Dynamical Reduction Models: present status and future developments

We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss the difficulties in generalizing the existing models in order to comprise also relativistic quantum field theories. We point out possible future lines of research, ranging from mathematical physics to phenomenology.Comment: 12 pages. Contribution to the Proceedings of the "Third International Workshop DICE2006", Castello di Piombino (Tuscany), September 11-15, 2006. Minor changes mad

Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis - Calculational Details

We give details of calculations analyzing the proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester within different stochastic models for state vector collapse. We give two methods for exactly calculating the fringe visibility in these models, one proceeding directly from the equation of motion for the expectation of the density matrix, and the other proceeding from solving a linear stochastic unravelling of this equation. We also give details of the calculation that identifies the stochasticity parameter implied by the small displacement Taylor expansion of the CSL model density matrix equation. The implications of the two results are briefly discussed. Two pedagogical appendices review mathematical apparatus needed for the calculations.Comment: 9 pages, LaTeX. Minor changes mad

On the Electromagnetic Properties of Matter in Collapse Models

We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and under only the dipole approximation, we are able to solve the equation of motion exactly. In this way, both the finite time and large time behavior can be analyzed accurately. We discovered new features, which did not appear in previous works on the same subject. Since, so far, the spontaneous photon emission process places the strongest upper bounds on the collapse parameters, our results call for a further analysis of this process for those atomic systems which can be employed in experimental tests of collapse models, as well as of quantum mechanics.Comment: 17 pages, LaTeX, updated version with minor change

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

The quantum theory of measurement within dynamical reduction models

We analyze in mathematical detail, within the framework of the QMUPL model of spontaneous wave function collapse, the von Neumann measurement scheme for the measurement of a 1/2 spin particle. We prove that, according to the equation of the model: i) throughout the whole measurement process, the pointer of the measuring device is always perfectly well localized in space; ii) the probabilities for the possible outcomes are distributed in agreement with the Born probability rule; iii) at the end of the measurement the state of the microscopic system has collapsed to the eigenstate corresponding to the measured eigenvalue. This analysis shows rigorously how dynamical reduction models provide a consistent solution to the measurement problem of quantum mechanics.Comment: 24 pages, RevTeX. Minor changes mad

The Hilbert space operator formalism within dynamical reduction models

Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the postulates defining these models. In this paper, we show why and how the Hilbert-space operator formalism, which standard quantum mechanics postulates, can be derived from the fundamental evolution equation of dynamical reduction models. Far from having any special ontological meaning, we show that within the dynamical reduction context the operator formalism is just a compact and convenient way to express the statistical properties of the outcomes of experiments.Comment: 25 pages, RevTeX. Changes made and two figures adde

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

Entangling macroscopic diamonds at room temperature: Bounds on the continuous-spontaneous-localization parameters

A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in detecting entanglement between two macroscopic specks of diamonds, separated by a macroscopic distance, at room temperature. This impressive results is a further confirmation of the validity of quantum theory in (at least parts of) the mesoscopic and macroscopic domain, and poses a challenge to collapse models, which predict a violation of the quantum superposition principle, which is the bigger the larger the system. We analyze the experiment in the light of such models. We will show that the bounds placed by experimental data are weaker than those coming from matter-wave interferometry and non-interferometric tests of collapse models.Comment: 7 pages, 3 figures, v2: close to the published version, LaTe

Collapse models with non-white noises II: particle-density coupled noises

We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schr\"odinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision

Effect of lhcsr gene dosage on oxidative stress and light use efficiency by Chlamydomonas reinhardtii cultures

Unicellular green algae, a promising source for renewable biofuels, produce lipid-rich biomass from light and CO2. Productivity in photo-bioreactors is affected by inhomogeneous light distribution from high cell pigment causing heat dissipation of light energy absorbed in excess and shading of the deep layers. Contrasting reports have been published on the relation between photoprotective energy dissipation and productivity. Here, we have re-investigated the relation between energy quenching (qE) activity, photodamage and light use efficiency by comparing WT and two Chlamydomonas reinhardtii strains differing for their complement in LHCSR proteins, which catalyse dissipation of excitation energy in excess (qE). Strains were analysed for ROS production, protein composition, rate of photodamage and productivity assessed under wide light and CO2 conditions.The strain lacking LHCSR1 and knocked down in LHCSR3, thus depleted in qE, produced O-2 at significantly higher rate under high light, accompanied by enhanced singlet oxygen release and PSII photodamage. However, biomass productivity of WT was delayed in respect for mutant strains under intermittent light conditions only, implying that PSII activity was not the limiting factor under excess light. Contrary to previous proposals, domestication of Chlamydomonas for carbon assimilation rate in photo-bioreactors by down-regulation of photoprotective energy dissipation was ineffective in increasing algal biomass productivity