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Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theori...

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Detalles Bibliográficos
Autor principal: Schuch, Dieter
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-65594-9
http://cds.cern.ch/record/2303165
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author Schuch, Dieter
author_facet Schuch, Dieter
author_sort Schuch, Dieter
collection CERN
description This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.
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spelling cern-23031652021-04-21T18:55:22Zdoi:10.1007/978-3-319-65594-9http://cds.cern.ch/record/2303165engSchuch, DieterQuantum theory from a nonlinear perspective: Riccati equations in fundamental physicsGeneral Theoretical PhysicsThis book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.Springeroai:cds.cern.ch:23031652018
spellingShingle General Theoretical Physics
Schuch, Dieter
Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics
title Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics
title_full Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics
title_fullStr Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics
title_full_unstemmed Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics
title_short Quantum theory from a nonlinear perspective: Riccati equations in fundamental physics
title_sort quantum theory from a nonlinear perspective: riccati equations in fundamental physics
topic General Theoretical Physics
url https://dx.doi.org/10.1007/978-3-319-65594-9
http://cds.cern.ch/record/2303165
work_keys_str_mv AT schuchdieter quantumtheoryfromanonlinearperspectivericcatiequationsinfundamentalphysics