672 research outputs found
Dynamical Reduction Models with General Gaussian Noises
We consider the effect of replacing in stochastic differential equations
leading to the dynamical collapse of the statevector, white noise stochastic
processes with non white ones. We prove that such a modification can be
consistently performed without altering the most interesting features of the
previous models. One of the reasons to discuss this matter derives from the
desire of being allowed to deal with physical stochastic fields, such as the
gravitational one, which cannot give rise to white noises. From our point of
view the most relevant motivation for the approach we propose here derives from
the fact that in relativistic models the occurrence of white noises is the main
responsible for the appearance of untractable divergences. Therefore, one can
hope that resorting to non white noises one can overcome such a difficulty. We
investigate stochastic equations with non white noises, we discuss their
reduction properties and their physical implications. Our analysis has a
precise interest not only for the above mentioned subject but also for the
general study of dissipative systems and decoherence.Comment: 22 pages, Late
Calculation of X-Ray Signals from Karolyhazy Hazy Space-Time
Karolyhazy's hazy space-time model, invented for breaking down macroscopic
interferences, employs wave-like gravity disturbances. If so, then electric
charges would radiate permanently. Here we discuss the observational
consequences of the radiation. We find that such radiation is excluded by
common experimental situations.Comment: 7 pages, PlainTe
Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson
We discuss why, contrary to claims recently made by P. W. Anderson,
decoherence has not solved the quantum measurement problem
Numerical analysis of a spontaneous collapse model for a two-level system
We study a spontaneous collapse model for a two-level (spin) system, in which
the Hamiltonian and the stochastic terms do not commute. The numerical solution
of the equations of motions allows to give precise estimates on the regime at
which the collapse of the state vector occurs, the reduction and delocalization
times, and the reduction probabilities; it also allows to quantify the effect
that an Hamiltonian which does not commute with the reducing terms has on the
collapse mechanism. We also give a clear picture of the transition from the
"microscopic" regime (when the noise terms are weak and the Hamiltonian
prevents the state vector to collapse) to the "macroscopic" regime (when the
noise terms are dominant and the collapse becomes effective for very long
times). Finally, we clarify the distinction between decoherence and collapse.Comment: 7 pages, RevTeX. Significative improvements made. To appear on Phys.
Rev.
Stochastic Schroedinger Equations with General Complex Gaussian Noises
Within the framework of stochastic Schroedinger equations, we show that the
correspondence between statevector equations and ensemble equations is
infinitely many to one, and we discuss the consequences. We also generalize the
results of [Phys. Lett. A 224, p. 25 (1996)] to the case of more general
complex Gaussian noises and analyze the two important cases of purely real and
purely imaginary stochastic processes.Comment: 5 pages, LaTeX. To appear on Phys. Rev.
Remarks on a Proposed Super-Kamiokande Test for Quantum Gravity Induced Decoherence Effects
Lisi, Marrone, and Montanino have recently proposed a test for quantum
gravity induced decoherence effects in neutrino oscillations observed at
Super-Kamiokande. We comment here that their equations have the same
qualitative form as the energy conserving objective state vector reduction
equations discussed by a number of authors. However, using the Planckian
parameter value proposed to explain state vector reduction leads to a neutrino
oscillation effect many orders of magnitude smaller than would be detectable at
Super-Kamiokande. Similar estimates hold for the Ghirardi, Rimini, and Weber
spontaneous localization approach to state vector reduction, and our remarks
are relevant as well to proposed meson and meson tests of gravity
induced decoherence.Comment: 10 pages, plain Tex, no figure
General criterion for the entanglement of two indistinguishable particles
We relate the notion of entanglement for quantum systems composed of two
identical constituents to the impossibility of attributing a complete set of
properties to both particles. This implies definite constraints on the
mathematical form of the state vector associated with the whole system. We then
analyze separately the cases of fermion and boson systems, and we show how the
consideration of both the Slater-Schmidt number of the fermionic and bosonic
analog of the Schmidt decomposition of the global state vector and the von
Neumann entropy of the one-particle reduced density operators can supply us
with a consistent criterion for detecting entanglement. In particular, the
consideration of the von Neumann entropy is particularly useful in deciding
whether the correlations of the considered states are simply due to the
indistinguishability of the particles involved or are a genuine manifestation
of the entanglement. The treatment leads to a full clarification of the subtle
aspects of entanglement of two identical constituents which have been a source
of embarrassment and of serious misunderstandings in the recent literature.Comment: 18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems
added, reference [1] corrected. To appear on Phys.Rev.A 70, (2004
Collapse Models
This is a review of formalisms and models (nonrelativistic and relativistic)
which modify Schrodinger's equation so that it describes wavefunction collapse
as a dynamical physical process.Comment: 40 pages, to be published in "Open Systems and Measurement in
Relativistic Quantum Theory," F. Petruccione and H. P. Breuer eds. (Springer
Verlag, 1999
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