WORLD SCIENTIFIC eBooks

Nonlinear, deformed and irreversible quantum systems : proceedings of the International Symposium on Mathematical Physics, Arnold Sommerfeld Institute 15-19 August 1994, Clausthat, Germany

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

Published Jan 1, 1995• 4 citations

Abstract

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).

Related papers

Advances in Chemical Physics

Prigogine, Ilya, Stuart A. Rice

In Resonances, Instability, and Irreversibility: The LiouvilleSpace Extension of Quantum Mechanics T. Petrosky and I. Prigogine Unstable Systems in Generalized Quantum Theory E. C. G. Sudarshan, Charles B. Chiu, and G. Bhamathi Resonances and Dilatation Analyticity in Liouville Space Erkki J. Brandas Time, Irreversibility, and Unstable Systems in QuantumPhysics E. Eisenberg and L. P. Horwitz Quantum Systems with Diagonal Singularity I. Antoniou and Z. Suchanecki Nonadiabatic Crossing of Decaying Levels V. V. and Vl. V. Kocharovsky and S. Tasaki Can We Observe Microscopic Chaos in the Laboratory? Pierre Gaspard Proton Nonlocality and Decoherence in Condensed Matter --Predictions and Experimental Results C. A. Chatzidimitriou-Dreismann "We are at a most interesting moment in the history of science.Classical science emphasized equilibrium, stability, and timereversibility. Now we see instabilities, fluctuations, evolution onall levels of observations. This change of perspective requires newtools, new concepts. This volume invites the reader not to anenumeration of final achievements of contemporary science, but toan excursion to science in the making." --from the Foreword by I.Prigogine What are the dynamical roots of irreversibility? How can past andfuture be distinguished on the fundamental level of description?Are human beings the children of time --or its progenitors? Inrecent years, a growing number of chemists and physicists haveagreed that the solution to the problem of irreversibility requiresan extension of classical and quantum mechanics. There is, however, no consensus on which direction this extension should take toinclude the dynamical description of irreversible processes. Resonances, Instability, and Irreversibility surveys recentattempts --both direct and indirect --to address the problem ofirreversibility. Internationally recognized researchers report ontheir recent studies, which run the gamut from experimental tohighly mathematical. The subject matter of these papers falls intothree categories: classical systems with emphasis on chaos anddynamical instability, resonances and unstable quantum systems, andthe general problem of irreversibility. Presenting the cutting edge of research into some of the mostcompelling questions that face contemporary chemical physics, Resonances, Instability, and Irreversibility is fascinating readingfor professionals and students in every area of the discipline.

Advances in chemical physicsJan 1, 199641 citations

Nonlinear Extension of Quantum Mechanics: Remarks and Recent Results

H. D. Doebner, Gerald A. Goldin

We discuss the problem of extending the framework of quantum mechanics so that observables are represented by nonlinear operators in a Hilbert space or manifold. Our motivation includes the derivation of certain nonlinear Schrödinger equations from diffeomorphism group representations. In this context we review some groups of nonlinear gauge transformations.

CRC Press eBooksNov 30, 20030 citations

Nonlinear quantum mechanics: Results and open questions

Gerald A. Goldin

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.

Physics of Atomic NucleiMay 1, 20087 citations

"Quantum Mechanics in Mathematics, Chemistry, and Physics"

