New asymptotic behavior of the surface-atom force out of thermal equilibrium

The Casimir-Polder-Lifshitz force felt by an atom near the surface of a substrate is calculated out of thermal equilibrium in terms of the dielectric function of the material and of the atomic polarizability. The new force decays like 1/z3 at large distances (i.e., slower than at equilibrium), exhibits a sizable temperature dependence, and is attractive or repulsive depending on whether the temperature of the substrate is higher or smaller than the one of the environment. Our predictions can be relevant for experiments with ultracold atomic gases. Both dielectric and metal substrates are considered.     

Fluctuations in fluids out of thermal equilibrium

After a brief review of dynamic correlations in equilibrium fluids, we consider the long-range correlations between the fluctuations in a fluid subjected to a large stationary temperature gradient. These long-range correlations enhance and modify the Rayleigh spectrum of the fluid. We elucidate that the modifications of the Rayleigh line are determined by the coupling of the entropy fluctuations to the transverse velocity fluctuations. Recent attempts to test the theoretical predictions with the aid of light-scattering experiments are discussed.     

Generalized hydrodynamics of thermal transpiration,thermal force and friction force

Transport processes in a rarefied gas are treated phenomenologically by means of generalized hydrodynamics with appropriate boundary conditions. The integral mass and heat flows through a capillary of arbitrary width are calculated from the differential constitutive laws and boundary conditions. The coefficients connecting these flows with the driving forces - pressure and temperature differences - automatically fulfil the well-known integral second law requirements and Onsager symmetry which de facto had been incorporated in the basic generalized hydrodynamics and boundary conditions. The formula obtained for thermal transpiration can account for the experimental data over a wide pressure range. Furthermore, expressions for the frictional and thermal forces on a spherical particle suspended in a gas are derived. These expressions have the correct behavior all the way from the ordinary hydrodynamical to the Knudsen regime. In particular, thermal force data are well represented, with suitably chosen surface coefficients, for small and large ratios of the particle/gas heat conductives.     

Fluctuation-induced forces in and out of equilibrium

In a fluctuating medium of quantum, thermal, or non-thermal origin, an interaction is induced between external objects that modify the fluctuations. These interactions can appear in a vast variety of systems, leading to a plethora of interesting phenomena. Notable examples of these include: (1) like-charge attraction in the presence of multivalent counterions, (2) Ludwig-Soret effect in charged colloids, (3) mass renormalization of moving defects in a phononic background and moving metallic objects in EM quantum vacuum, and (4) dissipation due to motion-induced radiation. The fluctuationinduced forces are statistical in nature, and this could make their measurement very difficult, because the actual value of the force might deviate most of the time from the predicted average value.     

Confined colloidal crystals in and out of equilibrium

Recent studies on confined crystals of charged colloidal particles are reviewed, both in equilibrium and out of equilibrium. We focus in particular on direct comparisons of experiments (light scattering and microscopy) with lattice sum calculations and computer simulations. In equilibrium we address buckling and crystalline multilayering of charged systems in hard and soft slit confinement. We discuss also recent crystalline structures obtained for charged mixtures. Moreover we put forward possibilities to apply external perturbations, in order to drive the system out of equilibrium. These include electrolyte gradients as well as the application of shear and electric fields.     

Classical dissipation and asymptotic equilibrium via interaction with chaotic systems

We study the energy flow between a one-dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories of the chaotic system, which plays the role of an environment for the oscillator. We show numerically that the oscillator's average energy exhibits irreversible dynamics and ‘thermal’ equilibrium at long times. We use linear response theory to describe the dynamics at short times and we derive a condition for the absorption or dissipation of energy by the oscillator from the chaotic system. The equilibrium properties at long times, including the average equilibrium energies and the energy distributions, are explained with the help of statistical arguments. We also check that the concept of temperature defined in terms of the ‘volume entropy’ agrees very well with these energy distributions.     

Kaluza-Klein Casimir cosmology and thermal equilibrium

A Kaluza-Klein early universe scenario with massless higher dimensional particles and toroidal compactification is studied. Solutions which may take into account the Casimir effect and the thermal equilibrium condition are found. A correspondence is made with solutions for some 4D supergravity theories.     

