Nonlinear, Deformed and Irreversible Quantum Systems

E. B. Davies

Аурелиан Исар

Heinz Dietrich Doebner, V. K. Dobrev, P. Nattermann

Intrinsically irreversible representations of unstable quantum systems, I. Antoniou quantum mechanical arrows of time, A. Bohm isotropic harmonic oscillator on the quantum euclidean space, G. Fiore relevant and irrelevant nonlinear schrodinger equation, N. Gisin diffeomorphism groups and nonlinear quantum mechanics, G.A. Goldin from Hamiltonian mechanics to nonlinear Schrodinger equations, J.-D. Hennig nonlinear Schrodinger dynamics and nonlinear observables, W. Lucke nonlinear gauge transformations and the Doebner-Goldin equation, P. Nattermann chaos and the limit of classical and quantum mechanics, T. Petrosky why irreversibility? the formulation of classical and quantum mechanics for unstable dynamical systems, I. Prigogine harmonic oscillators on quantum space, S. Watamura. (Part Contents).

A N F Aleixo, A. B. Balantekin

A nonlinear deformed algebraic theory for quantum confined systems is constructed using a supersymmetric and shape-invariant approach. In the framework of this model, we present a mathematical Barut–Girardello procedure which leads to nonlinear deformed coherent states by the successive application of a deformed raising operator on the ground state of these systems. As an application, we use a simple exponential form for the nonlinearity function to study in detail the mathematical and physical properties of such states and their evolution in time.

Ilya Prigogine, A.P. Grécos

Abdelmalek Bouzenada

We develop a unified framework for studying superposed coherent states in coupled nonlinear bosonic systems using a q-deformed Kerr oscillator model. A quantitative measure, termed catability, is introduced to quantify robustness and structural coherence of Schrödinger-cat-like states under nonlinear and deformation effects within the framework. Within the q-deformed bosonic algebra, we analyze the dynamics of two coupled Kerr oscillators to demonstrate that the deformation parameter governs coherence redistribution and nonlinear coupling-induced state transformation. Establish local cat states emerge from the relation between Kerr nonlinearity and q-deformed interactions, coherence transfer between subsystems becomes sensitive to the deformation strength. In this case, construct a phase diagram of catability, revealing distinct regimes of quantum behavior, identifying coupling-driven quantum phase transitions in a deformed algebraic structure system. The generalized analysis extended the covariant formulation and graphene-inspired catability operators generalized curved space-time backgrounds, establishing a connection between nonlinear quantum optics, condensed matter analog systems, relativistic quantum structures framework. In this context, results explain complete description deformationcontrolled quantum coherence and establish new directions for engineered nonclassical states in complex quantum systems.