Entropic Corrections to Coulomb’s Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde’s argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb’s law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb’s law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb’s law as well as the entropy corrected Poisson’s equation which governing the evolution of the scalar potential ϕ. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.     

有限温度下一维Gaudin-Yang模型的热力学性质

本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.     

On the theory of short light pulse propagation in a turbulent medium

We consider the problem of propagation of light pulses in a turbulent medium. Within the framework of the used approximation, we obtain a formula for the average intensity of the pulsed signal. Using this formula, we estimate the time delay of the pulse and its broadening. We find the characteristic time scales determining the light pulse transformation in a turbulent medium. The physical meaning of these time scales is explained qualitatively. The quantitative estimates for the Earth’s atmosphere show that the phenomena in question are significant only for very short, picosecond pulses. a. M. Obukhov Institute of the Physics of Atmosphere, Moscow, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 456–467, September, 2000.     

Strong suppression of Coulomb corrections to the <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> pair production cross section in ultrarelativistic nuclear collisions

The semiclassical correction to Molière’s formula for multiple scattering is derived. The consideration is based on the scattering amplitude obtained with the first semiclassical correction taken into account for an arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to Molière’s formula contains the target density n and thickness L not only in the combination nL (areal density). Therefore, this correction can be referred to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide range of applicability of Molière’s formula. The article is published in the original.     

Correction to Molière’s formula for multiple scattering

The semiclassical correction to Molière’s formula for multiple scattering is derived. The consideration is based on the scattering amplitude obtained with the first semiclassical correction taken into account for an arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to Molière’s formula contains the target density n and thickness L not only in the combination nL (areal density). Therefore, this correction can be referred to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide range of applicability of Molière’s formula.     

Grad’s 13 Moment Equations in a Modified Form

We describe a hierarchy of formal expansions that represent the Fourier transform of a solution of the Boltzmann equation. The constructed approximations are based on the family of weighted Taylor expansions. The first two representations correspond to the Maxwellian and to the Gaussian expansions. The third representation has a weight that generalizes the Gaussian and it depends on the first 13 moments of the Boltzmann density f. It can be shown that this weight is Galilean invariant and it is close to the Gaussian, providing that the heat fluxes are not too large. The 13 moment weight yields a revised form of Grad’s 13 moment expansion for the Boltzmann equation. In search for the entropy dissipation inequality, we also examine the relation between Levermore’s 14 moment density and Grad’s 13 moment expansion. First, we show that the coefficients of the Godunov potential are described by a system of partial differential equations, with coefficients that depend on the Fourier transform of the Levermore’s density f _Λ itself. Then, we argue that the same Taylor expansion exploited in the Grad’s scheme, can be used to approximate Levermore’s 14 moment density. We also show that the weighted Taylor expansions are related to a formal solution of the Hamburger problem.     

Grad’s 13 Moment Equations in a Modified Form

We describe a hierarchy of formal expansions that represent the Fourier transform of a solution of the Boltzmann equation. The constructed approximations are based on the family of weighted Taylor expansions. The first two representations correspond to the Maxwellian and to the Gaussian expansions. The third representation has a weight that generalizes the Gaussian and it depends on the first 13 moments of the Boltzmann density f. It can be shown that this weight is Galilean invariant and it is close to the Gaussian, providing that the heat fluxes are not too large. The 13 moment weight yields a revised form of Grad’s 13 moment expansion for the Boltzmann equation. In search for the entropy dissipation inequality, we also examine the relation between Levermore’s 14 moment and Grad’s 13 moment expansion. First, we show that the coefficients of the Godunov potential are described by a system of partial differential equations, with coefficients that depend on the Fourier transform of the Levermore’s density fΛ. Then, we argue that the same Taylor expansion exploited in the Grad’s scheme can be used to approximate Levermore’s 14 moment density. We also show that the weighted Taylor expansions are related to a formal solution of the Hamburger problem.     

Light-beat method to process phase fluctuations of a laser light beam

A method for real-time processing of phase fluctuations of a laser beam is described. A beat photocurrent whose phase undergoes random fluctuations is generated by two laser beams at different frequencies, propagating through a turbulent atmosphere. The phase fluctuation component of the beat can be recovered in real-time over a wide range of phase angle, not restricted within 2π, by a specially designed circuit. Probability density functions, autocorrelation functions, and variances of the phase fluctuations are displayed in real-time as most basic quantities of the fluctuations. Visiting Fellow at Department of Electronics, The University of Southampton, England, October 1974–September 1975.     

Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere

With the help of the generalized Huygens–Fresnel integral and the ABCD matrix approach a bistatic LIDAR system involving a rough target at a distant location in a turbulent atmosphere is modeled. The system operates by means of an optical beam which has arbitrary spectral composition, and states of coherence and polarization. The rough target is modeled as a combination of a Gaussian mirror and a thin phase screen which induces phase perturbations of the components of the electric field. The analytical form of the cross-spectral density matrix of the returned beam is determined, from which the effect of the rough target on the spectral density (intensity) and polarization of the returned wave is analyzed. E. Watson’s work performed while assigned to the Ladar and Optical Communications Institute, University of Dayton, Dayton, OH 45469, USA.     

Measuring optical characteristics of the atmosphere with a laser heterodyne system

A laser heterodyne system for measuring optical characteristics of a turbulent atmosphere is described. Continuous readout data on the fluctuations in the phase of the radiation propagating in a channel in the atmosphere are presented. These data can be used to determine the major parameters of the turbulent state. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 906–908, November–December, 2008.     

