Showing papers on "Thermal equilibrium published in 2004"

Matrix product density operators: simulation of finite-temperature and dissipative systems.

Abstract: We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of matrix product states which is variational.

The second law, Maxwell's demon, and work derivable from quantum heat engines.

Abstract: With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.

Comprehensive study of noise processes in electrode electrolyte interfaces

Abstract: A general circuit model is derived for the electrical noise of electrode–electrolyte systems, with emphasis on its implications for electrochemical sensors. The noise power spectral densities associated with all noise sources introduced in the model are also analytically calculated. Current and voltage fluctuations in typical electrode–electrolyte systems are demonstrated to originate from either thermal equilibrium noise created by conductors, or nonequilibrium excess noise caused by charge transfer processes produced by electrochemical interactions. The power spectral density of the thermal equilibrium noise is predicted using the fluctuation-dissipation theorem of thermodynamics, while the excess noise is assessed in view of charge transfer kinetics, along with mass transfer processes in the electrode proximity. The presented noise model not only explains previously reported noise spectral densities such as thermal noise in sensing electrodes, shot noise in electrochemical batteries, and 1/f noise in corrosive interfaces, it also provides design-oriented insight into the fabrication of low-noise micro- and nanoelectrochemical sensors.

Fourier's law for a harmonic crystal with self-consistent stochastic reservoirs

Abstract: We consider a d-dimensional harmonic crystal in contact with a stochastic Langevin type heat bath at each site. The temperatures of the “exterior” left and right heat baths are at specified values T L and T R , respectively, while the temperatures of the “interior” baths are chosen self-consistently so that there is no average flux of energy between them and the system in the steady state. We prove that this requirement uniquely fixes the temperatures and the self consistent system has a unique steady state. For the infinite system this state is one of local thermal equilibrium. The corresponding heat current satisfies Fourier's law with a finite positive thermal conductivity which can also be computed using the Green–Kubo formula. For the harmonic chain (d=1) the conductivity agrees with the expression obtained by Bolsterli, Rich, and Visscher in 1970 who first studied this model. In the other limit, d>>1, the stationary infinite volume heat conductivity behaves as (l d d)−1where l d is the coupling to the intermediate reservoirs. We also analyze the effect of having a non-uniform distribution of the heat bath couplings. These results are proven rigorously by controlling the behavior of the correlations in the thermodynamic limit.

Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory

Abstract: The quantum time evolution of ${\ensuremath{\varphi}}^{4}$-field theory for a spatially homogeneous system in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym equations including the tadpole and sunset self-energies. Whereas the tadpole self-energy yields a dynamical mass, the sunset self-energy is responsible for dissipation and an equilibration of the system. In particular we address the dynamics of the spectral (``off-shell'') distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. The investigation explicitly demonstrates that the only translation invariant solutions representing the stationary fixed points of the coupled equation of motions are those of full thermal equilibrium. They agree with those extracted from the time integration of the Kadanoff-Baym equations for $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}.$ Furthermore, a detailed comparison of the full quantum dynamics to more approximate and simple schemes such as that of a standard kinetic (on-shell) Boltzmann equation is performed. Our analysis shows that the consistent inclusion of the dynamical spectral function has a significant impact on relaxation phenomena. The different time scales that are involved in the dynamical quantum evolution towards a complete thermalized state are discussed in detail. We find that far off-shell $1\ensuremath{\leftrightarrow}3$ processes are responsible for chemical equilibration, which is missed in the Boltzmann limit. Finally, we briefly address the case of (bare) massless fields. For sufficiently large couplings $\ensuremath{\lambda}$ we observe the onset of Bose condensation, where our scheme within symmetric ${\ensuremath{\varphi}}^{4}$ theory breaks down.

Entanglement generation in uniformly accelerating atoms: Reexamination of the Unruh effect

Abstract: The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. The moving system is found to be subjected to dissipation that drives its density matrix to a purely thermal equilibrium state, exhibiting a nonvanishing probability of spontaneous excitation, this phenomenon being usually referred to as the Unruh effect. Remarkably, when the uniformly accelerating system is composed by two, independent two-level atoms, the corresponding asymptotic, equilibrium state turns out to be entangled.

