Stochastic dynamics of atoms in a resonant light field in the quasi-classical approximation

The stochastic dynamics of atoms with degenerate energy levels in a resonant nonuniformly polarized laser field is considered within the framework of the quasi-classical approach. The regular force entering into the Langevin equation and the correlation function of a random force are represented in the form of expansions in spatial gradients of the total light field. Specific features of kinetic distributions that are caused by the multiplicative character of noise, by anisotropy of dissipative processes, and by the presence of a vortex component in the light-induced force are considered for the example of a model system and a two-dimensional field configuration.     

Kinetic theory of the interaction in an electron current-electromagnetic wave system

The interaction between an electron beam and a retarded electromagnetic field with an accelerating electrostatic field (traveling wave tube with bunching) is considered. An exact steady-state solution of the kinetic equation is found for the case of a zero electrostatic field and an approximate solution is found for the case of a slowly varying electrostatic potential. A theory is constructed for the amplification of the electromagnetic wave; a critical value is indicated for the power of the amplified wave, above which stable amplification is possible. The dependence of the differential efficiency on the power of the amplified wave is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 17–21, April, 1982.     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Kinetic theory of radiation in non-equilibrium relativistic plasmas

Many-particle QED is applied to kinetic theory of radiative processes in many-component plasmas with relativistic electrons and non-relativistic heavy particles. Within the framework of non-equilibrium Green’s function technique, transport and mass-shell equations for fluctuations of the electromagnetic field are obtained. We show that the transverse field correlation functions can be decomposed into sharply peaked (non-Lorentzian) parts that describe resonant (propagating) photons and off-shell parts corresponding to virtual photons in plasmas. Analogous decompositions are found for the longitudinal field correlation functions and the correlation functions of relativistic electrons. As a novel result a kinetic equation for the resonant photons with a finite spectral width is derived. The off-shell parts of the particle and field correlation functions are shown to be essential to calculate the local radiating power in relativistic plasmas and recover the results of vacuum QED. The influence of plasma effects and collisional broadening of the relativistic quasiparticle spectral function on radiative processes is discussed.     

Conductivity of 2D multi-component electron gas partially-quantized by magnetic field

The 2D semimetal consisting of heavy holes and light electrons is studied. The consideration is based on the assumption that electrons are quantized by magnetic field while holes remain classical. We assume also that the interaction between components is weak and the conversion between components is absent. The kinetic equation for holes colliding with quantized electrons is utilized. It has been stated that the inter-component friction and corresponding correction to the dissipative conductivity σ _xx do not vanish at zero temperature due to degeneracy of the Landau levels. This correction arises when the Fermi level crosses the Landau level. The statement will keep in force until the degeneracy remains. The limits of kinetic equation applicability were found. We also study the situation of kinetic memory when particles repeatedly return to their meeting points.     

M-shaped asymmetric nonlinear oscillator for broadband vibration energy harvesting: Harmonic balance analysis and experimental validation

Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is validated experimentally, analytically, and numerically. As compared to the 3 dB bandwidth of the corresponding linear system with the same linear damping ratio, the M-shaped oscillator offers 3200, 5600, and 8900 percent bandwidth enhancement at the root-mean-square base excitation levels of 0.03g, 0.05g, and 0.07g, respectively. The M-shaped configuration can easily be exploited in piezoelectric and electromagnetic energy harvesting as well as their hybrid combinations due to the existence of both large strain and kinetic energy regions. A demonstrative case study is given for electromagnetic energy harvesting, revealing the importance of higher harmonics and the need for multi-term harmonic balance analysis for predicting the electrical power output accurately.     

Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments

The matrix 8-component Dirac-like form of the P-odd equations for boson fields of spin 1 and 0 are obtained and the symmetry group of the equations is derived. We found exact solutions of the field equation for vector particles with arbitrary electric and magnetic moments in external constant and uniform electromagnetic fields. The differential probability of pair production of vector particles with electric dipole moments and anomalous magnetic moments by an external constant and uniform electromagnetic field has been found using exact solutions. We have calculated the imaginary and real parts of the electromagnetic field Lagrangian that takes into account the vacuum polarization of vector particles. Received: 14 April 2001 / Revised version: 13 July 2001 / Published online: 19 September 2001     

