Radiation In Thermal Equilibrium Research Articles

Correction of self-absorption effect in laser-induced breakdown spectroscopy based on temperature iteration

Laser-induced breakdown spectroscopy (LIBS) is an ideal real-time on-line method for the detection of minor elements in alloy steel, but it needs to solve the undesired self-absorption effect in plasma. Since the plasma electron temperature (T), radiation particle number density and absorption path length (Nl) determine the degree of self-absorption and affect the corrected spectral line intensity, a new temperature iterative self-absorption correction method based on the plasma thermal equilibrium radiation model is proposed to continuously calculate and correct these two parameters. Compared with generally applied self-absorption correction methods, this method has obvious advantages of simple programming, high computational efficiency, and independence of the availability or accuracy of Stark broadening coefficients. The quantitative analysis results of Cu show that the linearity of calibration curves and the measurement accuracy of elemental content are significantly improved with the self-absorption correction. In addition, this method can directly obtain the accurate radiation particle number density and absorption path length, which benefits the plasma diagnostics and quantitative analysis.

Negative entropy production in L-lactate dehydrogenase kinetics

Fröhlich theory of coherent excitations in biological systems is analyzed. L-lactate dehydrogenase kinetics is studied using the activation process model for non-equilibrium cases. The model explains the process of energy accumulation necessary for carrying out catalytic reactions in a living cell by means of interaction of quantum subsystems with thermal equilibrium radiation, light, and radiation energy of metabolic processes occurring in the cell. It is shown that lactate dehydrogenase catalyzes the interconversion of pyruvate and lactate with concomitant interconversion of NADH and NAD+ in three ways, that is, three reactions occur simultaneously. Negative information entropy for the reactions under consideration is calculated. Its absolute value is equal to that of information entropy of the elementary activation act. This fact ensures the principle of stable non-equilibrium and indicates the reaction under consideration belongs to a living cell.

The global optimal reference field for the difference formulation in the implicit Monte Carlo radiation transport

Statistical noise has always been one of the most important problems hindering the wide application of the Monte Carlo method in thermal radiative transfer. The difference formulation which has been introduced in recent years is a source manipulation variance reduction technique, in which the radiation intensity is defined relative to a reference field. In this formulation, the transport operator remains unchanged, but the solution and source functions are changed. Numerical results show that in this formulation the symbolic implicit Monte Carlo (SIMC) method can significantly reduce statistical noise in some cases. The standard formulation can be considered as a special formulation where the reference field is zero. In general, the reference field is chosen as the thermal equilibrium radiation field at the beginning or end of the time step. However, we found that this choice can lead to a larger statistical noise than in the standard formulation in some cases, and even non-physical oscillation of the calculation results, which severely restrict the application of this method.In this paper, we develop the difference formulation based on generalized reference fields, and the Fleck-Cummings implicit Monte Carlo technique is employed to solve the functions. Through analysis, we find that the choice of the reference field is the key to reduce statistical noise. We define the global optimal reference field, which satisfies the minimum for the L1 norm of energy weights of the particles emitted during a time step. Although it is difficult to find the global optimal reference field, we propose a scheme to select a reference field which satisfies that the statistical noise is lower than the zero reference field in most cases. Numerical results show that the new method can avoid the nonphysical oscillation that occurs in regions of the problem with sharp spatial gradients in the solution in the classical difference formulation. The method also leads to a remarkable reduction in noise comparing to the Fleck-Cummings implicit Monte Carlo method in the standard formulation.

