Collapse models with non-white noises

We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the non-Schrodinger terms of the equation induce the collapse of the wave function to one of the common eigenstates of the collapsing operators, and that the collapse occurs with the correct quantum probabilities. We also develop a perturbation expansion of the solution of the equation with respect to the parameter which sets the strength of the collapse process; such an approximation allows one to compute the leading order terms for the deviations of the predictions of collapse models with respect to those of standard quantum mechanics. This analysis shows that to leading order, the ``imaginary'' noise trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J. Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.Comment: 20 pages, Plain Te

Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter lambda, coming from the analysis of the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the original bound, in agreement with more recent analysis. This implies that the collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and thus falls within the range of testability with present-day technology. We also compare the spectrum of the collapsing field with those of known cosmological fields, showing that a typical cosmological random field can yield an efficient wave function collapse.Comment: 13 pages, LaTeX, 3 figure

Rain estimation from satellites: An examination of the Griffith-Woodley technique

The Griffith-Woodley Technique (GWT) is an approach to estimating precipitation using infrared observations of clouds from geosynchronous satellites. It is examined in three ways: an analysis of the terms in the GWT equations; a case study of infrared imagery portraying convective development over Florida; and the comparison of a simplified equation set and resultant rain map to results using the GWT. The objective is to determine the dominant factors in the calculation of GWT rain estimates. Analysis of a single day's convection over Florida produced a number of significant insights into various terms in the GWT rainfall equations. Due to the definition of clouds by a threshold isotherm the majority of clouds on this day did not go through an idealized life cycle before losing their identity through merger, splitting, etc. As a result, 85% of the clouds had a defined life of 0.5 or 1 h. For these clouds the terms in the GWT which are dependent on cloud life history become essentially constant. The empirically derived ratio of radar echo area to cloud area is given a singular value (0.02) for 43% of the sample, while the rainrate term is 20.7 mmh-1 for 61% of the sample. For 55% of the sampled clouds the temperature weighting term is identically 1.0. Cloud area itself is highly correlated (r=0.88) with GWT computed rain volume. An important, discriminating parameter in the GWT is the temperature defining the coldest 10% cloud area. The analysis further shows that the two dominant parameters in rainfall estimation are the existence of cold cloud and the duration of cloud over a point

Comment about pion electro-production and the axial form factors

The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form factor of the nucleon cannot be accessed through threshold pion electroproduction is unfounded

Representations of U(1,q) and Constructive Quaternion Tensor Products

The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecc

Formal Design of Asynchronous Fault Detection and Identification Components using Temporal Epistemic Logic

Autonomous critical systems, such as satellites and space rovers, must be able to detect the occurrence of faults in order to ensure correct operation. This task is carried out by Fault Detection and Identification (FDI) components, that are embedded in those systems and are in charge of detecting faults in an automated and timely manner by reading data from sensors and triggering predefined alarms. The design of effective FDI components is an extremely hard problem, also due to the lack of a complete theoretical foundation, and of precise specification and validation techniques. In this paper, we present the first formal approach to the design of FDI components for discrete event systems, both in a synchronous and asynchronous setting. We propose a logical language for the specification of FDI requirements that accounts for a wide class of practical cases, and includes novel aspects such as maximality and trace-diagnosability. The language is equipped with a clear semantics based on temporal epistemic logic, and is proved to enjoy suitable properties. We discuss how to validate the requirements and how to verify that a given FDI component satisfies them. We propose an algorithm for the synthesis of correct-by-construction FDI components, and report on the applicability of the design approach on an industrial case-study coming from aerospace.Comment: 33 pages, 20 figure

Phonon-modulated magnetic interactions and spin Tomonaga-Luttinger liquid in the p-orbital antiferromagnet CsO2

The magnetic response of antiferromagnetic CsO2, coming from the p-orbital S=1/2 spins of anionic O2- molecules, is followed by 133Cs nuclear magnetic resonance across the structural phase transition occuring at Ts1=61 K on cooling. Above Ts1, where spins form a square magnetic lattice, we observe a huge, nonmonotonic temperature dependence of the exchange coupling originating from thermal librations of O2- molecules. Below Ts1, where antiferromagnetic spin chains are formed as a result of p-orbital ordering, we observe a spin Tomonaga-Luttinger-liquid behavior of spin dynamics. These two interesting phenomena, which provide rare simple manifestations of the coupling between spin, lattice and orbital degrees of freedom, establish CsO2 as a model system for molecular solids.Comment: 9 pages, 5 figures (with Supplemental Material), to appear in Physical Review Letter

Non-colliding Brownian Motions and the extended tacnode process

We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.Comment: 38 pages. In the revised version a few arguments have been expanded and many typos correcte