Schrodinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00479625" target="_blank" >RIV/61389005:_____/17:00479625 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3390/sym9080165" target="_blank" >http://dx.doi.org/10.3390/sym9080165</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym9080165" target="_blank" >10.3390/sym9080165</a>

Result language
angličtina
Original language name
Schrodinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels
Original language description
Schrodinger equations with non-Hermitian, but PT -symmetric quantum potentials V(x) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an 'anomalous' refraction index. This turned attention to the nonlinear Schrodinger equations in which the interaction term becomes state-dependent, V(x) -> W(psi(x),x). Here, the state-dependence in W(psi(x),x) is assumed logarithmic, and some of the necessary mathematical assumptions, as well as some of the potential phenomenological consequences of this choice are described. Firstly, an elementary single-channel version of the nonlinear logarithmic model is outlined in which the complex self-interaction W(psi(x),x) is regularized via a deformation of the real line of x into a self-consistently constructed complex contour C. The new role played by PT -symmetry is revealed. Secondly, the regularization is sought for a multiplet of equations, coupled via the same nonlinear self-interaction coupling of channels. The resulting mathematical structures are shown to extend the existing range of physics covered by the logarithmic Schrodinger equations.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project
<a href="/en/project/GA16-22945S" target="_blank" >GA16-22945S: Quantum Wheeler-DeWitt equation and its unitary evolution interpretation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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