Fluctuation Dissipation Theorem and Electrical Noise Revisited

The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter. By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the linear-response regime, the theorem interrelates the macroscopic spontaneous fluctuations of an observable with the kinetic coefficients that are responsible for energy dissipation in the linear response to an applied perturbation. In the quantum form provided by Callen and Welton in their pioneering paper of 1951 for the case of conductors [H. B. Callen and T. A. Welton, Irreversibility and generalized noise, Phys. Rev. 83 (1951) 34], electrical noise in terms of the spectral density of voltage fluctuations, [Formula: see text], detected at the terminals of a conductor was related to the real part of its impedance, [Formula: see text], by the simple relation [Formula: see text] where [Formula: see text] is the Boltzmann constant, [Formula: see text] is the absolute temperature, [Formula: see text] is the reduced Planck constant and [Formula: see text] is the angular frequency. The drawbacks of this relation concern with: (i) the appearance of a zero-point contribution which implies a divergence of the spectrum at increasing frequencies; (ii) the lack of detailing the appropriate equivalent-circuit of the impedance, (iii) the neglect of the Casimir effect associated with the quantum interaction between zero-point energy and boundaries of the considered physical system; (iv) the lack of identification of the microscopic noise sources beyond the temperature model. These drawbacks do not allow to validate the relation with experiments, apart from the limiting conditions when [Formula: see text]. By revisiting the FDT within a brief historical survey of its formulation, since the announcement of Stefan–Boltzmann law dated in the period 1879–1884, we shed new light on the existing drawbacks by providing further properties of the theorem with particular attention to problems related with the electrical noise of a two-terminals sample under equilibrium conditions. Accordingly, among others, we will discuss the duality and reciprocity properties of the theorem, the role played by different statistical ensembles, its applications to the ballistic transport-regime, to the case of vacuum and to the case of a photon gas.

A Study of Fundamental Law of Thermal Radiation and Thermal Equilibrium Process

The fundamental law of thermal equilibrium radiation includes two elements: the law of energy distribution of matter vibrators in the radiation field and the law of energy exchange between vibrators and the radiation field. This paper discovers the law of how vibrators stimulate and absorb radiation, by a study of the black-body radiation law and the characteristics of vibrators’ absorption of radiation. As for the fundamental law of thermal equilibrium radiation, its complete expression should be: the energy distribution of vibrators in the thermal equilibrium radiation field follows the energy distribution law by L. Boltzmann; the probability of vibrators’ stimulating radiation is directly proportional to their state of energy levels and that of their absorbing radiation is directly proportional to their energy distribution probability. The author, on the basis of the fundamental law of thermal radiation, proposes conditions for thermal equilibrium radiation and analyses the micro momentum theory and characteristics in the process of thermal equilibrium.

Bose–Einstein condensation of photons in an optical microcavity

Bose-Einstein condensation (BEC)-the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density-has been observed in several physical systems, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state. Theoretical works have considered thermalization processes that conserve photon number (a prerequisite for BEC), involving Compton scattering with a gas of thermal electrons or photon-photon scattering in a nonlinear resonator configuration. Number-conserving thermalization was experimentally observed for a two-dimensional photon gas in a dye-filled optical microcavity, which acts as a 'white-wall' box. Here we report the observation of a Bose-Einstein condensate of photons in this system. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. The photons thermalize to the temperature of the dye solution (room temperature) by multiple scattering with the dye molecules. Upon increasing the photon density, we observe the following BEC signatures: the photon energies have a Bose-Einstein distribution with a massively populated ground-state mode on top of a broad thermal wing; the phase transition occurs at the expected photon density and exhibits the predicted dependence on cavity geometry; and the ground-state mode emerges even for a spatially displaced pump spot. The prospects of the observed effects include studies of extremely weakly interacting low-dimensional Bose gases and new coherent ultraviolet sources.

Activation process model: Einstein coefficients for activation barrier

Analytical calculation of Einstein coefficients is made for activation barrier of the Boltzmann–Arrhenius model and an activation process model. For the activation process model an activation barrier is shown to have discrete energy structure due to its thermodynamic equilibrium with thermal radiation. This structure is determined by interaction of conformation substates of a molecule with thermal radiation. The Boltzmann–Arrhenius model represents an activation process as a result of the work of high-energy spectral components of thermal equilibrium radiation. The process is realized by overcoming a potential barrier with continuous energy structure. However, it is shown, that such process is essentially non-equilibrium and hard to achieve at thermal equilibrium radiation.

GRAVITATIONAL THERMODYNAMICS OF SPACETIME FOAM IN ONE-LOOP APPROXIMATION

We show from one-loop quantum gravity and statistical thermodynamics that the thermodynamics of quantum foam in flat spacetime and Schwarzschild spacetime is exactly the same as that of Hawking–Unruh radiation in thermal equilibrium. This means we show unambiguously that Hawking–Unruh thermal radiation should contain thermal gravitons or the contribution of quantum spacetime foam. As a by-product, we give also the quantum gravity correction in one-loop approximation to the classical black hole thermodynamics.

