The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis

We have investigated the proof of the H theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it happens in the nonrelativistic limit, the molecular chaos hypothesis is slightly extended within the Kaniadakis formalism. It is shown that the collisional equilibrium states (null entropy source term) are described by a κ power law generalization of the exponential Juttner distribution, e.g., , with θ=α(x)+β_μp^μ, where α(x) is a scalar, β_μ is a four-vector, and p^μ is the four-momentum. As a simple example, we calculate the relativistic κ power law for a dilute charged gas under the action of an electromagnetic field F^μν. All standard results are readly recovered in the particular limit κ→0.     

Phase Space Portraits of an Unresolved Gravitational Maxwell Demon

In 1885, during initial discussions of J. C. Maxwell's celebrated thermodynamic demon, Whiting ⁽¹⁾ observed that the demon-like velocity selection of molecules can occur in a gravitationally bound gas. Recently, a gravitational Maxwell demon has been proposed which makes use of this observation [D. P. Sheehan, J. Glick, and J. D. Means, Found. Phys. 30, 1227 (2000)]. Here we report on numerical simulations that detail its microscopic phase space structure. Results verify the previously hypothesized mechanism of its paradoxical behavior. This system appears to be the only example of a fully classical mechanical Maxwell demon that has not been resolved in favor of the second law of thermodynamics.     

A simple model of DNA denaturation and mutually avoiding walks statistics

Recently Garel, Monthus and Orland [Europhys. Lett. 55, 132 (2001)] considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition. Received 8 July 2002 / Received in final form 25 July 2002 Published online 17 September 2002     

Weak point disorder in strongly fluctuating flux-line liquids

We consider the effect of weak uncorrelated quenched disorder (point defects) on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which is based on mapping the flux-line system onto a quantum liquid ofrelativistic charged bosons in 2 + 1 dimensions [P Benetatos and M C Marchetti,Phys. Rev. B64, 054518 (2001)]. In this model, flux lines are allowed to be arbitrarily curved and can even form closed loops. Point defects can be scalar or polar. In the latter case, the direction of their dipole moments can be random or correlated. Within the Gaussian approximation of our hydrodynamic model, we calculate disorder-induced corrections to the correlation functions of the flux-line fields and the elastic moduli of the flux-line liquid. We find that scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease the tilt modulus.     

Conservative force fields in non-Gaussian statistics

In this Letter, we determine the κ-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the κ-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory.     

Casimir-Polder interaction of excited media

The potential of long-range interaction between two dissimilar atoms, one of which is excited, drops as 1/R ₂ with the distance for the Casimir-Polder limit of large distances in comparison with the wave-length of atom transitions (E.A. Power and T. Thirunamachandran, Phys. Rev. A 51, 3660 (1995)). It is shown that such a dependence, obtained with the help of perturbation technique, results in a divergence for the interaction potential between an excited atom and a medium of dilute gas. We develop a nonperturbative method based upon quantum Green’s functions (Yu. Sherkunov, Phys. Rev. A 72, 052703 (2005)) to calculate the interaction potential for an excited atom and a ground-state atom embedded in a dielectric medium, taking into account the absorption of photons in the dielectric medium. The exponential suppression of the interaction between the atoms is demonstrated. The force acting on an excited atom near the interface of dilute gas medium is calculated. The result is no more divergent. The force between gas media in Casimir-Polder regime is calculated as well. The text was submitted by the author in English.     

Pump-probe spectroscopy of atoms cooled in a 3D lin lin optical lattice

We describe the pump-probe spectroscopy of atoms cooled in a 3D lin⊥lin optical lattice. Our pump-probe configuration consists of two laser fields detuned with respect to the lattice fields. This scheme allows to clearly identify in the probe transmission spectrum the Brillouin and Raman resonances, by studying their positions as functions of the angle between the pump and probe beams. We describe these resonances in detail, and compare the experimental results to the theoretical predictions. Our conclusions are supported by transport-spectroscopy measurements, which allow to distinguish between contributions to the light scattering from propagating and non-propagating atoms. Received 8 April 2002 / Received in final form 9 September 2002 Published online 12 November 2002     

Experimental observations of methane–oxygen diffusion flame structure in a sub-millimetre microburner

