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Article overview
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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 | Abstract: | A 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 | Services: | Forum | Review | PDF | Favorites |
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