System and method for determining the temperature of a semiconductor wafer

Abstract: A system and method for determining the temperature of a semiconductor wafer at the time of thermal contact of the semiconductor wafer with a temperature sensing element. According to the invention, a temperature profile of the temperature sensing element is recorded from the time of thermal contact up to the time of thermal equilibrium between the semiconductor wafer and the temperature sensing element and the temperature of the semiconductor wafer at the time of thermal contact is determined on the basis of a time period between the time of thermal contact and the time of thermal equilibrium and the temperature T G of the semiconductor wafer reached at the time t G of thermal equilibrium is determined by back calculation with the aid of an equation derived from Newton's law of cooling.

Rotational, vibrational, and excitation temperatures of a microwave-frequency microplasma

Abstract: Integration of microplasma sources in portable systems sets constraints in the amount of power and vacuum levels employed in these plasma sources. Moreover, in order to achieve good power efficiency and prevent physical deterioration of the source, it is desirable to keep the discharge temperature low. In this paper, the thermal characteristics of an atmospheric argon discharge generated with a low-power microwave plasma source are investigated to determine its possible integration in portable systems. The source is based on a microstrip split-ring resonator and is similar to the one reported by Iza and Hopwood, 2003. Rotational, vibrational, and excitation temperatures are measured by means of optical emission spectroscopy. It is found that the discharge at atmospheric pressure presents a rotational temperature of /spl sim/300 K, while the excitation temperature is /spl sim/0.3 eV (/spl sim/3500 K). Therefore, the discharge is clearly not in thermal equilibrium. The low rotational temperature allows for efficient air-cooled operation and makes this device suitable for portable applications including those with tight thermal specifications such as treatment of biological materials.

Must cosmological perturbations remain nonadiabatic after multifield inflation

Abstract: Even if nonadiabatic perturbations are generated in multifield inflation, the perturbations will become adiabatic if the Universe after inflation enters an era of local thermal equilibrium, with no nonzero conserved quantities, and will remain adiabatic as long as the wavelength is outside the horizon, even when local thermal equilibrium no longer applies. Small initial nonadiabatic perturbations associated with imperfect local thermal equilibrium remain small when baryons are created from out-of-equilibrium decay of massive particles, or when dark matter particles go out of local thermal equilibrium.

Two-temperature chemically non-equilibrium modelling of high-power Ar–N2 inductively coupled plasmas at atmospheric pressure

Abstract: A two-dimensional thermal and chemical non-equilibrium model was developed for high-power Ar–N2 inductively coupled plasmas (ICPs) at atmospheric pressure, which are conventionally assumed to be under local thermal equilibrium condition. The energy conservation equation of electrons was treated separately from that of heavy particles. These equations consider reaction heat effects and energy transfer between electrons and heavy particles as well as enthalpy flow resulting from diffusion due to the particle density gradient. Chemical non-equilibrium effects were also accounted for by solving mass conservation equations for each particle, considering diffusion, convection and net production terms resulting from 30 reactions. Transport and thermodynamic properties of Ar–N2 plasmas were self-consistently calculated using the first-order approximation of the Chapman–Enskog method at each iteration using the local particle composition, heavy particle temperature and electron temperature. Power balance for the electron energy and the mass balance of atoms and ions in a high-power Ar–N2 ICP were investigated using the model developed. Calculational results obtained by the present model were compared with results from two other models such as a one-temperature chemical equilibrium model and a one-temperature chemical non-equilibrium model. This comparison supported the discussion of chemical and thermal non-equilibrium effects in the high-power induction plasma.

Fate of oscillating scalar fields in a thermal bath and their cosmological implications

Abstract: Relaxation process of a coherent scalar field oscillation in the thermal bath is investigated using nonequilibrium quantum field theory. The Langevin-type equation of motion is obtained which has a memory term and both additive and multiplicative noise terms. The dissipation rate of the oscillating scalar field is calculated for various interactions such as Yukawa coupling, three-body scalar interaction, and biquadratic interaction. When the background temperature is larger than the oscillation frequency, the dissipation rate arising from the interactions with fermions is suppressed due to the Pauli-blocking, while it is enhanced for interactions with bosons due to the induced effect. In both cases, we find that the microphysical detailed-balance relation drives the oscillating field to a thermal equilibrium state. That is, for low-momentum modes, the classical fluctuation-dissipation theorem holds and they relax to a state the equipartition law is satisfied, while higher-momentum modes reach the state the number density of each quanta consists of the thermal boson distribution function and zero-point vacuum contribution. The temperature-dependent dissipation rates obtained here are applied to the late reheating phase of inflationary universe. It is found that in some cases the reheat temperature may take a somewhat different value from the conventional estimates, and inmore » an extreme case the inflaton can dissipate its energy without linear interactions that leads to its decay. Furthermore the evaporation rate of the Affleck-Dine field at the onset of its oscillation is calculated.« less