Black-body radiation in plasmas

The theory of black-body radiation in thermal equilibrium with a homogeneous and isotropic plasma is presented. The relevant thermodynamic quantities of the radiation are obtained. The presence of the plasma changes qualitatively and often quantitatively the concept of black-body radiation, essentially through the effect of plasma density.

What cavities? Containers in black-hole thermodynamics

Most spherical thin shells, enclosing black-body radiation satisfy the dominant energy condition if their matter--energy is at least of the total mass--energy. Containers with less matter--energy may be able to sustain high radiation pressures, but the radiation will be mostly unstable. Containers with negligible energy are either unable to sustain the radiation pressure or the radiation is unstable to gravitational collapse (or both at the same time). Containers with black holes and radiation in thermal equilibrium, considered in the literature, are often unrealistic.

Methods of quantum mechanics applied to partially coherent light beams

Whenever the natural modes of the modal expansion of the cross-spectral density have a common waist, the wave equation in the waist plane has the form of a two-dimensional Schrodinger equation. Thus the results of quantum mechanics and quantum statistics, including the quantized Schrodinger field, can be transferred to partially coherent light. Such conceptions as temperature, entropy, and energy are used advantageously. A subclass of radiation, radiation in thermal equilibrium, is introduced, and, as examples, the Gaussian Schell-model beam and the quasi-rectangle model beam are investigated. The M2 factor is strongly related to the mean value of energy.

Kerr black hole in equilibrium with a rotating heat bath.

The equilibrium and stability of a rotating black hole in a finite heat bath is discussed. An axisymmetric box of radiation in thermal equilibrium rotates rigidly, and some radiation slumps towards the outer wall. When such a heat bath is in equilibrium with a black hole, the temperatures and angular velocities of the hole and the bath are equal. The situation in which the heat bath is in a cylindrical box much larger than the hole, and contains only massless modes, is particularly simple and may be examined in detail. A sufficient condition for the stability of the equilibrium can be derived, analogous to the stability condition derived by Davies and by Gibbons and Perry for the nonrotating case. Depending on the total energy {ital E}, total angular momentum {ital J}, and radius {ital R} of the heat bath, the system at equilibrium may be in one of three thermodynamic regimes: a radiation-only state, a state dominated by a black hole, or a transition state in which both the black hole and the heat bath contain significant energy, angular momentum, and entropy.

Entropy and other thermodynamic properties of classical electromagnetic thermal radiation.

Building upon previous work, several new thermodynamic properties are found for classical electromagnetic random radiation in thermal equilibrium with classical electric dipole harmonic oscillators. Entropy is calculated as a function of temperature and as a function of the positions of the dipole oscillators. In the process, a new derivation is obtained for what is often called Wien's displacement law. The original derivation of this law makes a number of implicit assumptions not found in the present derivation, which prevents the original analysis from being sufficiently general to address an important class of thermal radiation spectrum candidates: namely, those that are nonzero at T=0. While leading up to the entropy calculation, a number of other thermodynamic properties are deduced. For example, a natural development is presented for reformulating the St\'efan-Boltzmann law to correspond to experimental observations about changes in thermal radiation energy. Also, the Rayleigh-Jeans spectrum is shown to conflict with basic concepts of thermodynamic processes, and asymptotic limits are found for the spectrum of classical electromagnetic thermal radiation. One asymptotic restriction arises from the demand of finite specific heat for thermal radiation. This restriction is sufficient to ensure that the classical electrodynamic system of dipole oscillators and thermal radiation must obey the third law of thermodynamics. The calculations described here include full nonperturbative evaluations of retarded van der Waals thermodynamic functions.

