The irreversible thermodynamics of black holes

The action of quantum fluctuations of the gravitational field may be regarded as the origin of the dissipative processes associated with Hawking radiation. In this picture the black hole possesses internal coherence by virtue of the localization of its mass. The cumulative effect of the quantum fluctuations in the geometry is that this coherence is corrupted and the mass is sapped away.This essay was awarded the fourth prize for 1977 by the Gravity Research Foundation.     

Spontaneous quantum gravity: A soluble model

We present a model of gravity in which the Planck mass is generated spontaneously by a similar mechanism that is responsible for the tension in a recent membrane model of strings. The action describes very floppy fluctuations of the physical space in some large flat embedding space. The coupling constant is dimensionless but the fluctuations are so violet that they produce spontaneously a mass which plays the role of the dimensionally transmuted coupling constant and can be identified with the Planck mass.     

Optical conductivity of single-layer graphene induced by temporal mass-gap fluctuations

We consider the dynamics of charge carriers in single-layer graphene that are subject to random temporal fluctuations of their mass gap. The optical conductivity is calculated by incorporating the quantum-stochastic time evolution into the standard linear-response (Kubo) theory. We find that, for an intermediate range of frequencies below the average gap size, electron transport is enhanced by fluctuations. At the same time, in the limit of high as well as low frequencies, the conductivity is suppressed as the variance of gap fluctuations increases. In particular, the dc conductivity is always suppressed by a random temporal mass with nonvanishing mean value and vanishes in the zero-temperature limit. Our results are complementary to those obtained recently for static random-gap disorder in finite-size systems.     

Quantum fluctuations in the conformally flat and the schwarzschild space-times

A general technique is described for dealing with the quantum fluctuations between conformally flat space-times. The second part of the paper deals with the Schwarzschild spacetime. It is shown there that this space-time is stable against fluctuations of mass, but transitions between two space-times of different masses can be obtained via conformai fluctuations. Purely conformal fluctuations of the Schwarzschild metric are, however, damped at the event horizon. Similar conclusions are drawn about the Reissner-Nordstrom space-time.     

In-beam study of105In and103In

The effects on pair density fluctuations in superfluid nuclei, associated with the projection on good particle number, are studied. The model, which is based on standard particle number projection techniques, is developed for the case of one and two-body density fluctuations in spherical superfluid nuclei. The results, for the case of some even mass isotopes of Sn, show that pair density fluctuations and the derivative of the one body density almost coincide in a number projected BCS treatment of pairing correlations.     

Validity of the law of mass action in three-dimensional coagulation processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long-wavelength fluctuations and is a universal function of the macroscopic decay rate.     

Decoherence and Bare Mass Induced by Nonconformal Metric Fluctuations

The effects, upon the Klein–Gordon field, of nonconformal stochastic metric fluctuations, are analyzed. It will be shown that these fluctuations allow us to consider an effective mass, i.e., the mass detected in a laboratory is not the parameter appearing in the Klein–Gordon equation, but a function of this parameter and of the fluctuations of the metric. In other words, in analogy to the case of a nonrelativistic electron in interaction with a quantized electromagnetic field, we may speak of a bare mass, where the observed mass shows a dependence upon the stochastic terms included in the metric. Afterwards, we prove, resorting to the influence functional, that the energy–momentum tensor of the Klein–Gordon field inherites this stochastic behavior, and that this feature provokes decoherence upon a particle immersed in the region where this tensor is present.     

Electronic polarizability of superconductors and inertial mass of a moving vortex

The problem of a vortex electromagnetic mass in a superconductor is considered accounting for the self-interaction effect conditioned by the coupling of the moving vortex to the excited fluctuations of the superfluid density. The obtained polaron-type mass exceeds the earlier obtained electromagnetic mass in view of the large value of the light speed relation to the Fermi velocity and can dominate over the vortex core mass.     