Karl E. Gustafson, William P. Reinhardt

Total Cross Sections in Non-Relativistic Scattering Theory.- Classical-Quantum Correspondence in Non-Linear Systems.- Real Axis Asymptotics and Estimates of Hamiltonian Resolvent Kernels.- Statistical Inference in Quantum Mechanics.- Schrodinger Operators with Oscillating Potentials.- Time Delay and Resonance in Simple Scattering.- A Study of the Helmholtz Operator.- Invariant Manifolds and Bifurcations in the Taylor Problem.- On the Dimension of a Finite Difference Approximation to Divergence-Free Vectors.- Intramolecular Dynamics in the Quasiperiodic and Stochastic Regimes.- Problems in the Semiclassical Quantization of Integrable and Nonintegrable Classical Dynamical Systems.- Nonselfadjoint Operators in Diffraction and Scattering.- One-Dimensional Crystals in an External Field.- Dynamics of Forced Coupled Oscillators: Classical Phenomenology of Infrared Multiphoton Absorption.- Irreversibility and Stochasticity of Chemical Processes.- On the Representations of the Local Current Algebra and the Group of Diffeomorphisms (I).- Regular and Chaotic Regimes in Quantum Mechanics.- Barrier Penetration and Exponential Decay in the Stark Effect.- A Nonlinear Schrodinger Equation Yielding the Shape of Molecules by Spontaneous Symmetry Breaking.- Classical Limit of the Number of Quantum States.- Formal Integrals for a Nonintegrable Dynamical System: Preliminary Report.- On a Generalized Weyl-Von Neumann Converse Theorem.- Scattering Theory in Many-Body Quantum Systems. Analyticity of the Scattered Matrix.- Existence, Uniqueness, Stability and Calculation of the Stationary Regimes in Some Nonlinear Systems.- Weighted Trigonometric Approximations in L2(Rn).- The Phenomenon of Magnetic Pairing and Exactly Soluble Models of Magnetic Resonances.- Dyons Solutions to Yang-Mills Equations.- Asymptotic Resonance Properties of the Finite-Dimensional Friedrichs Model.- Self-Consistent Field Methods for Metastable Electronic States: A Promising Extension of the Complex Coordinate Technique.- Timestep Control for the Numerical Solutions of Initial-Boundary-Value Problems.- Quantum Mechanical Angular Distributions and Group Representations on Banach Spaces.- Tensor Product Decomposition of Holomorphically Induced Representations and Clebsch-Gordan Coefficients.- Orthogonal Laurent Polynomials and Gaussian Quadrature.- Measurement Theory with Instruments Treated Partially Quantum Mechanically.- Transition Maps and Locality.- The Feynman-Kac Formula for Boson Wiener Processes.- On Nonunitary Equivalence Between Unitary Group of Dynamics and Contraction Semigroups of Markov Processes.

Nov 1, 201150 citations

Quantum Mechanics, Diffusion and Chaotic Fractals

Mohamed Saladin El Naschie, Otto E. Rössler, Ilya Prigogine

Quantum mechanics and chaotic fields quantum chaos, complex spectral representation and time-symmetry breaking, T. Petrosky and I. Prigogine scale relativity, fractal space-time and quantum mechanics, L. Nottale introduction to wave phenomena and uncertainty in a fractal space - I, A. Le Mehaute et al young double-slit experiment, Heisenberg uncertainty principle and cantoria space-time, M.S. El Naschie the quantum dimension of space-time, E. Alvarez et al intra-observer chaos - hidden root of quantum mechanics?, O.E. Rossler amplification of superpositional effects through electronic - conformational interactions, M. Conrad quantum cellular automation in 1-D, D.W. Belousek et al an energy-barrier model of biased transport in disordered systems, M. Giona chaos in the Einstein equations, S.E. Rugh.

May 1, 1995210 citations

Quantization and coherent states methods : proceedings of the XI Workshop on Geometric Methods in Physics : Białowieza, Poland, 7-14 July 1992

S. Twareque Ali, Ivaïlo M. Mladenov, Anatol Odzijewicz

Half-forms and Berry's phase, N.M.J. Woodhouse quantum particle on a Torus in a magnetic field, H.D. Doebner and J. Tolar loop spaces and a geometrical approach to path integral quantization, R.F. Picken on the connection between orbits and representations, N.V. Pedersen geometric quantization of Riemann rotors, G. Rosensteel and E. Ihrig large on the decomposition of the oscillator representation, A. Strasburger symplectic and Kahler coherent state representations of unimodular Lie groups, W. Lisiecki local and non-local probabilities in Einstein-Podolsky-Rosen correlations, K. Wodkiewicz the Lorentz force equation in twistor terms - a symplectic framework, A. Bette Green's function for crossed time-dependent-electric and magnetic fields phase-space quantum mechanics approach, L.M. Nieto quantization on coadjoint orbits of diffeomorphism groups - some research directions, G.A. Goldin semiclassical behaviour of coherent states on the circle, S. de Bievre and J.A. Gonzalez.

Jan 1, 19930 citations