Related papers: A General Framework for Nonlinear Quantum Dynamics
A generalization of the recently formulated nonlinear quantization of a parameterized theory is presented in the context of quantum gravity. The parametric quantization of a Friedmann universe with a massless scalar field is then considered…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in last the decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a…
This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes that attain that precision. In this article we present a…
We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…