Fluctuations in apparent mass at the bottom of granular columns due to different arrangements

We report the fluctuations in apparent mass at the bottom of granular columns due to various configurations. It is found that the fluctuations decrease with the increase in the ratio of diameters of silo to grain. For the arrangement of different grain layers in a column, the higher fluctuations appear when the larger grains are stacked at the bottom layer while reversing the order of grain-layers leads to smaller fluctuations. We attribute this behavior to the randomness in the direction of frictional forces between the grains and the confining wall. Moreover, due to polydisperse media, the development of inhomogeneous force transmission in grains may cause this to happen.     

Energy Mechanism of Charges Analyzed in Real Current Environment

We analyze in this work the energy transfer process of accelerated charges, the mass fluctuations accompanying this process, and their inertial properties. Based on a previous work, we use here the dipole antenna, which is a very convenient framework for such analysis, for analyzing those characteristics. We show that the radiation process can be viewed by two energy transfer processes: one from the energy source to the charges and the second from the charges into the surrounding space. Those processes, not being in phase, result in mass fluctuations. The same principle is true during absorption. We show that in a transient period between absorption and radiation the dipole antenna gains mass according to the amount of absorbed energy and loses this mass as radiated energy. We rigorously prove that the gain of mass, resulting from electrical interaction has inertial properties in the sense of Newton's third low. We arrive to this result by modeling the reacting spacetime region by an electric dipole.     

Phase space dependence of the correlations among particles produced in high energy nuclear collisions

The fluctuations of produced particles are investigated in central collisions of proton, oxygen and sulphur projectiles with (Ag,Br) target nuclei at 200 GeV per nucleon. The analysis is carried out in terms of factorial moments and correlation integrals in different pseudorapidity regions. Evidence is found for nonstatistical fluctuations. These fluctuations depend weakly on the phase space, although a slightly stronger effect is seen in the forward pseudorapidity region. The dependence of the observed effect on the mass of the projectile particle disagrees with the expectations of superposition models. The results of this analysis indicate that a self-similar cascade process is the origin of the fluctuations, even though the association of the observed effect with the occurence of a second order phase transition cannot be definitely ruled out.     

Fluctuation interactions of colloidal particles

For like-charged colloidal particles, two mechanisms of attraction between them survive when the interparticle distance is larger than the Debye screening length. One of them is the conventional van der Waals attraction and the second is the attraction mechanism mediated by thermal fluctuations of particle position. The latter is related to the effective variable mass (Euler mass) of the particles produced by the fluid motion. The strongest attraction potential (up to the value of the temperature T) corresponds to the case of uncharged particles and a relatively large Debye screening length. In this case, the third attraction mechanism is involved. It is mediated by thermal fluctuations of the fluid density.     

Squeezing of quantal fluctuations

We solve the Schrödinger equation for a harmonic oscillator with time-dependent mass. When this mass increases boundlessly, quantum uncertainties are strongly diminished. This effect is used for a collective theory of charge equilibration. We conclude that present data cannot prove the existence of quantal fluctuations in deep inelastic reactions.     

The Angular Dependence of the Coherence Energy in Dissipative Reaction of 19F+51V

Excitation function fluctuations for projectile-like fragments from ¹⁹F+⁵¹V dissipative reaction within the energy region of 102.25—109.50MeV are reported.The statistical method is applied to the analysis of energy coherence in the cross rection fluctuations and the strong cross correlation between exit channels is obtained.The dependences on charge number and on mass number are presented.The relation between angular velocity damping and the rotational energy dissipation is discussed.     

Description of evaporation of a spherical liquid drop by a non-Markovian random process based on integral stochastic equations

Processes of evaporation (condensation) of vapor particles from the surface of a spherical drop and processes of their diffusion into surrounding volume are considered. Special features of evaporation are investigated taking into account vapor particle fluctuations caused by random changes in the temperature, concentration, etc. Statistical characteristics of fluctuations of the corresponding quantities, including the mass flow through the liquid-vapor boundary and concentration on the liquid surface, are presented. The distribution of completely evaporated drop number versus time is presented.     

