Showing papers on "Master equation published in 1986"
TL;DR: In this article, an exact gauge covariant equation of motion for the SU(N) quantum chromodynamic Wigner operator was derived, which naturally splits up into an on-shell constraint equation and a transport equation.
187 citations
TL;DR: In this article, an abstract diffusion-convection equation is introduced and the physical content of this equation is compatibility with equilibrium thermodynamics, which means that properties of solutions of the abstract diffusion convection equation are mathematical formulations of the experience on which thermodynamics is based.
115 citations
TL;DR: In this paper, it was shown that the usual master equation formalism of markovian open quantum systems is completely equivalent to a certain state vector formalism, where the state vector of the system satisfies a given frictional Schrodinger equation except for random instant transitions of discrete nature.
86 citations
TL;DR: In this article, a stochastic theory of entropy production for steady states in chemical reaction systems is presented, where small scale internal fluctuations around steady states are considered in the Gaussian regime.
Abstract: We present a stochastic theory of entropy production for steady states in chemical reaction systems. Small scale internal fluctuations around steady states are considered in the Gaussian regime. It is shown that in addition to the usual Gibbsian form of entropy production, there is an entropy production due to fluctuation which is of order O(V0). This comes from the non‐Poisson character of the probability distribution in a nonequilibrium system. Two approaches are considered: in the first, we use an entropy balance equation based on the master equation; in the second, we use a stochastic potential related to the probability distribution and built from the generalized Einstein relation. We show that both approaches give the same result for the entropy production of fluctuation (diS/dt) f . Next we consider a simple one‐component nonequilibrium system under the perturbation of a macroscopically large external fluctuation as a power generator. We interpret (diS/dt) f in terms of net power gain factor under...
67 citations
TL;DR: In this article, the classical limit of the quantum-mechanical theory, describing resonant electron transfer in atom-metal collisions, was studied and it was shown that the charge transfer process can be described in terms of a classical master equation, if the position of the atomic valence level depends on atom-surface distance z.
46 citations
TL;DR: In this paper, it was shown that the Schrodinger equation can be obtained from the one of a system of coupled differential equations generated from the potential harmonic expansion of the bound-state wave function of the system of identical particles governed by two-body central interactions.
Abstract: The solution of the Schrodinger equation can be obtained from the one of a system of coupled differential equations generated from the potential harmonic expansion of the bound-state wave function of a system of identical particles governed by two-body central interactions. It is shown that the system of coupled equations can be transformed into an equivalent integro-differential equation. For three bosons inS states this equation is identical to the Faddeev equation as written by Noyes. The integro-differential equations describing the triton for non-central realisticN-N forces are explicitly given.
43 citations
TL;DR: In this article, the theory of linear quantum amplifiers is reviewed and a simplified method using a "faked vacuum" is introduced to derive amplifier master equations and the solution is derived and used as the amplifier transfer function.
Abstract: The theory of linear quantum amplifiers is reviewed. A simplified method using a "faked vacuum" is introduced to derive amplifier master equations. Properties of various amplifiers are summarized. The solution is derived and used as the amplifier transfer function. The Caves' theory for amplifier added noise is discussed. The properties of squeezed states are reviewed, the use of the Wigner function to describe them is advocated. Finally the amplification of squeezed states is discussed in the Wigner representation.
43 citations
TL;DR: In this article, the stationary probability distributions of master equations in the leading order of the system-size are the Lyapounov functions of the corresponding kinetic equations and may be candidates of the potentials of the systems far from equilibrium.
Abstract: It is shown that the stationary probability distributions of master equations in the leading order of the system-size are the Lyapounov functions of the corresponding kinetic equations and may be candidates of the potentials of the systems far from equilibrium.
40 citations
37 citations
TL;DR: A theoretical framework for analyzing multiregional migration as a stochastic process is presented and how the approach can be applied to empirical migration data in a study of migration processes in Canada is described.
31 citations
TL;DR: In this paper, a fully quantum-mechanical treatment of an atomic radiation field interaction is developed with the aim of deriving basic equations for a nondegenerate four-wave mixer.
