Diffeomorphism Group Representations and Nonlinear Quantum Theories

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary waveâ€™s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear SchrÃ¶dinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

Download Full-text

Strong coupling: resonant effects

10.1093/oso/9780198782995.003.0007 ◽

2017 ◽

Author(s):

Alexey V. Kavokin ◽

Jeremy J. Baumberg ◽

Guillaume Malpuech ◽

Fabrice P. Laussy

Keyword(s):

Strong Coupling ◽

Experimental Studies ◽

Strong Coupling Regime ◽

Theoretical Studies ◽

Stimulated Scattering ◽

Quantum Theories ◽

Pump Probe ◽

Exciton Polaritons ◽

Linear Optical Properties ◽

Experimental And Theoretical Studies

This chapter presents experimental studies performed on planar semiconductor microcavities in the strong-coupling regime. The first section reviews linear experiments performed in the 1990s that evidence the linear optical properties of cavity exciton-polaritons. The chapter is then focused on experimental and theoretical studies of resonantly excited microcavity emission. We mainly describe experimental configuations in which stimulated scattering was observed due to formation of a dynamical condensate of polaritons. Pump-probe and cw experiments are described in addition. Dressing of the polariton dispersion and bistability of the polariton system due to inter-condensate interactions are discussed. The semiclassical and the quantum theories of these effects are presented and their results analysed. The potential for realization of devices is also discussed.

Download Full-text

The Centralizer

10.1093/oso/9780198821656.003.0005 ◽

2018 ◽

Author(s):

Ercüment H. Ortaçgil

Keyword(s):

Lie Group ◽

Group Structure ◽

Diffeomorphism Group ◽

Group Diff ◽

Local Solutions

The pseudogroup of local solutions in Chapter 3 defines another pseudogroup by taking its centralizer inside the diffeomorphism group Diff(M) of a manifold M. These two pseudogroups define a Lie group structure on M.

Download Full-text