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.

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 $K$ meson and $B$ meson tests of gravity induced decoherence.Comment: 10 pages, plain Tex, no figure

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.

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