Showing papers on "Thermal equilibrium published in 2001"

The Distribution of Thermal Pressures in the Interstellar Medium from a Survey of C I Fine-Structure Excitation

Abstract: We used the Space Telescope Imaging Spectrograph (STIS) with its smallest entrance aperture (003 wide slit) and highest resolution echelle gratings (E140H and E230H) to record the interstellar absorption features for 10 different multiplets of neutral carbon at a resolving power of ?/?? = 200,000 in the UV spectra of 21 early-type stars. Our objective was to measure the amount of C I in each of its three fine-structure levels of the ground electronic state, so that we could determine the thermal pressures in the absorbing gas and how much they vary in different regions. Our observations are principally along directions out to several kiloparsecs in the Galactic plane near longitudes l = 120? and 300?, with the more distant stars penetrating nearby portions of the Perseus and Sagittarius-Carina arms of the Galaxy. We devised a special analysis technique to decipher the overlapping absorption features in the different multiplets, each with different arrangements of the closely spaced transitions. In order to derive internally consistent results for all multiplets, we found that we had to modify the relative transition f-values in a way that made generally weak transitions stronger than amounts indicated in the current literature. We compared our measured relative populations of the excited fine-structure levels to those expected from equilibria calculated with collisional rate constants for various densities, temperatures, and compositions. The median thermal pressure for our entire sample was p/k = 2240 cm-3 K, or slightly higher if the representative temperatures of the material are much above or below a most favorable temperature of 40 K for the excitation of the first excited level at a given pressure. For gas that is moving outside the range of radial velocities permitted by differential Galactic rotation between us and the targets, about 15% of the C I indicates a thermal pressure p/k > 5000 cm-3 K. For gas within the allowed velocities, this fraction is only 1.5%. This contrast reveals a relationship between pressure enhancements and the kinematics of the gas. Regardless of velocity, we usually can register the presence of a very small proportion of the gas that seems to be at p/k 105 cm-3 K. We interpret these ubiquitous wisps of high-pressure material to arise either from small-scale density enhancements created by converging flows in a turbulent medium or from warm turbulent boundary layers on the surfaces of dense clouds moving through an intercloud medium. For turbulent compression, our C I excitations indicate that the barytropic index ?eff 0.90 must apply if the unperturbed gas starts out with representative densities and temperatures n = 10 cm-3 and T = 100 K. This value for ?eff is larger than that expected for interstellar material that remains in thermal equilibrium after it is compressed from the same initial n and T. However, if regions of enhanced pressure reach a size smaller than ~0.01 pc, the dynamical time starts to become shorter than the cooling time, and ?eff should start to approach the adiabatic value cp/cv = 5/3. Some of the excited C I may arise from the target stars' H II regions or by the effects of optical pumping from the submillimeter line radiation emitted by them. We argue that these contributions are small, and our comparisons of the velocities of strongly excited C I to those of excited Si II seem to support this outlook. For six stars in the survey, absorption features from interstellar excited O I could be detected at velocities slightly shifted from the persistent features of telluric origin. These O I* and O I** features were especially strong in the spectra of HD 93843 and HD 210839, the same stars that show exceptionally large C I excitations. In appendices of this paper, we present evidence that (1) the wavelength resolving power of STIS in the E14OH mode is indeed about 200,000, and (2) the telluric O I* and O I** features exhibit some evidence for macroscopic motions, since their broadenings are in excess of that expected for thermal Doppler broadening at an exospheric temperature T = 1000 K.

Classical-field method for time dependent Bose-Einstein condensed gases.

