Related papers: Remarks on a Nonlinear Quantum Theory
Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are…
Gauge-invariant Wigner theory describes the quantum-mechanical evolution of charged particles in the presence of an electromagnetic field in phase space, which is spanned by position and kinetic momentum. This approach is independent of the…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
There are fundamental reasons as to why there should exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. It follows as a consequence that quantum mechanics as we know it is a limiting case of a…
We argue that the conventional construction for quantum fields in curved spacetime has a grave drawback: It involves an uncountable set of physical field systems which are nonequivalent with respect to the Bogolubov transformations, and…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
The dynamical equation satisfied by the density matrix, when a quantum system is subjected to one or more constraints arising from conserved quantities, is derived. The resulting nonlinear motion of the density matrix has the property that…
A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schr\"{o}dinger equation is also introduced and extension of the analysis…
A quantum theory of noncommutative fields was recently proposed by Carmona, Cortez, Gamboa and Mendez (hep-th/0301248). The implications of the noncommutativity of the fields, intended as the requirements…
We present, in the framework of the canonical quantization, a class of nonlinear Schroedinger equations with a complex nonlinearity describing, in the mean field approximation, systems of collectively interacting particles. The quantum…
A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of dynamical symmetry is generalized from the level of classical Lie…
In the paper we review some recent results of the theory of hierarchies of quantum evolution equations.
We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
The nonlinear generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit. This equation can be cast into the integrable classical Riccati system of nonlinear ordinary…
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…
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium…