External Stochastic Field Research Articles

Relaxation of a three-level atom in stochastic fields and its spectroscopic properties

Relaxation of a motionless three-level atom with a non-equidistant spectrum in a photon heat bath and an external stochastic field is investigated. In the Markovian approximation of the relaxation processes a master equation for the reduced density matrix is derived by making use of the averaging over realizations of the stochastic field. The master equation is solved exactly. The correlation functions, the shapes of the radiation lines, the intensity correlation and photon number spectrums are calculated for the V, Ξ and Λ atoms and realizations of the stochastic field by a delta-correlated and a Kubo-Anderson processes.

Master equation averaged over stochastic process realizations for the description of a three-level atom relaxation

The relaxation of a three-level atom interacting with a photon heat bath and an external stochastic field is investigated. For the reduced density matrix, a master equation averaged over stochastic process realizations is derived. An exact solution is obtained and the radiation line shapes are calculated.

The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

By generalizing Bogolyubov’s reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton’s equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the single-particle distribution function, we use a regular cutoff procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation, we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases are discussed by assuming either Gaussian statistics of external perturbation or homogeneity of the system.

Quantum systems in regular and stochastic fields. Creation and destruction of the coherence

The problem of the coherent state generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy the coherence. The competition of these processes is considered on the basis of the Fokker-Planck equations approach, derived from the master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochastic field in a nonideal resonator are considered. Average over the realizations of stochastic fields is performed for the case of the white Gaussian noise and the Kubo-Anderson process. Explicit formulas for probability and shape of radiation line are obtained.

Noise-driven nonlinear sigma model

We present a noise-driven model for obtaining the gap and line-width as functions of the temperature in the nonlinear sigma model. The method is phenomenological and rests on the following physical idea: a classical external stochastic field is introduced representing the coupling of the sigma field with a noise source. Moreover, we assume that the inelastic scattering length is much longer than the elastic one, justifying the neglect of dissipation for temperatures such that the nonlinear sigma model is a good approximation for antiferromagnetic spin chains. This phenomenological approach is justified by comparison with other theoretical predictions and with experiment.

Fluctuations of the magnetization in thin films due to conduction electrons

A detailed analysis of damping and noise due to a $sd$ interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey, in general, a nonlocal equation of motion, which differs from the the Gilbert equation and is extended to the nonadiabatic regime. To the lowest order in the exchange interaction and in the limit where the Gilbert equation applies, we show that the damping term is enhanced due to interfacial effects, but it also shows oscillations as a function of the film thickness. The noise calculation is, however, carried out to all orders in the exchange-coupling constant. The ellipticity of the precession of the magnetization is taken into account. The damping is shown to have a Gilbert form only in the adiabatic limit, while the relaxation time becomes strongly dependent on the geometry of the thin film. It is also shown that the induced noise characteristic of $sd$ exchange is inherently colored in character and depends on the symmetry of the Hamiltonian of the magnetization in the film. We show that the $sd$ noise can be represented in terms of an external stochastic field, which is white only in the adiabatic regime. The temperature is also renormalized by the spin accumulation in the system. For large intra-atomic exchange interactions, the Gilbert-Brown equation is no longer valid.

Spinodal decomposition of expanding nuclear matter and multifragmentation

Density fluctuations of expanding nuclear matter are studied within a mean-field model in which fluctuations are generated by an external stochastic field. Fluctuations develop about a mean one-body phase-space density corresponding to a hydrodinamic motion that describes a slow expansion of the system. A fluctuation-dissipation relation suitable for a uniformly expanding medium is obtained and used to constrain the strength of the stochastic field. The distribution of the liquid domains in the spinodal decomposition is derived. Comparison of the related distribution of the fragment size with experimental data on the nuclear multifragmentation is quite satisfactory.

Density fluctuations and multifragmentation of nuclear matter

The density fluctuations of nuclear matter are studied within a mean-field model in wich fluctuations are generated by an external stochastic field. The constraints imposed on the random force by the fluctuation-dissipation theorem are analyzed. It is shown that in the proximity of the borders of the spinodal region the assumption of a white-noise stochastic field can be reliably used. The domain distribution of the liquid phase in the spinodal decomposition of nuclear matter is derived. The related distribution of fragment sizes compares favourably with the experimental fragment distribution observed in heavy ion collisions.

Dynamics of the dissipative two-level system driven by external telegraph noise

The dissipative dynamics of a two-level system coupled to a thermal bath and driven by an external stochastic field is studied. Within an approach similar to the noninteracting-blip approximation, an integro-differential kinetic equation for the difference of the level populations averaged with respect to the bath is derived. An exact averaging of this kinetic equation is performed for the case of a dichotomous external force. The resulting equation is used to examine the long-range electron tunneling driven by external telegraph noise.

Kinetic effects in stochastic topologically nontrivial field

The kinetic description of a collisionless system of particles in an external stochastic field possessing helicity is examined. The kinetic equation which contains an additional term proportional to the helicity is obtained. The solution describing evolution of the distribution function for arbitrary initial conditions is found. Particular examples of such an evolution and some new kinetic effects connected with helicity are discussed. It is shown that a particle beam with inhomogeneous velocity profile in an external stochastic helical field generates a new particle flow in transverse direction.

Stochastically averaged master equation for a quantum-dynamic system interacting with a thermal bath.

The methods of nonequilibrium density-matrix and coarse-temporal conception are used to obtain the kinetic equation for the parameters ${\ensuremath{\gamma}}_{\mathit{n}\mathit{m}}$(t)=Sp[\ensuremath{\rho}^(t)\ensuremath{\Vert}n〉〈m\ensuremath{\Vert}] of a quantum-dynamic system (QDS) interacting with a thermal bath and external stochastic field. It is important that the stochastic field is taken exactly into consideration. For diagonal QDS parameters ${\ensuremath{\gamma}}_{\mathit{n}\mathit{n}}$(t) this equation is reduced to the generalized Pauli equation (GPE) with stochastic time-dependent coefficients ${\mathit{w}}_{\mathit{n}\mathit{m}}$(t). Special attention is given to the procedure of averaging over stochastic processes. It is shown that after averaging over energy fluctuations affected by the stochastic field, in the first cumulant approximation in terms of stochastic processes ${\mathit{w}}_{\mathit{n}\mathit{m}}$(t), the GPE is transformed to the Pauli equation for the QDS state population ${\mathit{P}}_{\mathit{n}}$(t)=〈${\ensuremath{\gamma}}_{\mathit{n}\mathit{n}}$(t)${\mathrm{〉}}_{\mathit{f}}$. As an example, the relaxation behavior of a two-level system interacting with a dichotomous field (dichotomous Markovian process of kangaroo type) and a harmonic oscillator coupled with a thermal bath is considered. It is shown that the probability of relaxation transitions between energy levels may be changed by several orders of magnitude under the influence of the dichotomous field.