Quantum theory of dissipative processes: The Markov approximation revisited

Adopting the standard mathematical framework for describing reduced dynamics, we derive two formal identities for the density operator of an open quantum system. Each of these is equivalent to the old Nakajima-Zwanzig equation. The first identity is local in time. It contains the inverse of the dynamical map which govern the evolution of the density operator. We indicate a time interval on which this inverse exists. The second identity constitutes a suitable starting point for going beyond the Markov approximation in a controlled way. On the basis of the Bloch equations we argue once more that in studying quantum dissipation one has to pay attention to the von Neumann conditions. In the Nakajima-Zwanzig equation we make the first Born approximation. The ensuing master equation possesses the correct weak-coupling limit. While proving this rather obvious but at the same time important statement, we elucidate the mathematical methods which underlie the weak-coupling limit. Moving to a two-dimensional Hilbert space, we find that both for short and for long times our approximate master equation respects the von Neumann conditions. Assuming exponential decay for correlation functions, we propose a physical limit in which the solutions for the density operator become Markovian in character. We confirm the well-known statement that, as seen from a macroscopic standpoint, the system starts from an effective initial condition. The approach to equilibrium is exponential. The accessory relaxation constants can differ from the usual Bloch parameters and by more than 50%.     

\bar pp-Annihilation processes in the tree approximation of SU(3) chiral effective theory

The $\bar pp$ -annihilation reactions $\bar pp \to \eta \eta \eta$ and $\bar pp \to \eta {\rm K}\bar {\rm K}$ at rest are considered in the tree approximation in the framework of SU(3) chiral effective theory at leading order. The calculated branchings are compared with the data. The results for neutral (????, $\eta {\rm K}^0 \bar {\rm K}^0$ ) and charged (??K ⁺ K ^?) channels are essentially different.     

Description of bimolecular fluorescence-quenching processes on the surface of pyrogenic silica

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 6, pp. 966–971, December, 1991.     

The long-wavelength approximation and the theory of Davydov solitons

We indicate some inconsistencies in the application of the long-wavelength approximation in the standard derivation of Davydov solitons. Consistent approach indicates that the scope of applicability of the theory is much smaller than previously thought.     

The ladder approximation in quantum optics and the Wigner-Weisskopf theory

It is shown that the Wigner-Weisskopf theory is an example of what Walls has called the ladder approximation in quantum optics.     

The theory of nonlinear dispersion interferometers in the constant intensity approximation

The operation of a dispersion interferometer with intracavity location of a medium under study is analyzed in the constant intensity approximation taking into account the reciprocal influence of a harmonic on the phase of the exciting wave. This approximation allows the effects of phase mismatch and losses in a medium on the course of a nonlinear process to be taken into account simultaneously. Intensity minima of the harmonic (as opposed to the constant field approximation) in the constant intensity approximation are shown to depend on dispersion of the refractive index of the medium under study, which makes it possible to determine dispersion of the refractive index of the substance under study directly and accurately     

Quasiisobaric approximation in combustion theory

Based on the laminar combustion of gases and the filtration combustion of porous condensed compounds, some general approaches to the study of their mathematical models are demonstrated that simplify their quantitative analysis. Processes in a wide circle of phenomena proceed under conditions of a weakly disturbed pressure field, though providing macroscopic convective transfer. Under conditions of the substantially changed temperature field, in contrast to condensed media, gaseous media change their specific volume and increase mobility, which should be considered in combustion processes. The suggested quasi-stationary consideration of reacting medium flows simplifies their computation and analysis.     

Eikonal approximation in the theory of X-ray interferometer

On the basis of eikonal approximation a theory of X-ray moiré formation is presented in the case where deformations are present in all three plates of the interferometer. The role of each plate of the interferometer in the process of moiré formation is revealed. The theory can be applied for the general case of weak deformations.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to the??-factoryDA??NE. For this collider about 5·10¹⁴ d E _??/E _?? photons per second are expected in the photon energyE _?? range from the visible light up to 25 eV.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to theφ-factoryDAΦNE. For this collider about 5·10¹⁴ d E _γ/E _γ photons per second are expected in the photon energyE _γ range from the visible light up to 25 eV.     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to theφ-factoryDAΦNE. For this collider about 5·10¹⁴ d E _γ/E _γ photons per second are expected in the photon energyE _γ range from the visible light up to 25 eV.     

Rosen-Zener approximation in surface-ion scattering theory

The Rosen-Zener formula, for transition probabilities in the atomic two-level problem, is used to develop a many-level treatment of the surface-ion-neutralization probability.     

Low-energy approximation in the theory of adsorption on graphene

Physics of the Solid State - The effect of the linear approximation of the electronic spectrum of single-layer graphene (low-energy approximation) on the magnitude of charge transfer between an...