Analysis of Variable Porosity, Thermal Dispersion, and Local Thermal Nonequilibrium on Free Surface Flows Through Porous Media

Abstract: Characteristics of momentum and energy transport for free surface flows through porous media are explored in this study. Effects of variable porosity and an impermeable boundary on the free surface front are analyzed. In addition, effects of thermal dispersion and local thermal nonequilibrium (LTNE) are also analyzed. Pertinent parameters such as porosity, Darcy number, inertia parameter, Reynolds number, particle diameter and solid-to-fluid conductivity ratio are used to investigate the significance of the above mentioned effects

A Two-Temperature Model for the Analysis of Passive Thermal Control Systems

Abstract: Passive control of steady and unsteady thermal loads using effective thermal conductivity enhancers, such as metal foams, internal fins and metal filler particles, is being explored for a variety of electronics applications. The interstices are filled with air, phase change materials, or other fluids. Local thermal equilibrium between the solid filler and the matrix is not ensured in such systems since their thermal diffusivities are frequently very different. The use of a single volume-averaged energy equation for both the phases cannot he justified in such situations. A two-medium approach is used in the present work to account for the local thermal non-equilibrium. Separate energy equations are written for the solid and fluid respectively, and are closed using a steady-state interphase heat transfer coefficient between the two phases. A general momentum equation which includes the Brinkman-Forchheimer extension to Darcy flow is employed

Dynamic thermal conductivity sensor for gas detection

Abstract: A dynamic thermal conductivity sensor for gas detection based on the transient thermal response of a SiC microplate slightly heated by a screen-printed Pt resistance is described. This sensor is developed for specific applications such as the determination of carbon monoxide content in hydrogen for fuel cell, or that of methane in biogas applications. On the contrary of existing devices, the apparatus developed here does not need any reference cell, it operates in transient mode near room temperature (�T ≈ 5 K in air), so has a very low power requirements (≈5 mW) and keeps the gas near thermal equilibrium which simplifies the mathematical model and eases data processing. In test gases mixtures (N2 + He), absolute and precise measurement of the gas thermal conductivity have been achieved, leading to the exact molar fraction of the gas to detect with a good reproducibility. © 2003 Elsevier B.V. All rights reserved.

Constraints on the energetics and plasma composition of relativistic jets in FR II sources

Abstract: We explore the energetics and plasma composition in FR II sources using a new simple method of combining shock dynamics and radiation spectrum. The hotspots are identified with the reverse-shocked region of jets. With the 1D shock jump conditions taking account of the finite pressure of hot intracluster medium (ICM), we estimate the rest mass and energy densities of the sum of thermal and non-thermal particles in hotspots. Independently, based on the Synchrotron Self-Compton (SSC) model, we estimate the number and energy densities of non-thermal electrons using the multifrequency radiation spectrum of hotspots. We impose the condition that the obtained rest mass, internal energy and number densities of non-thermal electrons should be lower than those of the total particles determined by shock dynamics. We apply this method to Cygnus A. We examine three extreme cases of pure electron-positron pair plasma (Case I), pure electron-proton plasma with separate thermalization (Case II) and pure electron-proton plasma in thermal equilibrium (Case III). By detailed SSC analysis for Cygnus A and 3C 123, we find that the energy density of non-thermal electrons is about 10 times larger than that of the magnetic field. We find that Case III is not acceptable because predicted photon spectra do not give a good fit to the observed one. We find that Case II can also be ruled out because the number density of non-thermal electrons exceeds that of the total number density. Hence we find that only pure e ± plasma (Case I) is acceptable among the three cases. Total kinetic power of jet and electron acceleration efficiency are also constrained by internal energy densities of non-thermal and total particles.