About a nonadditivity of energy and entropy

The mathematical expression of nonadditivity X(1 ?? 2) = X(1) + X(2) + ??X(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and ?? is hoped to be a parameter characterising the nonadditive property of the composite system (1 ?? 2). Here we show that this relationship cannot hold exactly. In general, ?? in this expression inevitably depends on how a given system with constant X(1 ?? 2) is divided into subsystems 1 and 2. Hence mathematical problems may arise when it is used to characterise the nonadditivity of the system. Nevertheless, under some conditions, it is possible to use it as a good approximation.     

Anharmonic force field and equilibrium structure of nitric acid

The quadratic, cubic and semi-diagonal quartic force field of nitric acid has been calculated at the CCSD(T) level of theory employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. It is found that the A and B semi-experimental equilibrium rotational constants of the ¹⁸O isotopologues (for which the rotation of principal axes is large) cannot be accurately reproduced. This problem is discussed and a remedy is proposed. Finally, the semi-experimental structure is in agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of at least quadruple-ζ quality and a core correlation correction, except for the long NO single bond for which the CCSD(T) value is too short due to inadequate treatment of electron correlation. The empirical structures are also determined and their accuracy is discussed. The best equilibrium structure is: r_e(NO_syn) = 1.209(1) Å, r_e(NO_anti) = 1.194(1) Å, r_e(NO) = 1.397(1) Å, r_e(OH) = 0.968(1) Å, ∠(ONO_syn) = 115.8(1)°, ∠(ONO_anti) = 114.2(1)° and ∠(NOH) = 102.2(1)°.     

Ab initio calculation of force constants and equilibrium geometries

Force constants of the molecules HF, NH₃, CH₄ and BH₄ ^- have been calculated ab initio by the force method with a 73/3 + 1 gaussian lobe basis set. The results, including a former calculation on H₂O, agree well with experiment: the average relative error is 12 per cent for the diagonal force constants and the average absolute error is 0·06 mdyn/Å for the off-diagonal ones. The trends are also correctly reproduced. It is concluded that ab initio calculations of this accuracy can help to solve a number of spectroscopic problems. Force constants of BH₄ ^- have been determined from a combination of spectroscopic and ab initio information. Geometries have been obtained with little computing work and show good agreement with experiment.     

The anharmonic force field and equilibrium structure of methane

The anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species ¹²CH₄, ¹³CH₄, ¹²CH₄, ¹²CH₃D, ¹²CHD₃ and ¹²CH₂D₂. Six of the thirteen cubic force constants have been determined experimentally, the remaining cubic constants being fixed at values derived from ab initio calculations. The quartic force field is very crude, in that only f_rrrr has been refined. It is concluded however that the cubic and quartic force fields, even though they are subject to limitations, provide a considerable improvement in the experimental determination of the r _e structure and the quadratic force field. The equilibrium bond length is found to be r _e(CH) = 1·085₈ ± 0·001 Å.     

Relativistic thermal equilibrium of non-neutral plasmas

Finite temperature effects on the relativistic radial equilibrium of a non-neutral plasma are analyzed. An equation for an effective potential governing the self-consistent radial density profile is derived in the case of global thermal equilibrium. The effect of a finite temperature turns out to be particularly strong for the fast mode of rigid plasma rotation, where the density profile can extend beyond the cold limiting radius.     

Coherent transport in disordered metals out of equilibrium

We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the conductivity of a disordered metal. The current formula is obtained by a direct diagrammatic approach, and is shown to agree with what is obtained within the Keldysh formulation of the non-linear sigma model. As an application we calculate the current of a mesoscopic wire. We find a current-voltage characteristics that scales with eV/kT, and calculate the different scaling curves for a wire in the hot-electron regime and in the regime of full non-equilibrium. Received 13 June 2001     

Infrared and pinching singularities in out of equilibrium QCD plasmas

We examine collinear, infrared and pinching singularities in the production of weakly interacting particles from out of equilibrium relativistic plasmas. We show that collinear singularities cancel out in a scalar theory, exactly as at equilibrium. The same result holds in a quark-gluon plasma, provided the matter degrees of freedom are quantized in a physical gauge. However the cancellation does not hold in a covariant gauge; we comment on a possible explanation of this result. Finally we show that pinching singularities give contributions of order g ² δn, where δn is the deviation from equilibrium of the distribution function and g the QCD coupling constant.