Abstract: We propose a method to study the time evolution of Bose-Einstein condensed gases perturbed from an initial thermal equilibrium, based on the Wigner representation of the N-body density operator. We show how to generate a collection of random classical fields sampling the initial Wigner distribution in the number conserving Bogoliubov approximation. The fields are then evolved with the time dependent Gross-Pitaevskii equation. We illustrate the method with the damping of a collective excitation of a one-dimensional Bose gas

Bose condensation of cavity polaritons beyond the linear regime: The thermal equilibrium of a model microcavity

Abstract: We consider a generalization of the Dicke model. This model describes localized, physically separated, saturable excitations, such as excitons bound on impurities, coupled to a single long-lived mode of an optical cavity. We consider the thermal equilibrium of this model at a fixed total number of excitons and photons. We find a phase in which both the cavity field and the excitonic polarization are coherent. This phase corresponds to a Bose condensate of cavity polaritons, generalized to allow for the fermionic internal structure of the excitons. It is separated from the normal state by an unusual reentrant phase boundary. We calculate the excitation energies of the model, and hence the optical absorption spectra of the cavity. In the condensed phase the absorption spectrum is gapped. The presence of this gap distinguishes the polariton condensate from the normal state and from a conventional laser, even when the inhomogeneous linewidth of the excitons is so large that there is no observable polariton splitting in the normal state.

Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses.

Abstract: We study the nonequilibrium state of heat conduction in a one-dimensional system of hard point particles of unequal masses interacting through elastic collisions. A BBGKY-type formulation is presented and some exact results are obtained from it. Extensive numerical simulations for the two-mass problem indicate that, even for arbitrarily small mass differences, a nontrivial steady state is obtained. This state exhibits local thermal equilibrium and has a temperature profile as predicted by kinetic theory. The temperature jumps typically seen in such studies are shown to be finite-size effects. The thermal conductivity appears to have a very slow divergence with system size, different from that seen in most other systems.

Transport properties in a two-temperature plasma: theory and application.

Abstract: An alternate derivation of transport properties in a two-temperature plasma has been performed. Indeed, recent works have shown that the simplified theory of transport properties out of thermal equilibrium introduced by Devoto and then Bonnefoi, very often used in two-temperature modeling, is questionable and particularly does not work when calculating the combined diffusion coefficients of Murphy. Thus, in this paper, transport properties are derived without Bonnefoi's assumptions in a nonreactive two-temperature plasma, assuming chemical equilibrium is achieved. The electron kinetic temperature T(e) is supposed to be different from that of heavy species T(h). Only elastic processes are considered in a collision-dominated plasma. The resolution of Boltzmann's equation, thanks to the Chapman-Enskog method, is used to calculate transport coefficients from sets of linear equations. The solution of these systems allows transport coefficients to be written as linear combinations of collision integrals, which take into account the interaction potential for a collision between two particles. These linear combinations are derived by extending the definition and the calculation of bracket integrals introduced by Chapman et al. to the thermal nonequilibrium case. The obtained results are rigorously the same as those of Hirschfelder et al. at thermal equilibrium. The derivation of diffusion velocity and heat flux shows the contribution of a new gradient, that of the temperature ratio straight theta=T(e)/T(h). An application is presented for a two-temperature argon plasma. First, it is shown that the two-temperature linear combinations of collision integrals are drastically modified with respect to equilibrium. Secondly, the two-temperature simplified theory of transport coefficients of Devoto and Bonnefoi underestimates the electron thermal conductivity with respect to the accurate value at T(e)=20 000 K. Lastly, contrary to the simplified theory of transport coefficients, the diffusion coefficients satisfy the symmetry conditions. An example is given at T(e)=6000 K for different values of straight theta for the diffusion coefficient between electrons and heavy species D(e-Ar) as well as for that between argon atoms and argon ions D(Ar-Ar+).

Coupled Normal Heat and Matter Transport in a Simple Model System

Abstract: We introduce the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system is a Lorentz gas with fixed freely rotating circular scatterers which scatter point particles via perfectly rough collisions. Upon imposing either a temperature gradient and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds. Transport in this system is normal in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are nontrivially coupled, satisfying Onsager{close_quote}s reciprocity relations.

Observation of a 1/t decay law for hot clusters and molecules in a storage ring.

