small Silver Nanoclusters

We explore the lowest energy structures and investigate the structural and electronic properties of small Ag_N (N = 1–10) clusters by employing an ab-initio self-consistent density functional method in the local density approximation. The calculation of binding energy, bond length and the energy difference of HOMO–LUMO states have been carried out in a large energy interval for different isomeric forms of Ag clusters. The cluster binding energies increases rapidly with cluster size, which is consistent with the size dependence properties of clusters but our values are slightly higher than the other calculations.     

Thermodynamics of a Sine-Gordon breather gas

A consistent, divergence-free approach to classical soliton-gas phenomenology of integrable nonlinear systems is presented. Difficulties with current approaches are assessed and a method to achieve consistent phase-space sharing between linear and nonlinear excitations is presented. Results for the free energy of the Sine-Gordon chain exhibit only slight discrepancies when compared to exact (transfer integral) calculations. An interesting cutoff structure is revealed, with the exclusion of breathers with energies less than 2k _B T.     

A stochastic theory of non-ideal behaviour

An approximate theory is proposed for the thermal relaxation of condensed binary [A, B] systems. During the relaxation the composition varies, or is kept constant. (The former case corresponds to an Ising lattice, the latter to a binary alloy, for example.) A variation of the composition is described with the help of a stochastic exchange A?B (as in the Glauber Model), but the microscopic transition probabilities are replaced by smoothed probabilities which depend on the system's composition and internal energy, as proposed in Part I. The variation of the internal energy is estimated with the help of a dynamic counter-part of the quasi-chemical approximation. The equations can be integrated numerically, describing the time dependence of the system's composition (if varying), internal energy, entropy and of intensive parameters corresponding to transient ‘quasi-equilibria’. The theory is applied to an Ising lattice undergoing heating or cooling through the critical temperature and compared with Monte Carlo simulation of identical processes. The agreement is judged to be very good, especially since it involves no parameter fitting. The relaxation of an [A, B] system of fixed composition, undergoing cooling to inside the co-existence curve is also studied. Three alternative lines for the evolution of internal energy are estimated: (i) unstable, with no decomposition into two phases; (ii) metastable, with spinodal decomposition and (iii) stable, with binodal decomposition. Comparison with a computer simulation of the process indicates that the initial relaxation (up to order of 100 trial exchanges per particle, depending on the system's size) fits the metastable line, the initial stage being followed by an extremely slow crossover to the stable line.