Analytical Study of Giant Fluctuations and Temporal Intermittency

We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the boundaries. We calculate various static and dynamical properties of the total mass in the system for both biased and unbiased movement of particles and different boundary conditions. These calculations show that (i) in the unbiased case, the total mass has a non-Gaussian distribution and shows giant fluctuations which scale as system size (ii) in all the cases, the system shows strong intermittency in time, which is manifested in the anomalous scaling of the dynamical structure functions of the total mass. The results are derived by taking a continuum limit in space and agree well with numerical simulations performed on the discrete lattice. The analytic results obtained here are typical of the full phase of a more general model with fragmentation, which was studied earlier using numerical simulations.     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. II. Quantum bipolarons

We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the vicinity of the adiabatic limit. Several approaches to investigate the quantum mobility of polarons and bipolarons are proposed for this model. First, the quantum fluctuations are treated as perturbations of the mean-field (or adiabatic) approximation of the electron-phonon coupling in order to calculate the bipolaron bands. It is found that the bipolaron mass generally remains very large except in the vicinity of the triple point of the phase diagram (see [1]), where the bipolarons have several degenerate configurations at the adiabatic limit (single site (S0), two sites (S1) and quadrisinglet (QS)), while the polarons are much lighter. This degeneracy reduces the bipolaron mass significantly. Next we improve this result by variational methods (modified Toyozawa Exponential Ansatz or TEA) valid for larger quantum perturbations away from the adiabatic limit. We first test this new method for the single polaron. We find that the triple point of the phase diagram is washed out by the lattice quantum fluctuations which thus suppress the light bipolarons. Further improvements of the method by hybridization of several TEA states do not change this conclusion. Next we show that some model variations, for example a phonon dispersion may increase the stability of the (QS) bipolaron against the quantum lattice fluctuations. We show that the triple point of the phase diagram may be stable to quantum lattice fluctuations and a very sharp mass reduction may occur, leading to bipolaron masses of the order of 100 bare electronic mass for realistic parameters. Thus we argue that such very light bipolarons could condense as a superconducting state at relatively high temperature when their interactions are not too large, that is, their density is small enough. This effect might be relevant for understanding the origin of the high superconductivity of doped cuprates far enough from half filling. Received 15 September 1999     

Gibbs ensembles in relativistic classical and quantum mechanics

Classical and quantum Gibbs ensembles are constructed for equilibrium statistical mechanics in the framework of an extension to many-body theory of a relativistic mechanics proposed by Stueckelberg. In addition to the usual chemical potential in the grand canonical ensemble, there is a new potential corresponding to the mass degree of freedom of relativistic systems. It is shown that in the nonrelativistic limit the relativistic ensembles we have obtained reduce to the usual ones, and mass fluctuations for the free-particle gas approach the fluctuations in N. The ultrarelativistic limit of the canonical ensemble for the free-particle gas differs from the corresponding limit of the ensemble proposed by Jüttner and Pauli. Due to the mass degree of freedom, the quantum counting of states is different from that of the nonrelativistic theory. If the mass distribution is sufficiently sharp, the thermodynamical effects of this multiplicity will not be large. There may, however, be detectable effects such as a shift in the Fermi level and the critical temperature for Bose-Einstein condensation, and some change in specific heats.     

Transverse collective modes in liquid binary alloys

Transverse current correlations in binary liquid alloys are investigated by molecular dynamics simulation. The study includes several Li-Mg, Li-Na and Li-Pb alloys. The characteristics of both shear and transverse optic-like modes are discussed. The former modes are associated with the number density fluctuations whereas the latter are related to the concentration fluctuations. Special attention is paid to the dependence of the results on the mass ratio and composition of the alloy.     

Ion acoustic turbulent resistivity of a two-ion plasma

A multicomponent plasma consisting of two-ion species having different mass and temperature is considered. Linear and non-linear dispersion relations have been derived. These are used to study the effect of turbulent fluctuations on the plasma resistivity. Results have been applied to the cases of a hydrogen-helium and a hydrogen-argon mixture. It is seen that the resistivity increases or decreases significantly with the addition of a light ion impurity depending upon temperature and mass ratio.