scholarly journals Trace Formulas for Stochastic Evolution Operators: Weak Noise Perturbation Theory

1998 ◽  
Vol 93 (3/4) ◽  
pp. 981-999 ◽  
Author(s):  
Predrag Cvitanović ◽  
C. P. Dettmann ◽  
Ronnie Mainieri ◽  
Gábor Vattay
Keyword(s):  
Perturbation Theory ◽  
Stochastic Evolution ◽  
Trace Formulas ◽  
Evolution Operators ◽  
Weak Noise ◽  
Noise Perturbation

scholarly journals Solitons in a box-shaped wavefield with noise: perturbation theory and statistics

2021 ◽  
Author(s):  
Andrey Gelash ◽  
Rustam Mullyadzhanov
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Waves ◽  
Fundamental Problem ◽  
Scattering Data ◽  
Linear Perturbation ◽  
Initial Condition ◽  
Russian Science ◽  
Noise Perturbation ◽  
Scattering Transform ◽  
Theoretical Predictions

<p>The propagation of nonlinear waves is well-described by a number of integrable models leading to the concept of the scattering data also known as the nonlinear Fourier spectrum. Here we investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear perturbation framework to evaluate first-order corrections of the full set of the scattering data within the integrable one-dimensional focusing nonlinear Schrodinger (NLSE) equation, see our recent preprint [1]. The general scattering data portrait reveals nonlinear coherent structures - solitons - playing the key role in the wavefield evolution. Applying the developed theory to a classic box-shaped wavefield we solve the derived equations analytically for a single Fourier mode acting as a perturbation to the initial condition, thus, leading to the sensitivity closed-form expressions for basic soliton characteristics, i.e. the amplitude, velocity, phase and its position. With the appropriate statistical averaging we model the soliton noise-induced effects resulting in compact relations for standard deviations of soliton parameters. Relying on a concept of a virtual soliton eigenvalue we derive the probability of a soliton emergence or the opposite due to noise and illustrate these theoretical predictions with direct numerical simulations of the NLSE evolution. Note that the evolution of the box field within the NLSE model represents a classical so-called dam-break problem. A wide box-shaped field is unstable to long wave perturbations constituting the phenomena of modulation instability. In conclussion we discuss possible applications of the developed theory to these fundamental problems of physics of nonlinear waves.</p><p><br>The work was supported by Russian Science Foundation grant No. 20-71-00022.</p><p><br>[1] R. Mullyadzhanov and A. Gelash. Solitons in a box-shaped wavefield with noise: perturbation theory and statistics. arXiv preprint arXiv:2008.08874, 2020.</p>

scholarly journals Spectrum of stochastic evolution operators: Local matrix representation approach

1999 ◽  
Vol 60 (4) ◽  
pp. 3936-3941 ◽  
Author(s):  
Predrag Cvitanović ◽  
Niels Søndergaard ◽  
Gergely Palla ◽  
Gábor Vattay ◽  
C. P. Dettmann
Keyword(s):  
Matrix Representation ◽  
Stochastic Evolution ◽  
Evolution Operators

scholarly journals Trace formulae for stochastic evolution operators: smooth conjugation method

Nonlinearity ◽  
1999 ◽  
Vol 12 (4) ◽  
pp. 939-953 ◽  
Author(s):  
Predrag Cvitanovic ◽  
C P Dettmann ◽  
Ronnie Mainieri ◽  
Gábor Vattay
Keyword(s):  
Stochastic Evolution ◽  
Evolution Operators ◽  
Trace Formulae ◽  
Conjugation Method

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

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