The paper shows the results of theoretical research concerning the modeling and characterization of the dissipative structures generally, the dissipation being an essential property of the system with self‐organization which include the laser‐type systems also. The most important results presented are new formulae which relate the coupling parametersainfrom Lindblad equation with environment operators Γi; microscopic quantitative expressions for the dissipative coefficients of the master equations; explicit expressions which describe the changes of the environment density operator during the system evolution for fermion systems coupled with free electromagnetic field; the generalized Bloch‐Feynman equations forN‐level systems with microscopic coefficients in agreement with generally accepted physical interpretations. Based on Maxwell‐Bloch equations with consideration of the interactions between nearing atomic dipoles, for the dense optical media we have shown that in the presence of the short optical pulses, the population inversion oscillates between two extreme values, depending on the strength of the interaction and the optical pulse energy.
The paper shows the results of theoretical research concerning the modeling and characterization of the dissipative structures generally, the dissipation being an essential property of the system with self‐organization which include the laser‐type systems also. The most important results presented are new formulae which relate the coupling parametersainfrom Lindblad equation with environment operators Γi; microscopic quantitative expressions for the dissipative coefficients of the master equations; explicit expressions which describe the changes of the environment density operator during the system evolution for fermion systems coupled with free electromagnetic field; the generalized Bloch‐Feynman equations forN‐level systems with microscopic coefficients in agreement with generally accepted physical interpretations. Based on Maxwell‐Bloch equations with consideration of the interactions between nearing atomic dipoles, for the dense optical media we have shown that in the presence of the short optical pulses, the population inversion oscillates between two extreme values, depending on the strength of the interaction and the optical pulse energy.
An essential problem of the quantum information systems is the controllability and observability of the quantum states, generally described by Lindblad's master equation with phenomenological coefficients. However, in its general form, this equation describes a decay of the mean-values, but not necessarily the expected decaying transitions. We propose a quantum master equation with microscopic coefficients where these transitions are correctly described, and investigate the properties of the dissipative coefficients. Being of Lindblad's form, this equation preserves the quantum-mechanical properties of the density matrix during the whole evolution of the system and is in accordance with the entropy principle. On this basis, generalized Bloch-Feynman equations with microscopic coefficients for N-level systems are obtained.
Abstract Due to their intuitiveness, flexibility, and relative numerical efficiency, the macroscopic Maxwell–Bloch (MB) equations are a widely used semiclassical and semi‐phenomenological model to describe optical propagation and coherent light–matter interaction in media consisting of discrete‐level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the 1D MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening, and local‐field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed.
In a previous paper, we derived a master equation for fermions, of Lindblad's form, with coefficients depending on microscopic quantities. In this paper, we study the properties of the dissipative coefficients taking into account the explicit expressions of: (a) the matrix elements of the dissipative potential, evaluated from the condition that, essentially, this potential induces transitions among the system eigenstates without significantly modifying these states, (b) the densities of the environment states according to the Thomas–Fermi model, and (c) the occupation probabilities of these states taken as a Fermi–Dirac distribution. The matrix of these coefficients correctly describes the system dynamics: (a) for a normal, Fermi–Dirac distribution of the environment population, the decays dominate the excitation processes; (b) for an inverted (exotic) distribution of this population, specific to a clustering state, the excitation processes are dominant.
This thesis examines dissipative forces in physical systems in both microscopic and quantum level. The system-environment interaction is modeled by assuming that the environment is composed of simple harmonic oscillators and that there is a linear interaction between these oscillators and the system. The classical case is solved by determining the retarded Green’s function, which yields the equation of motion of the system. For quantum dissipation, the Lindblad master equation is used to describe the time evolution of the reduced density matrix of the system, and the propagator is investigated to identify important parameters, including the term of Newton's friction force.
A theory of dispersive soliton of the self-induced transparency in a medium consisting of atoms or semiconductor quantum dots of two types is considered. A two-component medium is modeled by a set of two-level atoms of two types embedded into a conductive host material. These types of atoms correspond to passive atoms (attenuator atoms) and active atoms (amplifier atoms) with inverse population of the energetic levels. The complete solution is given of the Maxwell--Bloch equations for ensembles of two-type atoms with different parameters and different initial conditions by inverse scattering transform. The solutions of the Maxwell--Bloch equations for many-component atomic systems by inverse scattering transform are also discussed. The influence of the difference between dipole moments of atoms, the longitudinal and transverse relaxation times, pumping, and conductivity on the soliton is taken into account by means of perturbation theory. The memory effects are described in terms of generalized non-Markovian optical Bloch equations. The condition of a balance between the energy supplied and lost is obtained.
The Maxwell-Bloch equations describe the interaction of light (treated classically with Maxwell's equations) and matter, where the latter is modeled as an ensemble of quantum mechanical systems with two energy levels. The dynamical behavior of the systems is described by the optical Bloch equations. This concept can be generalized to an arbitrary number of energy levels with the help of the density matrix ∧ρ and the Lindblad master equation ∂t ∧ρ = -i ħ-1[∧H, ∧ρ] + D(∧ρ), where ∧H is the Hamiltonian of the system and D accounts for dissipation.