Abstract: By closely following the work of Reid and Walls, a fully quantum-mechanical treatment of an atomic radiation-field interaction is developed with the aim of deriving basic equations for a nondegenerate four-wave mixer. The resultant equations are examined in forward and cavity geometries for their implications regarding squeezed states. Good agreement between our theory and the experiments of Slusher et al. is demonstrated.
TL;DR: In this article, the authors extended localized functions to obtain master equations for random walk processes among non equivalent sites, starting from a diffusional equation that includes a mean force potential, and showed that the transition rates and their Arrhenius behavior are computed by projecting the diffusion operator onto a function set whose dimension is equal to the number of potential minima.
Abstract: The use of localized functions is extended to obtain master equations for random walk processes among non equivalent sites, starting from a diffusional equation that includes a mean force potential. As a numerical application, the kinetic parameters are calculated for a collection of rotors in asymmetric double-minimum potentials, and for the trans-gauche isomerization of butane. These examples show that the transition rates and their Arrhenius behaviour are computed by projecting the diffusion operator onto a function set whose dimension is equal to the number of potential minima.
TL;DR: The use of the Wigner function is advocated for the description of squeezed states in this article, where the solution of the amplifier master equation for the WIGNer function was presented and the presence of squeezing after signal amplification was discussed.
TL;DR: In this article, the authors derived time-convolutionless forms of the quantal master equations for driven open systems from the Liouville equation for the total system under an arbitrary initial condition for the two cases of weak external driving fields and of arbitrary ones.
Abstract: Time-convolutionless forms of the quantal master equations for driven open system are derived from the Liouville equation for the total system under an arbitrary initial condition for the two cases of weak external driving fields and of arbitrary ones. They have forms convenient for the perturbational expansions, and are respectively compared with the time-convolution forms of equations in the lowest Born approximation for the interaction H SB of the system with its surroundings. It is shown that the time-convolutionless forms of equations prevail over the time-convolution ones, and that the conventional Markoffian approximation for the latter in the narrowing limit leads to the incorrect conclusion. The time-convolutionless form of master equation is expanded up to n -th order in powers of the external driving fields in the lowest Born approximation for H SB .
TL;DR: In this paper, generalised master equations in two equivalent forms, namely differential master equations (DME) and integro-differential master equation (IDME), are obtained and the non-linear optical problems of high-power radiation absorption, the resonance fluorescence spectrum and the free induction decay signal are discussed.
Abstract: Generalised master equations in two equivalent forms, namely differential master equations (DME) and integro-differential master equations (IDME), are obtained. Both differ from the Bloch ones in that they take into account the density matrix dynamics during the correlation time tau C of the relaxational perturbations. On the basis of these equations, the non-linear optical problems of high-power radiation absorption, the resonance fluorescence spectrum and the free induction decay signal are discussed.
TL;DR: In this article, the authors considered a linear chain of adsorption sites in an Ising model with nearest neighbor interactions and showed that desorption is frequently of fractional (including zero) order.
TL;DR: The normal resistance of a hysteretic Josephson junction is model by writing a master equation to describe the individual quasiparticle tunneling and is found to be nonsymmetric, non-Boltzmann distribution of voltage fluctuations, similar to the results obtained in a previous discussion based on the Fokker-Planck equation.
Abstract: We model the normal resistance of a hysteretic Josephson junction by writing a master equation to describe the individual quasiparticle tunneling. We solve the master equation by a WKB method near the zero-voltage state and near the nonzero-voltage state. We find that near the zero-voltage state the solution is given by the Boltzmann distribution with second-order corrections while near the nonzero-voltage state we obtain a nonsymmetric, non-Boltzmann distribution of voltage fluctuations, similar to the results obtained in a previous discussion based on the Fokker-Planck equation.
TL;DR: In this paper, a density operator formalism is used to describe the fluorescence of a molecule in a 1Π electronic state in a static electric field under both pulsed and cw excitation.
Abstract: A density operator formalism is used to describe the fluorescence of a molecule in a 1Π electronic state in a static electric field under both pulsed and cw excitation. Coherences can be created both between M levels as well as between the e and f Λ‐doublet levels. Explicit solution of the generalized master equation allows the development of general expressions for the excited state density matrix elements, under conditions where collisions, hyperfine structure, optical pumping, and optical saturation are ignored. Simple expressions are obtained for the fluorescence intensities, valid at high J and whenever the Stark shifts are significantly smaller than zero‐field Λ‐doublet splitting. A simulation study of the expected quantum beat patterns is reported based on the parameters reported by Mandich, Gaebe, and Gottscho [J. Chem. Phys. 83, 3349 (1985)] in their experimental study of BCl(A1Π). Attention is focused on the extent to which quantum beat effects will be obscured by the finite widths of the laser ...