First measurement of the velocity of slow antihydrogen atoms

Abstract: The speed of antihydrogen atoms is deduced from the fraction that passes through an oscillating electric field without ionizing. The weakly bound atoms used for this first demonstration travel about $20$ times more rapidly than the average thermal speed of the antiprotons from which they form, if these are in thermal equilibrium with their 4.2 K container. The method should be applicable to much more deeply bound states, which may well be moving more slowly, and should aid the quest to lower the speed of the atoms as required if they are to be trapped for precise spectroscopy.

Topological thermal instability and length of proteins.

Abstract: We present an analysis of the effects of global topology on the structural stability of folded proteins in thermal equilibrium with a heat bath. For a large class of single domain proteins, we computed the harmonic spectrum within the Gaussian Network Model (GNM) and determined their spectral dimension, a parameter describing the low frequency behavior of the density of modes. We found a surprisingly strong correlation between the spectral dimension and the number of amino acids in the protein. Considering that larger spectral dimension values relate to more topologically compact folded states, our results indicate that, for a given temperature and length of protein, the folded structure corresponds to a less compact folding, one compatible with thermodynamic stability.

Heat transfer characteristics of a porous radiant burner under the influence of a 2-D radiation field

Abstract: This paper deals with the heat transfer analysis of a 2-D rectangular porous radiant burner. Combustion in the porous medium is modelled as a spatially dependent heat generation zone. The gas and the solid phases are considered in non-local thermal equilibrium, and separate energy equations are used for the two phases. The solid phase is assumed to be absorbing, emitting and scattering, while the gas phase is considered transparent to radiation. The radiative part of the energy equation is solved using the collapsed dimension method. The alternating direction implicit scheme is used to solve the transient 2-D energy equations. Effects of various parameters on the performance of the burner are studied.

A re-evaluation of the ClO/Cl 2 O 2 equilibrium constant based on stratospheric in-situ observations

Abstract: . In-situ measurements of ClO and its dimer carried out during the SOLVE II/VINTERSOL-EUPLEX and ENVISAT Validation campaigns in the Arctic winter 2003 suggest that the thermal equilibrium between the dimer formation and dissociation is shifted significantly towards the monomer compared to the current JPL 2002 recommendation. Detailed analysis of observations made in thermal equilibrium allowed to re-evaluate the magnitude and temperature dependence of the equilibrium constant. A fit of the JPL format for equilibrium constants yields KEQ=3.61x10-27exp(8167/T), but to reconcile the observations made at low temperatures with the existing laboratory studies at room temperature, a modified equation, KEQ=5.47x10-25(T/300)-2.29exp(6969/T), is required. This format can be rationalised by a strong temperature dependence of the reaction enthalpy possibly induced by Cl2O2 isomerism effects. At stratospheric temperatures, both equations are practically equivalent. Using the equilibrium constant reported here rather than the JPL 2002 recommendation in atmospheric models does not have a large impact on simulated ozone loss. Solely at large zenith angles after sunrise, a small decrease of the ozone loss rate due to the ClO dimer cycle and an increase due to the ClO-BrO cycle (attributed to the enhanced equilibrium ClO concentrations) is observed, the net effect being a slightly stronger ozone loss rate.

Approach to thermalization in the classical φ 4 theory in 1 + 1 dimensions: Energy cascades and universal scaling

Abstract: We study the dynamics of thermalization and the approach to equilibrium in the classical f 4 theory in 1 11 spacetime dimensions. At thermal equilibrium we exploit the equivalence between the classical canonical averages and transfer matrix quantum traces of the anharmonic oscillator to obtain exact results for the temperature dependence of several observables, which provide a set of criteria for thermalization. In this context, comparing to the exact results we find that the Hartree approximation is remarkably accurate in equilibrium. The nonequilibrium dynamics is studied by numerically solving the equations of motion in light-cone coordinates for a broad range of initial conditions and energy densities. The long time evolution is described by several distinct stages, all characterized by a cascade of energy towards the ultraviolet. After an initial transient stage, the spatiotemporal gradient terms become larger than the nonlinear term, and there emerges a stage of universal cascade. This cascade starts at a time scale t 0 independent of the initial conditions ~except for very low energy density!. During this stage the power spectra feature universal scaling behavior and the front of the cascade k ¯ (t) moves to the ultraviolet as a power law k ¯ (t);t a with a&0.25 an exponent weakly dependent on the energy density alone. The wake behind the cascade is described as a state of Local Thermodynamic Equilibrium ~LTE! with all correlations being determined by the equilibrium functional form with an effective time dependent temperature Teff(t), which slowly decreases with time as ;t 2a . Two well separated time scales emerge: while Teff(t) varies slowly, the wave vectors in the wake with k,k ¯ (t) attain LTE on much shorter time scales. This universal scaling stage ends when the front of the ultraviolet cascade reaches the cutoff at a time scale t 1;a 21/a . Virialization starts to set much earlier than LTE. We find that strict thermalization is achieved only for an infinite time scale.

