Quantum mechanical theory of fluctuations and relaxation in semiconductor lasers

Pumping, spontaneous emission and electron-electron scattering lead to relaxation terms in the mean equations of motion for the electron system. These terms are derived from a quantum mechanical basis by second order perturbation theory and by appropriate reservoir averaging. If the electron distribution is not too strongly degenerate, then a relaxation time approximation can be derived. The quantum mechanical Langevin method is used to include noise. The correlation functions of all fluctuation operators are calculated. From the knowledge of the equations of motion and of the correlation functions it is possible to calculate the noise properties of the laser light and of the junction current, as will be shown in other publications.     

Equations of motion for rotational motion in liquids

The equations of motion corresponding to master equations describing rotational relaxation in liquids are shown to be purely deterministic and, in general, nonlocal in time.     

Microscopic derivation of kinetic equations for interacting optical two-level systems

Kinetic equations are derived for optical two-level atoms interacting with a molecular subsystem treated as a thermostat. It is assumed that the kinetics is determined by the electric dipole interaction perturbed by the thermal motion. Dynamic parts of the kinetic equations coincide with the corresponding terms of optical Bloch equations, whereas nonlinear relaxation and shift terms have the specific form and are absent in the phenomenological generalized Bloch equations. It is shown that the relaxation kinetics can be substantially different from the exponential one and depends on the initial state of the system. In particular, the inversion relaxation is frozen at small deviations from the equilibrium. The possibility of observation of the optical bistability is discussed.     

Linear relaxation processes governed by fractional symmetric kinetic equations

The fractional symmetric Fokker-Planck and Einstein-Smoluchowski kinetic equations that describe the evolution of systems influenced by stochastic forces distributed with stable probability laws are derived. These equations generalize the known kinetic equations of the Brownian motion theory and involve symmetric fractional derivatives with respect to velocity and space variables. With the help of these equations, the linear relaxation processes in the force-free case and for the linear oscillator is analytically studied. For a weakly damped oscillator, a kinetic equation for the distribution in slow variables is obtained. Linear relaxation processes are also studied numerically by solving the corresponding Langevin equations with the source given by a discrete-time approximation to white Levy noise. Numerical and analytical results agree quantitatively.     

A direct method for numerical analysis of relaxation of the statistical characteristics of brownian motion

We propose a numerical method for analyzing the relaxation of coordinate moments of the Brownian motion of a system described by a stochastic Liouville equation of the 1st or 2nd order with moderate-order polynomial nonlinearity. Using exact or approximate recurrence relations for the stationary values, at a certain step, we break the chain of equations for the moments of the Brownian motion. The evolution of the model probability distribution of coordinates is found from the numerical solution of the differential equations of relaxation of moments. This method is used for analyzing the nonstationary probability characteristics of a system with nonlinear rigidity described by a third-degree polynomial. The relaxation of moments and of the model probability distribution is plotted and tabulated. The results obtained allow us to draw certain conclusions on the statistical dynamics of the Brownian motion of the systems studied. Nizhny Novgorod Architecture and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 922–930, September 1999     

On the transition to aperiodic motion in linear systems with strong relaxation

The Bloch equations are shown to possess purely aperiodic solutions at intermediate values of the transverse relaxation coefficient only. We present also a simple example of a mechanical system where the regions of aperiodic motion are separated by the region of damped oscillations.     

Molecular motion and internal rotation in C6H5CHCl2 as studied by 13C relaxation data

Carbon-13 spin-lattice relaxation times and nuclear Overhauser enhancement factors of C₆H₅CHCl₂ in deuteriochloroform solutions were measured at several temperatures in the range from 233 to 323 K. The dipole-dipole relaxation rates were used with the Woessner's equations to calculate the rotational diffusion coefficients for the anisotropic motion. A random jump model was used to evaluate the internal rotation rate of the CHCl₂ group, which was found to be about two times faster than the overall motion. The carbon-13 spin-spin relaxation times were also qualitatively analyzed in terms of the possible relaxation mechanisms.     

Librational effects on carbon-13 N.M.R. spin-lattice relaxation times of tricyclic condensed molecules

A general method is described for calculating the effect of internal librational motion on the correlation times in tricyclic molecules having a folded structure about the central hetero-ring. The relaxation equations have been derived for isotropic as well as anisotropic models of overall molecular re-orientation. In the case of the isotropic model of motion, the parameter which determines the effective relaxation times is the librational amplitude; for the anisotropic model a somewhat more complicated correlation function is found. The present treatment provides a tool for interpreting in a quantitative way the spin-lattice relaxation times of hydrogen bearing carbons in pharmacologically important tricyclic systems where internal conformational flexibility could be exclusively monitored by using such a non conventional N.M.R. spectroscopic approach. Application of the method and its limitations are discussed briefly.     