We examine the structure of confined, laminar methane–oxygen diffusion flames in an alumina microburner with a sub-millimetre dimension. To minimize termination of gas-phase combustion via surface radical quenching, the reactor walls are chemically treated and annealed. We show, through chemiluminescent images, that gas-phase methane–oxygen diffusion flames exist in the microburner without the need for catalytic reaction. However, their structure differs from the continuous laminar diffusion flame profiles that we would expect in a similar burner configuration on a macroscopic scale. Instead, we observe a sequence of isolated reaction zones structures (flame cells) that form along the length of the microburner combustion channel aligned in the direction of the gas flow. This form of cellular diffusion flame instability appears to be unique to wall-confined combustion in microscale devices. The number of flame cells observed depends on the inlet gas velocities and initial mixture strengths.     

On the validity of Fourier's law in systems with spatially varying strain rates

Non-equilibrium molecular dynamics (NEMD) simulations are used to study the generation of heat fluxes in systems with spatially varying shear rates. We show that the kinetic temperature, when used in Fourier's law of heat conduction, does not correctly account for the heat flux, and that the normal temperature as described by Rugh (1997, Phys. Rev. Lett., 78, 772), should be used. Only in the absence of normal temperature gradients can heat fluxes due to strain rate coupling be correctly calculated.     

An intense, slow and cold beam of metastable Ne(3s) 3 P 2 atoms

We employ laser cooling to intensify and cool an atomic beam of metastable Ne(3 s) atoms. Using several collimators, a slower and a compressor we achieve a ²⁰Ne^* flux of 6×10 ¹⁰ atoms/s in an 0.7 mm diameter beam traveling at 100 m/s, and having longitudinal and transverse temperatures of 25 mK and 300μK, respectively. This constitutes the highest flux in a concentrated beam achieved to date with metastable rare gas atoms. We characterize the action of the various cooling stages in terms of their influence on the flux, diameter and divergence of the atomic beam. The brightness and brilliance achieved are 2.1 ×10 ²¹ s^-1m^-2sr^-1 and 5.0 ×10 ²² s^-1m^-2sr^-1, respectively, comparable to the highest values reported for alkali-metal beams. Bright beams of the ²¹Ne and ²²Ne isotopes have also been created. Received 22 June 2001     

Instabilities in foam clusters related to the pressures in the bubbles

We reinterpret an instability in a two-dimensional free foam cluster previously discussed by Weaire et al. (Eur. Phys. J. E 7, 123 (2002)) in terms of the excess pressure in the bubbles. We conclude that in a free foam cluster no bubble can have a pressure below that of the surrounding gas. Received: 20 September 2002 / Accepted: 5 May 2003 / Published online: 27 May 2003 RID="a" ID="a"e-mail: fatima.vaz@ist.utl.pt     

Possible phases of the two-dimensional Hubbard model

We present a stability analysis of the 2D t - t' Hubbard model on a square lattice for various values of the next-nearest-neighbor hopping t' and electron concentration. Using the free energy expression, derived by means of the flow equations method, we have performed numerical calculation for the various representations under the point group C _4ν in order to determine at which temperature symmetry broken phases become more favorable than the symmetric phase. A surprisingly large number of phases has been observed. Some of them have an order parameter with many nodes in -space. Commonly discussed types of order found by us are antiferromagnetism, d _{x2 - y2} -wave singlet superconductivity, d-wave Pomeranchuk instability and flux phase. A few instabilities newly observed are a triplet analog of the flux phase, a particle-hole instability of p-type symmetry in the triplet channel which gives rise to a phase of magnetic currents, an s^*-magnetic phase, a g-wave Pomeranchuk instability and the band splitting phase with p-wave character. Other weaker instabilities are found also. A comparison with experiments is made. Received 25 July 2002 / Received in final form 28 November 2002 Published online 14 February 2003 RID="a" ID="a"Current address: Département de physique and Centre de recherche sur les propriétés électroniques de matériaux avancés, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1 e-mail: vaha@physique.usherb.ca     

Chemical reaction and diffusion: A comparison of molecular dynamics simulations with continuum solutions