A New Approach to Noise in Quantum Mechanics

Abstract: The standard way of describing noise in a quantum system consists in attaching to the system a reservoir or bath, which is assumed to be in thermal equilibrium. Subsequently the combined equation of motion is solved to second order in the interaction and by averaging the result over the bath one gets the density matrix of the system itself. However, the differential equation obtained in this way has a serious flaw, which can be attributed to the inappropriate initial condition. For this reason we here take as starting point the thermal equilibrium of the combined system; the averages and correlation functions of quantities of interest provide us with the required information about the noise. This is explicitly demonstrated on the special model of a harmonic oscillator coupled to a bath of harmonic oscillators at temperature T. The result is compared with the standard calculation and it is shown that the latter is incorrect for time intervals smaller than kT/ħ. As an example the energy fluctuations in equilibrium are computed.

Traces of thermalization from p(t) fluctuations in nuclear collisions.

Abstract: Scattering of particles produced in high energy nuclear collisions can wrestle the system into a state near local thermal equilibrium. I illustrate how measurements of the centrality dependence of the mean transverse momentum and its fluctuations can exhibit this thermalization.

Thermal entanglement in the two-qubit heisenberg xyz model

Abstract: We study the entanglement of a two-qubit one-dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the concurrence of this system in terms of the parameters of the Hamiltonian and T. We show that depending on the relation among the coupling constants, it is possible to increase the amount of entanglement of the system by increasing its anisotropy. We also show numerically that for all sets of the coupling constants entanglement is a monotonically decreasing function of the temperature T, proving that we must have at least an external magnetic field in the z-direction to obtain a behavior where entanglement increases with T.

Thermal equilibrium and efficient evaporation of an ultracold atom-molecule mixture

Abstract: We derive the equilibrium conditions for a thermal atom-molecule mixture near a Feshbach resonance. Under the assumption of low collisional loss, thermodynamical properties are calculated and compared to the measurements of a recent experiment on thermal fermionic lithium atoms. We discuss and evaluate possible collision mechanisms which can lead to atom-molecule conversion. Finally, we propose a novel evaporative cooling scheme to efficiently cool the molecules toward Bose-Einstein condensation.

Modeling the transient flow of undercooled glass-forming liquids

Abstract: n a recent experimental study on flow behavior of Vitreloy-1 (Zr41.25Ti13.75Cu12.5Ni10Be22.5), three distinct modes of flow are suggested: Newtonian, non-Newtonian, and localized flow. In a subsequent study, the experimental flow data is utilized in a self-consistent manner to develop a rate equation to govern local free volume production. In the present study the production-rate equation is transformed into a transport equation that can be coupled with momentum and energy transport via viscosity to formulate a model capable to govern the flow of undercooled glass forming liquids. The model is implemented to study the flow behavior of undercooled Vitreloy-1 melt. For a temperature of 700 K and shear loading of 1.0 MPa, the model predicts that the flow profile gradually stabilizes to its Newtonian limit while the liquid is maintained in structural and thermal equilibrium. For the conditions of 675 K and 100 MPa, the model predicts that the flow profile departs from its Newtonian limit and gradually stabilizes to a non-Newtonian limit. The non-Newtonian profile is evaluated independently by considering structurally quasistatic conditions, which yield the shear-rate dependency of flow. For the conditions of 650 K and 2.0 GPa, the model predicts that the flow continuously localizes and ultimately accelerates unconstrained, while the system is driven out of structural and thermal equilibration towards an unstable state associated with free volume generation, viscosity degradation, and temperature rise. The computed temperature and shear rate evolutions for the three distinct flow modes are superimposed on a temperature-shear rate diagram and appear to computationally reproduce the experimental flow map. The system's structural state that appears to dictate flow behavior is quantified by a dimensionless number, which results from a time scale analysis of the free volume production equation.