Wave propagation according to higher order field equations I

A detailed study is made of wave propagation according to a sixth-order partial differential equation with complex masses proposed by Swieca and Marques, which presents a kind of generalized Klein-Gordon equation. The choice of definite Green's functions in the corresponding Yang-Feldman integral equation corresponds to a certain choice of boundary conditions for the allowed solutions of the corresponding partial differential equation. The advanced and retarded Green's functions used possess the anomalous feature of having non-zero values in the neighbourhoods of those, past or future parts of the light cone, for which traditional advanced and retarded Green's functions are zero. However, it is shown that a suitable averaging procedure provides the possibility of defining sets of functions, such that solutions of the Yang-Feldman equations belonging to this set possess the property that the future behaviour of the solution is determined by its asymptotic initial conditions. Certain features of the wave propagation, according to the equations considered, can be usefully compared with the properties of the solutions of the ordinary differential equation - and corresponding integral equation - which represents the equation of motion of a charged particle including the force for radiation reaction. The particle then has a certain “size”. Analogously the “non-local field equations” have solutions characterized by a certain “fundamental length” indicating the space-time distances for which averaging occurs. The admitted solutions of the field equations seem to represent a relativistic field with a “finite a number of degrees of freedom” within a finite volume.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.     

Solitons and critical breakup fields in lithium niobate type uniaxial ferroelectrics

Ferroelectric materials, such as lithium niobate, show interesting non-linear hysteresis behavior that can be explained by a dynamical system analysis. By using variational principle, a non-linear Klein-Gordon (K-G) equation is derived for lithium niobate type of uniaxial ferroelectrics involving various types of energy, which was not considered previously to construct the Hamiltonian. This leads to soliton solutions under different conditions of soliton velocity. The critical value of the (dimensional) effective electric field has been estimated to be 54–58 kV/cm for lithium niobate depending on the impurity content in these type inhomogeneous ferroelectrics. Beyond this critical field, there is no existence of solitons. This critical field is related to a break-up mechanism of Landau-Ginzburg two-well potential to a single well, as the driving force is increased.     

量子等离子体中波的色散关系以及朗道阻尼

利用动理学理论研究量子等离子体中波的色散关系和电子朗道阻尼.从电子的量子流体动力学方程和动理学描述下的光子运动方程出发,研究量子效应对光子朗道阻尼的修正.研究发现量子效应只对纵波模式,即电子等离子体波的色散关系有修正,对横向电磁波的色散关系没有影响.量子效应减小了朗道阻尼,起着朗道增长的作用. 关键词： 量子等离子体 朗道阻尼 电子等离子体波 色散关系     

Radiation Reaction of a Nonrelativistic Quantum Charged Particle

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.     

Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field

For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad’s form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.     

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.     

Dissipative solitons in carbon nanotubes

The possibility of analogs of dissipative solitons occurring in arrays of carbon nanotubes under the action of a high-frequency external uniform electric field on the array has been established theoretically. The electromagnetic field has been considered in terms of the Maxwell equations, and the conduction electrons in carbon nanotubes have been described by the Boltzmann kinetic equation in the relaxation-time approximation. The external ac electric field serves for energy pumping of the electronic subsystem, whereas a finite relaxation time leads to energy dissipation. The generation of a periodic sequence of electromagnetic pulses has been revealed. This sequence can be used for producing terahertz frequencies.     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Modeling of low-pressure microwave discharges in Ar, He, andO2: similarity laws for the maintenance field and mean powertransfer

A kinetic study of low-pressure microwave discharges in Ar, He, and O₂ is carried out using electron-transport parameters and rate coefficients derived from solutions to the Boltzmann equation, together with the continuity and transport equations for the charged particles, taking into account stepwise-ionization processes. The Boltzmann equation is solved over a wide range of the applied frequency, ω/2π, but assuming that the angular frequency ω>τ _e^-1, with τ_e, denoting the characteristic time for electron-energy relaxation by collisions. The formulation provides discharge characteristics for the maintenance field and for mean absorbed power per electron in the three gases, which are shown to agree satisfactorily with experimental data obtained from surface-wave discharges. It is shown that such an agreement would not always be obtained without consideration of the role played by stepwise-ionization processes in sustaining the discharge