The structural function of entropy and turbulence scales

Structure functions of sound speed and local entropy in the turbulent atmosphere are analyzed. By long-term measurements in the atmospheric boundary layer the power dependence of these characteristics in the inertial sub-range is significantly diverged from the ??2/3 law??. Behavior of structure functions indicates deviation from the asymptotic Kolmogorov-Obukhov law on scales, which significantly exceed Taylor microscale. The exponent of 2/3 is regarded as the limit value, which can be reached under different synoptic conditions. Analytical expressions for the internal and ??energy?? scales of entropy fluctuations, as well as for relation of these scales with entropy dissipation rate and energy of adiabatic fluctuations are proposed.     

Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere

An analytical formula for the average intensity of cosh-Gaussian (ChG) beams diffracted by an aperture in turbulent atmosphere is derived and some limiting cases are discussed. By using the average intensity formula, some numerical simulation comparisons are made and some special cases are studied, especially the influences of the ChG beam parameter (Ω₀), the propagation distance, the aperture and its size on the average normalized intensity distribution. It is determined that the evolution properties of the average normalized intensity profile in turbulent atmosphere with aperture are different not only from those of free space with aperture but also from those in turbulent atmosphere without aperture. PACS 42.68.Bz; 42.79.Ag; 42.25.Fx     

Entropic entanglement criteria for Fermion systems

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.     

A Mechanical Model for Fourier’s Law of Heat Conduction

Nonequilibrium statistical mechanics close to equilibrium is a physically satisfactory theory centered on the linear response formula of Green-Kubo. This formula results from a formal first order perturbation calculation without rigorous justification. A rigorous derivation of Fourier’s law for heat conduction from the laws of mechanics remains thus a major unsolved problem. In this note we present a deterministic mechanical model of a heat-conducting chain with nontrivial interactions, where kinetic energy fluctuations at the nodes of the chain are removed. In this model the derivation of Fourier’s law can proceed rigorously.     

The energy and dissipation of turbulent fluctuations of wind velocity and temperature in the boundary layer of the atmosphere

The relationships between the energy of small-scale turbulence and its dissipation rate are studied based on the data of long-term high-frequency measurements of temperature and wind velocity fluctuations in urban area. It is shown that the energy of wind velocity turbulent fluctuations is linearly related to the dissipation rate ɛ. The proportionality coefficient between turbulent kinetic energy (TKE) and ɛ is dimensional and does not depend on the stratification of the atmosphere, the Richardson number, or the Monin-Obukhov scale. Measurements in different seasons show that this coefficient can be related to the mean velocity of adiabatic motions (sound speed or air temperature), which enables one to select a more universal constant, γ. A linear relationship between the temperature fluctuations variance (the characteristic of the inner energy of turbulence) and their dissipation rate is also shown. The revealed proportionality is confirmed by measurements in urban and forest conditions, as well as in the surface layer over a flat desert terrain.     

Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light

We investigate the inverse scattering problem for statistically homogeneous, isotropic random media under conditions of strong fluctuations of optical wavefields. We present a method for determining the spectral density of the dielectric constant fluctuations in such media from scattering of partially coherent light. The method may find applications to a wide class of turbulent media such as the turbulent atmosphere and certain turbulent plasmas where backscattering and depolarization effects are negligible.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

Clustering Properties in Turbulent Signals

We consider the telegraph approximation (TA) of turbulent signals by ignoring their amplitude variability and retaining only their ‘zero’-crossing information. We establish a unique relationship between the spectral exponent of a signal and that of its TA, whenever the signal possesses a Gaussian PDF and a spectral shape in which the high-frequency cut-off is sufficiently sharp. The velocity signals in most turbulent flows away from the wall satisfy these conditions adequately, so that the Kolmogorov spectral exponent of −5/3 for the turbulent velocity spectrum corresponds to a −4/3 spectral exponent for its TA. By introducing a new scaling exponent to characterize the tendency of small-scale fluctuations to cluster, we show that the velocity and passive scalar signals display a finite tendency to cluster even in the limit of Re . We advance the notion, on the basis of the properties of the TA, that turbulent processes belong to one of two classes—either the ‘white noise’ type or the ‘Markov-Lorentzian’ type. PACS: 47.27.-i, 47.27.Gs, 47.27.Nz     

A semi-empirical formula for the neutron total cross section and the interpretation of the empirical formula forA ⩾ 40

Weaknesses in Angeli and Csikai’s interpretation of their empirical formula for the neutron total cross section (σ _T) are pointed out. Using the Fourier-Bessel re-presentation of the scattering amplitude a semi-empirical formula forσ _T is obtained which has greater applicability and also explains the success of the empirical formula for mass numberA ⩾ 40 in terms of the established trends in neutron optical potential parameters.     

Off-axis Gaussian Schell-model beam and partially coherent laser array beam in a turbulent atmosphere

The propagation of an off-axis Gaussian Schell-model (GSM) beam in a turbulent atmosphere is investigated based on the extended Huygens-Fresnel integral formula. Analytical formulae for the cross-spectral density and corresponding partially coherent complex curvature tensor of an off-axis GSM beam propagating in a turbulent atmosphere are derived. Based on these formulae, the propagation properties of such kind of beam in a turbulent atmosphere are investigated in detail. Furthermore, the methods are extended to investigate the propagation properties of a partially coherent laser array beam in a turbulent atmosphere. The properties of an off-axis GSM beam and a partially coherent laser array beam in a turbulent atmosphere are closely related with the beam parameters and the structure constant of the turbulent atmosphere.