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28 March 2024
 
  » arxiv » quant-ph/0005030

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Darboux-integration of id ho/dt=[H,f( ho)]
N.V. Ustinov ; S.B. Leble ; M. Czachor ; M. Kuna ;
Date 6 May 2000
Journal Phys. Lett. A 279 (2001) 333
Subject Quantum Physics; Exactly Solvable and Integrable Systems | quant-ph nlin.SI
AbstractA Darboux-type method of solving the nonlinear von Neumann equation $idot ho=[H,f( ho)]$, with functions $f( ho)$ commuting with $ ho$, is developed. The technique is based on a representation of the nonlinear equation by a compatibility condition for an overdetermined linear system. von Neumann equations with various nonlinearities $f( ho)$ are found to possess the so-called self-scattering solutions. To illustrate the result we consider the Hamiltonian $H$ of a one-dimensional harmonic oscillator and $f( ho)= ho^q-2 ho^{q-1}$ with arbitary real $q$. It is shown that self-scattering solutions possess the same asymptotics for all $q$ and that different nonlinearities may lead to effectively indistinguishable evolutions. The result may have implications for nonextensive statistics and experimental tests of linearity of quantum mechanics.
Source arXiv, quant-ph/0005030
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