Molecular dynamics simulations using the Lennard-Jones energy potential are compared with continuum solutions of reaction and diffusion in a dilute gas. The reaction model is a passive one in which high-energy bath atoms create a species, at dilute concentrations, which may have a very fast consumption reaction. This construction is designed based on typical fast reaction pathways involved in the fuel breakup in a hydrocarbon flame. Using reaction rates and diffusivities obtained from the molecular simulations allows the continuum solution to describe the reactive atom density spatial distribution with good accuracy. Based on this agreement, it is possible to estimate which reaction rates will produce negligible diffusive spreading, and hence, which species might be assumed to be in chemical equilibrium in continuum reacting flow calculations.     

Ion flux's pressure dependence in an asymmetric capacitively coupled rf discharge in NF<Subscript>3</Subscript>

Starting from an analytical macroscopic/phenomenological model yielding the self-bias voltage as a function of the absorbed radio-frequency (rf) power of an asymmetric capacitively coupled discharge in NF₃ this paper studies the dependence of the ion flux onto the powered electrode on the gas pressure. An essential feature of the model is the assumption that the ions' drift velocity in the sheath near the powered electrode is proportional to E ^α, where E=−ΔU (U being the self-bias potential), and α is a coefficient depending on the gas pressure and cross section of elastic ion-neutral collisions. The model also considers the role of γ-electrons, stochastic heating as well as the contribution of the active electron current to the global discharge power balance. Numerically solving the model's basic equations one can extract the magnitude of the ion flux (at three different gas pressures) in a technological etching device (Alcatel GIR 220) by using easily measurable quantities, notably the self-bias voltage and absorbed rf power.     

Comment on “A local realist model for correlations of the singlet state” by K. De Raedt,K. Keimpema,H. De Raedt,K. Michielsen and S. Miyashita

De Raedt et al. [Eur. Phys. J. B 53, 139 (2006)] have claimed to provide a local realist model for correlations of the singlet state in the familiar Einstein-Podolsky-Rosen-Bohm (EPRB) experiment when time-coincidence is used to decide which detection events should count in the analysis, and furthermore that this suggests that it is possible to construct local realistic models that can reproduce the quantum mechanical expectation values. In this letter we show that these conclusions cannot be upheld since their model exploits the so-called coincidence-time loophole. When this is properly taken into account no startling conclusions can be drawn about local realist modelling of quantum mechanics.     

Numerical analysis of reversible A B C reaction-diffusion systems

We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B ↔ C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions of the space coordinate x, locally significantly exceeding their initial values. Received 6 June 2002 / Received in final form 20 January 2003 Published online 7 May 2003     

Electron flux distributions in photodetachment of HF~- near an interface: Theoretical imaging method study

The electron flux distributions in the photodetachment of HF- near an interface are studied using a two-center model and the theoretical imaging method. An analytical expression for electron flux distributions is derived, which displays oscillations on an observation plane similar to the recent results published by Wang but in the presence of a static electric field. We also discuss the expressions for soft and hard wall cases in detail. A comparison is made with the previous work. The expression is a more general result, and we can deduce from it the electron flux distributions for the photodetachment of H2- near an interface. Finally, we show that the expression reveals similar results as those in [Chin. Phys. B 19 020306 (2010)] when the wall effect is neglected.     

Pairing in the Hubbard model: the Cu O cluster versus the Cu-O plane

We study the Cu₅O₄ cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantization. The results extend earlier cluster studies and illustrate a canonical transformation approach to pairing that we have developed recently for the full plane. The quasiparticles that in the many-body problem behave like Cooper pairs are W =0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. The cluster allows W =0 pairs of d symmetry, due to a spin fluctuation, and ssymmetry, due to a charge fluctuation. Flux quantization is shown to be a manifestation of symmetry properties that hold for clusters of arbitrary size. Received 23 July 1999     

Propagation of cylindrical shock waves in a rotating atmosphere under the action of monochromatic radiation

Summary  A model of cylindrical shock waves is discussed in a non-uniform rotating atmosphere under the action of monochromatic radiation. We have assumed that the radiation flux moves through a rotating gas with constant intensity and the energy is absorbed only behind the shock wave which moves in opposite direction to the radiation flux.