Kinetic equations for electrons and phonons in a strong constant electric field

The kinetic equations for the electron and phonon distribution functions have been obtained for a system in an arbitrarily strong uniform constant electric field.     

Kinetic equations for a density matrix describing nonlinear effects in spectral line wings

Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.     

Linked cluster expansions in the equations of motion method II: Kinetic equations for the single-particle density matrix

The general method of paper I of this series is applied to derive kinetic equations (KE's), i.e. closed exact equations governing the time evolution of the single-particle density matrix. The short-memory approximation of these non-Markowian equations is formulated in such a way that it is valid even in strongly inhomogeneous systems. The c-number diagram expansion of the integral kernels of the KE's is obtained from the general rules of paper I. It is shown that certain secular divergent terms cancel each other. The diagrams decay into dynamic and correlational parts, the latter being given by cluster functions describing the correlations of the particles in the local equilibrium ensemble σ(t) which is formulated in terms of the single-particle density matrix and of the Hamiltonian. The appearance of the cluster functions is the most pronounced difference of our KE's in comparison with other KE's which are formulated in terms of the dynamics of isolated clusters of particles. It is argued that our KE's may be viewed as a highly summed version of these latter KE's and that the ultimate reason for this difference lies in the fact that in our theory the conservation of the average macroscopic energy is taken into account explicitly.     

Transformation of a Rabi oscillation spectrum for a two-level system in a strong resonant field

We have found an analytical expression describing the evolution of a two-level system in a strong resonant quantum field beyond the rotating wave approximation. The solution obtained has allowed us for the first time to identify the qualitative features of the behavior of the system in this case: suppression of the "collapse–revival" effect, and a change in the spectrum and shape of Rabi oscillations for an inverted population. The results are of interest for applied spectroscopy, quantum optics, and nanomechanics.     

Markovian master equation for a two-level atom in a strong field and/or a tailored reservoir

The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.     

An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force (the ‘Euler–Lorentz’ system). When the magnetic field is large, or equivalently, when the parameter ε$\epsilon$ representing the non-dimensional ion cyclotron frequency tends to zero, the so-called drift-fluid (or gyro-fluid) approximation is obtained. In this limit, the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines. In this paper, we provide a well-posed elliptic equation for the parallel velocity which in turn allows us to construct an Asymptotic-Preserving (AP) scheme for the Euler–Lorentz system. This scheme gives rise to both a consistent approximation of the Euler–Lorentz model when ε$\epsilon$ is finite and a consistent approximation of the drift limit when ε→0$\epsilon \to 0$. Above all, it does not require any constraint on the space and time-steps related to the small value of ε$\epsilon$. Numerical results are presented, which confirm the AP character of the scheme and its Asymptotic Stability.     

Relativistic kinetic equations for inelastically interacting particles in a gravitational field

The relativistic canonical formalism is used to construct the kinetic equations for a gas in a gravitational field, whose particles interact with one another via numerous inelastic collisions. Boltzmann's H-theorem is proved for T-invariant interactions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 19–23, August, 1983.     

Kinetic equation for electrons of a semiconductor in a strong electric field: Green's resolvent

Using the Laplace transform of Boltzmann's equation, a system of linking equations is obtained for the series expansion of the mapping of the distribution function in powers of the field. Since the form of the equations is identical, instead of direct integration it is possible to use the method of Green's functions for the solution of the system. Using the method of perturbances Green's resolvent is constructed in the form of an infinite series. Using the example of the evaluation of the distribution function in a high-frequency field, the convergence of the proposed method is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 22–25, July, 1973.     

The density matrix of scattered particles

The derivation of the expression for the density matrix of scattered particles in terms of that of the incident ones, taking different impact parameters into account, shows that under well-specified and realistic conditions, the final density matrix is of the same kind as the initial one. Thus the final mixed state after a collision can be used directly as the initial mixed state in a subsequent collision. Contrary to a recent claim by Band and Park, there are no “fundamental difficulties with quantum mechanical collision theory.”     

Quantum kinetic theory of trapped particles in a strong electromagnetic field

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green’s functions. The equation for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.     

Relativistic polarization density matrix for particles of arbitrary spin

The polarization density matrix for particles of arbitrary spin can be expressed as a linear function of the expectation values of the generators of the polarization symmetry group of the corresponding wave equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–88, April, 1984.     

对称强双色共振场中弛豫效应对二能级系统斯塔克分裂的影响

本文应用半径典理论、密度矩阵方法和探索场中二能级系统的能级斯塔克(Stark)分裂。指出与无弛豫效应相比较,弛予效应不仅改变了由光学斯塔克效应所产生的分裂能级的权重、展宽了这些能级,而且还出现新的分裂能级。     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.