Abstract: The exponential law is valid both for decay from a single quantum state into a continuum and for an ensemble maintained in thermal equilibrium. For statistical decay of an ensemble of isolated systems with a broad energy distribution, the exponential decay is replaced by a $1/t$ distribution. We present confirmation of this decay law by experiments with cluster anions in a small electrostatic storage ring. Deviations from the $1/t$ law for such an ensemble give important information on the dynamics of the systems. As examples, we present measurements revealing strong radiative cooling of anions of both metal clusters and fullerenes.

Simple one-dimensional model of heat conduction which obeys Fourier's law.

Abstract: We present the computer simulation results of a chain of hard-point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier{close_quote}s law at the thermodynamic limit. This result is against the actual belief that one-dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.

EQUILIBRIUM FLUCTUATIONS FOR ∇ϕ INTERFACE MODEL

Abstract: unchen We study the large scale space–time fluctuations ofan interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space–time scale these fluctuations are governed by an infinite-dimensional Ornstein–Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula. 1. Introduction. It is a common phenomenon that at low temperature two pure thermodynamic phases spatially coexist and are separated by an interface, which is very sharp with a width of a few atomic distances. In thermal equilibrium such an interface is planar and local deformations will relax back diffusively in order to minimize surface tension. To build a statistical mechanics model for the interface, one assumes that transverse deviations from the perfectly flat interface are given through a scalar field ϕ, that is, ϕ� � 2 → � with ϕ ≡ 0 corresponding to the flat interface. To have a mathematically well-defined model we discretize � 2 . We also generalize to arbitrary dimension. Then ϕ� � d → � with ϕ x is the height ofthe interf ace at site x ∈ � d . Neighboring heights are connected through an elastic potential V. While we need more stringent assumptions later on, at this point V should be bounded from below and increase sufficiently rapidly for large arguments. To each configuration ϕ we associate the (elastic) energy H� ϕ �= 1 � � x−y�= 1

Liquid-helium temperature long-path infrared spectroscopy of molecular clusters and supercooled molecules

Abstract: Collisional cooling and supersonic jet expansion both allow us to perform infrared spectroscopy of supercooled molecules and atomic and molecular clusters. Collisional cooling has the advantage of higher sensitivity per molecule and enables working in thermal equilibrium. A new powerful method of collisional cooling is presented in this article. It is based on a cooling cell with integrated temperature-invariant White optics and pulsed or continuous sample-gas inlet. The system can be cooled with liquid nitrogen or liquid helium and operated at gas pressures between <10−5 and 13 bar. Temperatures range from 4.2 to 400 K and can be adjusted to an accuracy of ±0.2 K over most of the useable range. A three-zone heating design allows homogeneous or inhomogeneous temperature distributions. Optical path lengths can be selected up to values of 20 m for Fourier transform infrared (FTIR) and 40 m for laser operation. The cell axis is vertical, so optical windows are at room temperature. Diffusive trapping shields ...

Nonequilibrium phonon and electron transport in heterostructures and superlattices

Abstract: Electron and phonon transport in nanostructures is characterized by interface effects and can deviate significantly from the assumption of local thermal equilibrium underlying the transport equations at macroscale. In this article, we elucidate some basic nonequilibrium characteristics for phonon and electron transport in thin films and superlattices. Based on a discussion of the thermal boundary resistance at a single interface, the nonequilibrium nature of phonon transport and the consistency of temperature definition are emphasized. Using a consistent definition for temperature, we obtain simplified expressions for phonon transport in thin films and superlattices, and give examples to illustrate the effectiveness of the approximation by comparing the thermal conductivity of thin films and superlattices obtained from solving the Boltzmann equation with the current approximation. Similar nonequilibrium processes occur for the electron transport in nanostructures. An example is given on concurrent electro...