TL;DR: A theoretical treatment for fast, multiple bond-switching reactions, such as NO + NH2 → N2 + H2O, is given in this article, where the collision complex involved (whether long or short lived) is shown to be extremely anharmonic.
Abstract: A theoretical treatment is given for fast, multiple bond-switching reactions, such as NO + NH2 → N2 + H2O. These reactions are characterized by all or most of the bonds being broken. The collision complex involved (whether long or short lived) is shown to be extremely anharmonic. Consideration of the master equation describing the competing processes of complex formation, internal rearrangement and collisional deactivation yields easily applied sufficient conditions for the recombination rate coefficient being independent of pressure.
TL;DR: In this article, the Lehmberg-Agarwal master equation is used to study cooperative spontaneous emission by a system of three identical two-level atoms, and a choice of basis states is described which allows an exact solution to be obtained for any geometrical configuration, any sample size, and any initial conditions of the atomic system, fully including both near field and super-radiance effects.
Abstract: The Lehmberg-Agarwal master equation is used to study cooperative spontaneous emission by a system of three identical two-level atoms. A choice of basis states is described which allows an exact solution to be obtained for any geometrical configuration, any sample size, and any initial conditions of the atomic system, fully including both near-field and super-radiance effects.
TL;DR: In this paper, the authors discuss the application of a systematic continued-fraction (CF) theory to problems in quantum mechanics with particular reference to atomic and molecular physics, and the methods applied to the perturbation theory of the Von Neumann equation for the density matrix, or to the master equation.
Abstract: Publisher Summary This chapter discusses the application of a systematic continued-fraction (CF) theory to problems in quantum mechanics with particular reference to atomic and molecular physics. The CF theory offers a number of advantages. First, certain subsets of terms in the conventional perturbation series are summed to all orders. Second, the rate of convergence is usually much faster than that of power series. Third, the solutions can be written down directly using fairly simple rules without solving the equations of motion and finally, the continued-fraction approach is a unifying one, as the various other perturbation methods such as Lennard–Jones–Wigner–Brillouin, Rayleigh–Schrodinger, and projection operator can all be understood within this framework. The methods applied to the perturbation theory of the Von Neumann equation for the density matrix, or to the master equation are discussed. Exact rate equations are derived, and examples of their use are cited.
TL;DR: In this paper, the authors examined the relaxation of a primary system coupled weakly to a bath of environmental modes from the standpoint of recent developments in the semiclassical theory of molecular bound states.
Abstract: The relaxation of a primary system coupled weakly to a bath of environmental modes is examined from the standpoint of recent developments in the semiclassical theory of molecular bound states. Emphasis is placed upon highly excited, strongly nonlinear (but quasiperiodic) primary systems and zero temperature baths. The starting point for the analysis is a master equation for the populations of the eigenstates of the primary system. The correspondence principle provides semiclassical approximations to the transition rates, allowing quantum state populations to be calculated from classical trajectories. A second semiclassical approximation leads to an equation of motion for a probability density in the classical action variables. As h→0, this density agrees with the density generated by running an ensemble of damped classical trajectories and averaging out the angle variables; retention of terms of order h provides smoothed quantum corrections. Numerical examples of both semiclassical approximations are presented.
TL;DR: In this article, the connection between a coupled non-Markovian Chapman-Kolmogorov equation and the coupled generalized master equation is established, in particular the model of coupled random walk is used for the description of correlated Brownian motion with anisotropic scattering.
Abstract: The connection between a coupled non-Markovian Chapman-Kolmogorov equation and the coupled generalized master equation is established. In particular the model of coupled random walk is used for the description of correlated Brownian motion with anisotropic scattering.
TL;DR: In this article, the authors examined the dependence on energy of the energy transfer step sizes of cyclobutene initiated by direct single photon excitation of C-H stretching overtones and interpreted the observed behavior using a treatment combining RRKM theory and models accounting for weak intermolecular energy transfer.
