4,210 research outputs found
Generalized quantum measurement
We overcome one of Bell's objections to `quantum measurement' by generalizing
the definition to include systems outside the laboratory. According to this
definition a {\sl generalized quantum measurement} takes place when the value
of a classical variable is influenced significantly by an earlier state of a
quantum system. A generalized quantum measurement can then take place in
equilibrium systems, provided the classical motion is chaotic. This paper deals
with this classical aspect of quantum measurement, assuming that the Heisenberg
cut between the quantum dynamics and the classical dynamics is made at a very
small scale. For simplicity, a gas with collisions is modelled by an `Arnold
gas'.Comment: 11 pages, LaTeX, no figures, title change
Quantum state diffusion, measurement and second quantization
Realistic dynamical theories of measurement based on the diffusion of quantum
states are nonunitary, whereas quantum field theory and its generalizations are
unitary. This problem in the quantum field theory of quantum state diffusion
(QSD) appears already in the Lagrangian formulation of QSD as a classical
equation of motion, where Liouville's theorem does not apply to the usual field
theory formulation. This problem is resolved here by doubling the number of
freedoms used to represent a quantum field. The space of quantum fields is then
a classical configuration space, for which volume need not be conserved,
instead of the usual phase space, to which Liouville's theorem applies. The
creation operator for the quantized field satisfies the QSD equations, but the
annihilation operator does not satisfy the conjugate eqation. It appears only
in a formal role.Comment: 10 page
Quantum transfer functions, weak nonlocality and relativity
The method of transfer functions is developed as a tool for studying Bell
inequalities, alternative quantum theories and the associated physical
properties of quantum systems. Non-negative probabilities for transfer
functions result in Bell-type inequalities. The method is used to show that all
realistic Lorentz-invariant quantum theories, which give unique results and
have no preferred frame, can be ruled out on the grounds that they lead to weak
backward causality.Comment: Plain TeX, 12 pages, no figures. To be submitted Physics Letters A
Derivation of Bell inequality corrected (14c) + minor change
Decoherence of quantum wavepackets due to interaction with conformal spacetime fluctuations
One of the biggest problems faced by those attempting to combine quantum
theory and general relativity is the experimental inaccessibility of the
unification scale. In this paper we show how incoherent conformal waves in the
gravitational field, which may be produced by quantum mechanical zero-point
fluctuations, interact with the wavepackets of massive particles. The result of
this interaction is to produce decoherence within the wavepackets which could
be accessible in experiments at the atomic scale.
Using a simple model for the coherence properties of the gravitational field
we derive an equation for the evolution of the density matrix of such a
wavepacket. Following the primary state diffusion programme, the most promising
source of spacetime fluctuations for detection are the above zero-point energy
fluctuations. According to our model, the absence of intrinsic irremoveable
decoherence in matter interferometry experiments puts bounds on some of the
parameters of quantum gravity theories. Current experiments give \lambda > 18.
, where \lambda t_{Planck} is an effective cut-off for the validity of
low-energy quantum gravity theories.Comment: REVTeX forma
Quantum state diffusion with a moving basis: computing quantum-optical spectra
Quantum state diffusion (QSD) as a tool to solve quantum-optical master
equations by stochastic simulation can be made several orders of magnitude more
efficient if states in Hilbert space are represented in a moving basis of
excited coherent states. The large savings in computer memory and time are due
to the localization property of the QSD equation. We show how the method can be
used to compute spectra and give an application to second harmonic generation.Comment: 8 pages in RevTeX, 1 uuencoded postscript figure, submitted to Phys.
Rev.
Quantum state diffusion, localization and computation
Numerical simulation of individual open quantum systems has proven advantages
over density operator computations. Quantum state diffusion with a moving basis
(MQSD) provides a practical numerical simulation method which takes full
advantage of the localization of quantum states into wave packets occupying
small regions of classical phase space. Following and extending the original
proposal of Percival, Alber and Steimle, we show that MQSD can provide a
further gain over ordinary QSD and other quantum trajectory methods of many
orders of magnitude in computational space and time. Because of these gains, it
is even possible to calculate an open quantum system trajectory when the
corresponding isolated system is intractable. MQSD is particularly advantageous
where classical or semiclassical dynamics provides an adequate qualitative
picture but is numerically inaccurate because of significant quantum effects.
The principles are illustrated by computations for the quantum Duffing
oscillator and for second harmonic generation in quantum optics. Potential
applications in atomic and molecular dynamics, quantum circuits and quantum
computation are suggested.Comment: 16 pages in LaTeX, 2 uuencoded postscript figures, submitted to J.
Phys.
The Square Root Depth Wave Equations
We introduce a set of coupled equations for multilayer water waves that
removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the
presence of shear. The new well-posed equations are Hamiltonian and in the
absence of imposed background shear they retain the same travelling wave
solutions as MGN. We call the new model the Square Root Depth equations, from
the modified form of their kinetic energy of vertical motion. Our numerical
results show how the Square Root Depth equations model the effects of
multilayer wave propagation and interaction, with and without shear.Comment: 10 pages, 5 figure
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