Ultrasound propagation in dielectric glasses

The susceptibility of a two-level system coupled to a phonon heat bath is calculated by setting up its equation of motion and expanding the memory function (or self energy) and the inhomogeneity to second order in the coupling potential. Averaging over disorder yields attenuation and variation with temperature of sound velocity, which are compared to previous results obtained in the framework of the Bloch equations. The relaxation time approximation is avoided; there are new terms in both relaxation and resonant contributions.     

Pseudo critical relaxation

Two different growth laws and a divergent thermal relaxation time are obtained from the equations of motion of the interphase boundary during a simple order-disorder transition. Pseudo critical exponents of 2 and $\text{4}\text{3}$ characterize the relaxation.     

The kinetic foundation of extended irreversible thermodynamics revisited

Extended irreversible thermodynamics (EIT) has been used mainly to study the short-time behavior of fluids and some other systems. It has also been shown how the structure of the equations of motion constructed for the so-called relaxation variables coincides with those obtained by means of Grad's method in kinetic theory. In this work we calculate the generalized entropy from the one-particle distribution function up to 26 moments. We find that the characteristics of such entropy and the equations of motion for the relaxing variables are supported by the kinetic theory. This is not the case for the hierarchical relaxation hypothesis which is used in the applications of EIT to the generalized hydrodynamic regime.On temporary leave at the Universidad Iberoamericana, Mexico.     

Soliton relaxation in antiferromagnets

We study the relaxation two-parameter one-dimensional solitons in antiferromagnets using the phenomenological theory. Allowing for relaxation terms of a relativistic and exchange nature, we set up a system of evolution equations for the constants of the motion of a soliton and calculate the corresponding integral curves, which describe the variation of the soliton parameters in the relaxation process. Zh. éksp. Teor. Fiz. 111, 1633–1650 (May 1997)     

Variational principle for derivation of macroscopic equations

It is pointed out that the Schwinger variational principle of scattering theory applies to the case of linear and nonlinear relaxation problems in quantum statistics. By means of this principle it is possible to derive closed sets of equations for expectation values. To illustrate this variational method and to clarify the connection to other standard approaches some simple examples are treated for which the equations of motion are already known.     

The influence of measurement and relaxation time on flux jumps in high temperature superconductors

The influence of the magnetization and relaxation time on flux jumps in high temperature superconductors (HTSC) under varying magnetic field is studied using the fundamental electromagnetic field equations and the thermal diffusion equation; temperature variety corresponding to flux jump is also discussed. We find that for a low sweep rate of the applied magnetic field, the measurement and relaxation times can reduce flux jump and to constrain the number of flux jumps, even stabilizing the HTSC, since much heat produced by the motion of magnetic flux can transfer into coolant during the measurement and relaxation times. As high temperature superconductors are subjected to a high sweep rate or a strong pulsed magnetic field, magnetization undergoes from stability or oscillation to jump for different pause times. And the period of temperature oscillation is equal to the measurement and relaxation time.     

Non-Markovian theory of electron paramagnetic resonance in localized and quasi-localized electron spins via an example of manganites with colossal magnetoresistance

An approach based on the memory functions formalism is applied to derive non-Markovian equations of motion for the magnetization components of localized and quasi-localized electron spins under electron paramagnetic resonance (EPR) conditions using the example of manganites with colossal magnetoresistance. General Hasegawa-Bloch-type equations are applied to describe certain experimental data concerning the shape and the width of EPR lines and the longitudinal and transverse relaxation rates. Particular cases of these equations reproduce well-known theoretical results concerning EPR in manganites with colossal magnetoresistance. The results obtained explain certain well-known experimental phenomena and may stimulate further research.     

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers: a leading model to describe the onset of Johari-Goldstein processes and their relationship with fully cooperative processes

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. By varying the external thermodynamic parameters, a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.     

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers A leading model to describe the onset of Johari-Goldstein processes and their relationship with fully cooperative processes

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. By varying the external thermodynamic parameters, a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.     

A numerical study of an expanding plasma of quarks in a chiral model

We numerically solve the transport equations for a quark gas described by the the Nambu-Jona-Lasinio model. The mean field equations of motion, which consist of the Vlasov equation for the density and the gap equation for the mean field, are discussed, and energy and momentum conservation are proven. Numerical solutions of the partial differential equations are obtained by applying finite difference methods. For an expanding fireball the light quark mass evolves from small values initially to the value of 350 MeV. This leads to a depletion of the high energy part of the quark spectrum and an enhancement at low momenta. When collisions are included one obtains an equation of the Boltzmann type, where the transition amplitudes depend on the properties of the medium. These equations are given for flavor SU(3), i.e. including strangeness. They are solved numerically in the relaxation time approximation and the time evolution of various observables is given. Medium effects in the relaxation times do not significantly influence the shape of the spectra. The mass of the strange quark changes little during the expansion. The strangeness yield and the slope temperatures of the final spectra are studied as a function of the size of the initial fireball.