Thermal transport through a mesoscopic weak link

Abstract: We calculate the rate of thermal energy flow between two macroscopic bodies, each in thermodynamic equilibrium at a different temperature, and joined by a weak mechanical link. The macroscopic solids are assumed to be electrically insulating, so that thermal energy is carried only by phonons. To leading order in the strength of the weak link, modeled here by a harmonic spring, the thermal current is determined by a product of the local vibrational density-of-states of the two bodies at the points of connection. Our general expression for the thermal current can be regarded as a thermal analog of the well-known formula for the electrical current through a tunneling barrier. It is also equivalent to the thermal Landauer formula in the weak-tunneling limit. Implications for heat transport experiments on dielectric quantum point contacts are discussed.

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model.

Abstract: The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.

How does a system respond when driven away from thermal equilibrium

Abstract: It is widely appreciated that our understanding of nonequilibrium phenomena has not kept pace with its equilibrium counterpart. In recent years, however, consideration of the above question, posed at the microscopic level of statistical mechanics, has yielded some intriguing theoretical results distinguished by two common features. First, the results remain valid far from equilibrium, that is, even if the system is disturbed violently from its initial equilibrium state. Second, they incorporate information about the history of the system over some span of time; effectively, these results are statistical predictions about what we would see if we could watch a movie of the system filmed at the atomic level, rather than predictions about individual snapshots.

An exact stochastic field method for the interacting Bose gas at thermal equilibrium

Abstract: We present a new exact method to numerically compute the thermodynamical properties of an interacting Bose gas in the canonical ensemble. As in our previous paper (Carusotto I, Castin Y and Dalibard J 2001 Phys. Rev. A 63 023606), we write the density operator ρ as an average of Hartree dyadics |N:1N:2| and we find stochastic evolution equations for the wavefunctions 1,2 such that the exact imaginary-time evolution of ρ is recovered after averaging over noise. In this way, the thermal equilibrium density operator can be obtained for any temperature T. The method is then applied to study the thermodynamical properties of a homogeneous one-dimensional N-boson system: although Bose-Einstein condensation cannot occur in the thermodynamical limit, a macroscopic occupation of the lowest mode of a finite system is observed at sufficiently low temperatures. If kBT>>µ, the main effect of interactions is to suppress density fluctuations and to reduce their correlation length. Different effects such as a spatial antibunching of the atoms are predicted for the opposite kBT≤µ regime. Our exact stochastic calculations have been compared with existing approximate theories.

How does a system respond when driven away from thermal equilibrium

Abstract: It is widely appreciated that our understanding of non-equilibrium phenomena has not kept pace with its equilibrium counterpart. In recent years, however, consideration of the above question, posed at the microscopic level of statistical mechanics, has yielded some intriguing theoretical results distinguished by two common features. First, they remain valid far from equilibrium, that is, even if the system is disturbed violently from its initial equilibrium state. Second, they incorporate information about the history of the system over some span of time: effectively, these are statistical predictions about what we would see if we could watch a movie of the system filmed at the atomic level, rather than predictions about individual snapshots. To date, this work has been theoretical, though supplemented with numerical simulations. However, in the current issue of PNAS, Hummer and Szabo [1] show how to combine these theoretical advances with single molecule manipulation experiments, so as to extract useful equilibrium information from non-equilibrium laboratory data. What these authors propose amounts to a novel method of deducing the equilibrium mechanical properties of individual molecules.

Statistical Mechanics of Stable States Far from Equilibrium: Thermodynamics of Turbulent Plasmas

Abstract: This paper reviews some recent developments in the theory of stationary states in collisionless media that are very far from thermal equilibrium. Such states may evolve under conditions when the binary collision time is much longer than any characteristic time of the processes under consideration. A typical example of such a system is collisionless turbulence in a plasma when the plasma evolves into a highly nonlinear state entirely dominated by wave generation, wave-wave and wave-particle interaction and generating a nearly stationary level of turbulence. Sometimes it is very difficult to describe the evolution of such a state. The present theory shows that it is nevertheless possible to develop a macroscopic picture in the framework of statistical mechanics and thermodynamics which allows for the macroscopic description of such states. This can be achieved introducing a control parameter κ. The equilibrium distribution which replaces the Maxwell-Boltzmann distribution is a generalized Lorentzian orκ-distribution. We sketch the underlying statistical mechanics and provide some arguments for the validity of this approach. On this level it is not possible to obtain a microscopic theory of κ, however, which must be constructed on the way of referring to the particular kind of turbulence. We note a number of unresolved problems.

