Quantum Theory from a Nonlinear Perspective

Beschreibung

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.
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.
A unique survey of the power of Riccati equations to describe reversible and irreversible processes in many areas of physics Particular attention paid to non-linear versions of the Schrödinger equation Reveals parallels in many seeming unrelated areas of physics, from quantum physics to fluid mechanics and cosmology Author is a foremost expert with many years of experience in the field

Autor*in

Dieter Schuch

Themen in »Quantum Theory from a Nonlinear Perspective«

Complex Riccati Equations Connecting Nonlinear Dynamics and Quantum Mechanics Dissipation in Classical and Quantum Mechanics Ermakov Systems and Invariants Irreversibility in Classical and Quantum Mechanics Nonlinear Riccati Equations Nonlinearities in Quantum Mechanics ordinary differential equations

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