Abstract: The kinetics of the gas phase isomerisation of cyclobutene initiated by direct single photon excitation of C–H stretching overtones have been studied and the observed behavior has been interpreted using a treatment which combines RRKM theory and models accounting for weak intermolecular energy transfer. Results obtained from the excitation of five different overtone states spanning an energy range of 5070 cm−1 have allowed us to examine the form of the dependence on energy of the energy transfer step sizes 〈ΔE〉 deduced from numerical solutions of the collisional master equation using an exponential‐down model, for the collider gases cyclobutene, SF6, CHF3, CH4, CO2, H2, CO, N2, Ar, and He. Our calculations indicate very small energy transfer step sizes, particularly for the most inefficient collider molecules. We discuss the factors which might contribute to the determination of low values for 〈ΔE〉 and the sensitivity of the master equation calculations to details of the RRKM model. Our results, when expr...
TL;DR: In this paper, the authors developed a method to compute corrections to the master equation for chemically reacting systems in particle number space that arise if the system is not a well-stirred tank reactor, but the transport occurs by diffusion.
Abstract: We develop a concise method to compute the corrections to the master equation for chemically reacting systems in particle number space that arise if the system is not a well-stirred tank reactor, but the transport occurs by diffusion. Starting from the master equation in theR N space of all reactant particle positions, we expand in inverse powers of the diffusion constant and eliminate all transport modes adiabatically. It is found that the overall effect of spatially nonuniform fluctuations cannot be treated as a mere renormalization of the reaction rate constants. From second order on there appear correction terms with a new structure that corresponds formally to additional virtual reaction paths. An intuitive interpretation along this line is impeded, however, by the formal occurrence of negative reaction rate constants in these terms, i.e., the reaction rate may depend on the concentrations of the final products of the virtual reaction rather than on the ingoing products. We also identify Avogadro's constant as the suitableΩ parameter and extend van Kampen'sΩ-expansion systematically, to spatially continuous systems. This secondary expansion then serves to interpret the corrections to the rate equation, and the average and autocorrelation of the density in the stationary state. It is seen that the limitsD→∞ andΩ→∞ do not commute. The relevant length and time scales are discussed.
TL;DR: General properties of the competing phonon induced redistribution and optical excitation of the level populations are presented, and exemplified by an explicit elaboration of a three level system.
Abstract: : Adsorbed atoms on the surface of a harmonic lattice are immersed in a strong laser field. The optical Bloch equations are derived, which include the thermal relaxation and the coherent excitation of the adbond. This is accomplished by a transformation to dressed states, which diagonalizes the interaction with the laser. The single phonon couplings are then understood as transitions between dressed states. The radiative contributions for arbitrary strong fields are obtained in the master equation, and it is shown that the coherences with respect to the dressed states decay exponentially, due to the phonon relaxation. General properties of the competing phonon induced redistribution and optical excitation of the level populations are presented, and exemplified by an explicit elaboration of a three level system. The results are amenable to analytical evaluation once the interaction potential is prescribed, and extensions of the approach to include multiphonon processes are straightforward.
15 Apr 1986
TL;DR: In this article, the authors measured the vibrational relaxation times of pure acetylene in the gas phase behind incident shock waves in the temperature range 613-1184 K using a laser-schlieren technique.
Abstract: Vibrational relaxation times of pure acetylene in the gas phase were measured behind incident shock waves in the temperature range 613–1184 K using a laser-schlieren technique. Overall, the results are in excellent agreement with those of acoustic and laser excitations. However, we find a marked intrinsic time dependence of the phenomenological time, which varies by factors of two to three over a wide dynamic time scale of at least six natural lifetimes. In other words, the Bethe—Teller law fails. This is confirmed by numerical solution of the master equation for a wide choice of intermode collisional coupling parameters. The density of states involved in the energy transfer process determines whether the relaxation time increases or decreases with time, and the effect is amplified by the importance of intermolecular VV processes relative to intramolecular processes.
TL;DR: Under the conditions that one or both these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude ensembles.
Abstract: A formalism is presented to treat the effects of finite-bandwidth excitations on the fluorescent spectra and second-order intensity-correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom. Under the conditions that one or both these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude ensembles. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity-correlation functions.