scholarly journals Redistribution of the Rydberg State Population Induced by Continuous-Spectrum Radiation

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 55
Author(s):  
Anastasia S. Chervinskaya ◽  
Dmitrii L. Dorofeev ◽  
Boris A. Zon
Keyword(s):  
Numerical Solution ◽  
Continuous Spectrum ◽  
Diffusion Approximation ◽  
Rydberg State ◽  
Population Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
State Population ◽  
Quantum Numbers ◽  
Cascade Transitions

We consider the redistribution of the Rydberg state population resulting from multistep cascade transitions induced by radiation with a continuous spectrum. The population distribution is analyzed within the space of quantum numbers n and l. The dynamics of the system are studied using both the numerical solution of kinetic equations and the diffusion approximation based on the Fokker–Planck equation. The main path of the redistribution process is determined.

scholarly journals Диффузионная динамика ридберговских состояний в поле излучения с непрерывным спектром

2021 ◽  
Vol 129 (7) ◽  
pp. 813
Author(s):  
А.C. Червинская ◽  
Д.Л. Дорофеев ◽  
Б.А. Зон
Keyword(s):  
Kinetic Equation ◽  
Diffusion Approximation ◽  
Kinetic Equations ◽  
Rydberg States ◽  
Planck Equation ◽  
Sodium Atom ◽  
Cascade Transitions ◽  
Atomic Rydberg ◽  
Good Agreement ◽  
Ionization Rates

Redistribution of population and ionization of atomic Rydberg states due to multistep cascade transitions between states under the influence of radiation with continuous spectrum is considered. Consideration is carried up both by simulation of kinetic equations for state populations and with the use of a diffusion approximation based on the Fokker-Planck equation. On the example of sodium atom under the influence of radiation with rectangular spectrum a good agreement between the diffusion approximation and the kinetic equation simulation is shown. In the frame of the diffusion approximation some estimations are derived for the state populations, ionization rates and minimal spectral density of radiation necessary for significant ionization.

Stochastic Particle Dynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Brownian Motion ◽  
Kinetic Theory ◽  
Stochastic Dynamics ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Central Place ◽  
Conclusive Evidence ◽  
Dense Fluids ◽  
Complementary Role ◽  
Collisional Interactions

Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

A numerical solution of the kinetic equations for a spectrum of Langmuir turbulence

1984 ◽  
Vol 31 (2) ◽  
pp. 253-261
Author(s):  
Denis Hayward
Keyword(s):  
Numerical Solution ◽  
Relativistic Electron Beam ◽  
Final Section ◽  
Plasma Heating ◽  
Kinetic Equations ◽  
Langmuir Turbulence ◽  
Quick Method ◽  
Isothermal Plasma ◽  
Principal Contributor ◽  
Made In

The main properties of a kinetic wave equation in an isothermal plasma, Te ≈ Ti, are discussed and a quick method of numerical solution based on factorization of the kernel of an integral equation is outlined. As an illustration the method is applied to the problem of plasma heating with a relativistic electron beam and it is shown how the evolution of a spectrum of Langmuir turbulence is the principal contributor to the heating of the plasma. The technique allows an estimate of the error which is present in the stationary solution, and this is made in the final section.

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

2020 ◽  
Vol 30 (04) ◽  
pp. 685-725 ◽  
Author(s):  
Giulia Furioli ◽  
Ada Pulvirenti ◽  
Elide Terraneo ◽  
Giuseppe Toscani
Keyword(s):  
Steady State ◽  
Wealth Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Logarithmic Sobolev Inequality ◽  
One Dimensional ◽  
Distribution Of Wealth ◽  
Multi Agent ◽  
Fokker Planck Equations ◽  
Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

Numerical Solution of the Fokker-Planck Equation for Postharvest Applications

2003 ◽  
Author(s):  
Nico Scheerlinck ◽  
Ann Peirs ◽  
Michèle Desmet ◽  
Sofie Clauwers ◽  
Bart M. Nicolaï
Keyword(s):  
Numerical Solution ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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