On the impossibility of a box for holding gravitational radiation in thermal equilibrium

In a recent paper David Garfinkle and Robert Wald argue that it is possible to build a “box” which will confine and thermalize gravitational radiation. Using the results of their calculations I will show that the Garfinkle-Wald (GW) box will fail to isolate and thermalize gravitational radiation in a universe with external gravitational radiation. The absence of alocal equilibrium distribution of gravitational radiation in this model is further evidence that an operational interpretation of a quantum theory of gravity based on General Relativity and traditional matter couplings does not exist.

On the possibility of a box for holding gravitational radiation in thermal equilibrium

We show that it is possible in principle to build a box which will hold gravitational radiation for a time long enough to thermalize it. The box is a thin spherical shell of charged matter with a large red shift at the surface of the shell. The radiation is kept in the box by the gravitational potential of the shell and is thermalized by the conversion between gravitational and electromagnetic radiation. We calculate the time for escape of the radiation and show that it is longer than the conversion time.

Accelerated observers do not detect isotropic thermal radiation

We investigate a model of a uniformly accelerated particle detector which possesses directional discrimination and find that it responds as though subjected to an anisotropic time-dependent flux of radiation. Only a detector responsive to disturbance in the forward and/or reversed directions of motion responds as though immersed in a bath of thermal equilibrium radiation.

Second law and radiation

The available energy of thermal radiation and solar radiation is examined in this paper. The extension of the available energy concept to the evaluation of the potential energy conversion in solar converters is outlined. The fundamental question discussed is: How much of a given solar radiation flux is convertible to thermodynamic work? The basic relations for evaluating the available energy in radiation processes are developed. The effects of both the spectral and spacial distribution of the radiation on the available energy are discussed. Atmospheric effects are examined, using NASA standard atmosphere solar spectral distributions. The available energy of the spectral characteristics is compared with the available energy of thermal equilibrium radiation at the same solar flux. This is used to illustrate the available energy losses in thermal energy converters. The technical evaluation of solar energy converters are discussed, based on the available energy of the input energy. A method for evaluating spectral sharing solar conversion devices and solar energy simulators is outlined.

The opacity of expanding media - The effect of spectral lines

Spectral lines are more effective in slowing the transport of radiation in expanding (or contracting) objects than in static ones. The velocity gradient associated with the expansion causes the frequency of the photons to be continuously redshifted relative to the rest frame of the gas through which they travel. Those photons which are redshifted to the frequency of a sufficiently strong line will be absorbed by the corresponding bound-bound transition, and the net effect will be to increase the effective opacity of the gas. In certain cases the effect can be taken into account by using an effective opacity, the expansion opacity, which is a function not only of the temperature and density but also of the velocity gradient.Practical formulae for computing the expansion opacity and its Rosseland mean in terms of sums over spectral lines are derived. It is shown that the cumulative effect of many weak lines can be important, implying that a large list of spectral lines is required to obtain results of even modest accuracy. Numerical computations using the 260,000-entry line list of Kurucz and Peytremann have been completed and some samples of the result are given. The general effect may be important in many astronomicalmore » objects, but only in some of these will be detailed approach of this paper be appropriate. In optically thick supernova shells, the effect is important both in maintaining the radiation in thermal equilibrium as it diffuses out of the shell and in increasing the value of the total opacity. The enhancement of the opacity ranges from less than 1% to more than an order of magnitude, depending on the temperature, density, and velocity gradient.« less

An Application of Green's Function in the Theory of Optical Coherence

The relation between the retarded Green's function and second-order correlation tensor of electromagnetic potential for a pure electromagnetic radiation in thermal equilibrium is derived. This relation holds also for a long wavelength electromagnetic radiation in media, so long as the radiation is in thermal equilibrium. The electromagnetic second-order correlation tensors for blackbody radiation is obtained, using the relation mentioned above. Upon following Abrikosov, Gorkov and Dzyaloshinski the retarded Green's function for a electromagnetic radiation interacting with matter is expressed in terms of the complex dielectric constant which is necessarily introduced for carrying out a macroscopic formulation. With the assumption of spatial homogeneity of media the electromagnetic second-order correlation tensors for an optical field are obtained. These correlation tensors are also expressed in tems of the complex dielectric constant. This retarded Green's function is simply related to the temperature Green's function, so that the diagram analysis will possibly be applied in the theory of optical coherence for an interacting radiation with matter.