相关论文: Sum rules in the oscillator radiation processes
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
Generalising a result of classical mechanics an infinite set of conserved quantities can be found for the bare equations of motion describing the evolution of a scalar field in out of equilibrium quantum field theory, in the large N…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general feature of harmonic…
In these lectures, I describe the techniques used within the QCD sum rule approach. The basic concepts of the approach are introduced using a simple model of quantum-mechanical oscillator in 2+1 dimensions. Then I discuss their…
We establish a set of exact sum rules that relate the interatomic force constants to the frequency-dependent electromagnetic susceptibility of a solid or molecule, thereby generalizing the long-established principles of rototranslational…
In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
We investigate the transition to perturbative QCD in Compton processes, by concentrating on the specific reactions $\pi \gamma \to \pi \gamma$ and pion photoproduction at moderate energy scales. New sum rules for each of the helicities…
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we…
We study the dynamics of a symmetric two-level system strongly coupled to a broadened harmonic mode. Upon mapping the problem onto a spin-boson model with peaked spectral density, we show how analytic solutions can be obtained, at arbitrary…
In deep-inelastic scattering experiments, there is a general connection between subtractions in dispersion relations, violations of sum-rules and $\delta$-functions in parton distribution functions. It is explained why one might expect a…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
A precise determination of |V_{ub}| can be obtained exploiting the sum rule for inclusive charmless semileptonic B-meson decays. The sum rule is derived on the basis of light-cone expansion and b-flavored quantum number conservation. The…
Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators,…