Equilibrium carrier mobility in disordered hopping systems

Abstract: It is shown that the charge carrier mobility in a positionally and energetically disordered hopping system can be evaluated by averaging either the hopping rates or the hopping times over the thermal equilibrium energy distribution of localized carriers. However, at variance with averaging the hopping rates, averaging the hopping times can be correct only if the energy dependence of the carrier energy relaxation time is also taken into consideration. The temperature and concentration dependences of the equilibrium carrier mobility were calculated by averaging the hopping rates. The consideration was based on the variable-range hopping approach with full account for the interplay between jump distance and energy difference. However, the obtained results prove that, in good quantitative agreement with both Monte Carlo simulations and experimental data, the mobility can be approximated as a product of two functions. The first function depends almost solely upon the temperature and reveals only a wea...

Si II transition probabilities measurements in a laser induced plasma

Abstract: Si II lines are observed in a laser-induced plasma, generated by a laser pulse focused on a silicon solid target, in a xenon plus hydrogen atmosphere. They are measured when the plasma reaches local thermal equilibrium (LTE). The spectra is numerically corrected from self-absorption. Transition probabilities of Si II Mult. (1)–(5); (8); (9); (3.01); (7.26) lines are measured, for the two last above-mentioned multiplets (3.01); (7.26) no prior measurements have been previously published. For others they agree within error bar with previous measurements and calculations.

Study of the structure and deviation from equilibrium in direct current supersonic plasma jets

Abstract: Mathematical modelling and optical emission spectroscopy are applied to study the effect of the chamber pressure on the structure and properties of supersonic plasma jets formed by a direct current arc. In this installation the plasma is created inside the nozzle where the flow is accelerated. As a result some deviation from thermal and ionization equilibrium can be found, even at the working chamber inlet. In this paper, by means of a two-temperature model, we study the argon jet flow using the data of the emission spectroscopy measurements to make realistic assumptions about the inlet boundary conditions. The results show that, when the chamber pressure is low, a strongly underexpanded jet with a Mach disc is formed. For the higher ambient pressure values, the core region of the jet changes to a mildly underexpanded structure with alternating oblique expansion and compression zones. The predicted shock zone positions are in a very good agreement with measurement. The general analysis shows that the deviation from local thermodynamic equilibrium in the jet is inversely related to the chamber pressure. Along the jet core the deviation from thermal equilibrium is less in the shock regions than in the expansion zones, where the electrons are heated by three-particle recombination. Downstream of the jet core the velocity drops, but the ionization and thermal equilibria are not attained because of the correlation between the characteristic recombination and the hydrodynamic times. Both the modelling and the emission spectroscopy show that the axial electron number density is much closer to its frozen value than to equilibrium value. The results obtained are helpful for different applications such as plasma processing, rocket propulsion systems and the simulation of re-entry conditions.

Finite-size effects on fluctuations in a fluid out of thermal equilibrium

Abstract: In this paper, we consider a horizontal liquid layer in the presence of a stationary temperature gradient. Specifically, we calculate the structure factor neglecting gravity, but taking into account the finite height of the liquid layer. For this purpose, we consider the linearized Boussinesq equations, in the limit of negligible Rayleigh number, supplemented with Langevin noise terms and assuming free-slip boundary conditions. The nonequilibrium temperature fluctuations are obtained by expanding the solution in a complete set of orthogonal functions satisfying the boundary conditions. It is shown that the finite height of the system restricts the spatial range of the temperature fluctuations not only in the direction of the temperature gradient, but also in the horizontal direction away from the boundaries. It is demonstrated that the q −4 dependence of the structure factor in the absence of finite-size effects now crosses over to a q 2 dependence for very small values of the wave number q . Estimates of the wave numbers where light-scattering experiments will be affected by these finite-size effects are presented.