The time evolution of quantum systems with discrete energy spectra

1986 ◽  
Vol 64 (11) ◽  
pp. 1546-1550 ◽  
Author(s):  
A. I. Lupaşcu ◽  
I. M. Popescu
Keyword(s):  
Time Evolution ◽  
Quantum Systems ◽  
The State ◽  
Energy Spectra ◽  
Matrix Functions ◽  
Level Crossing ◽  
Discrete Energy ◽  
Nonexponential Decay

Using the method of matrix functions, we describe the time evolution of quantum systems with discrete energy spectra. The time evolution of the state vectors and expressions for the perturbed eigenfunctions and their associated projectors are obtained for an atom with n discrete levels. The particular cases n = 2 and n = 3 are presented; level crossing and nonexponential decay of coupled states are emphasized.

scholarly journals Mono-energetic ions from collisionless expansion of spherical multi-species clusters

2009 ◽  
Vol 27 (2) ◽  
pp. 321-326 ◽  
Author(s):  
K.I. Popov ◽  
V.Yu. Bychenkov ◽  
W. Rozmus ◽  
V.F. Kovalev ◽  
R.D. Sydora
Keyword(s):  
Electron Temperature ◽  
Time Evolution ◽  
Hot Electrons ◽  
Ion Concentration ◽  
Energy Spectra ◽  
Plasma Expansion ◽  
Energetic Ions ◽  
Spherical Cluster ◽  
Light Ions ◽  
Unified Description

AbstractKinetic collisionless expansion of a spherical cluster composed of light and heavy cold ions and hot electrons is studied for arbitrary electron temperature. A wide set of regimes of plasma expansion, from nearly quasi-neutral to Coulomb explosion, is described from a unified description. The time evolution of the velocity, density, and energy spectra for accelerated ions is studied. The study demonstrates that an optimum light ion concentration from few percent to few tens percent, depending on the electron temperature, leads to a quasi-monoenergetic spectra with numbers as high as 70–80% of the total number of light ions.

scholarly journals Biased Continuous-Time Random Walks with Mittag-Leffler Jumps

2020 ◽  
Vol 4 (4) ◽  
pp. 51 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Federico Polito ◽  
Alejandro P. Riascos
Keyword(s):  
Cauchy Problem ◽  
Random Walks ◽  
Poisson Process ◽  
Continuous Time ◽  
Laplacian Matrix ◽  
Space Time ◽  
The State ◽  
Diffusion Limit ◽  
Matrix Functions ◽  
Continuous Time Random Walks

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time Mittag-Leffler process. The approach of constructing good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

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