High photovoltages in ferroelectric ceramics

The short-circuit currents and photo-emfs were measured for various ceramics including barium titanate, lead metaniobate, and lead titanate. It is suggested that the emfs and currents arise from the presence of photoconductor-insulator sandwiches in the presence of space-charge-produced internal fields. Results are in agreement with the proposed theory and indicate that the ferroelectric ceramics are not only producers of high-voltage photoelectricity but a photo-battery, the polarity and magnitude of which can be switched by application of an electrical signal

Efficient Simulation of Quantum State Reduction

The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the phenomenon of quantum state reduction. Here we construct a general closed form solution to this equation, for any given initial condition, in terms of a random variable representing the terminal value of the energy and an independent Brownian motion. The solution is essentially algebraic in character, involving no integration, and is thus suitable as a basis for efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur

Quantum noise and stochastic reduction

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schrodinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this article, two such models are investigated: one that achieves state reduction in infinite time, and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions--algebraic in character and involving no integration--are obtained for both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system, and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems.Comment: 50 page

Dynamical state reduction in an EPR experiment

A model is developed to describe state reduction in an EPR experiment as a continuous, relativistically-invariant, dynamical process. The system under consideration consists of two entangled isospin particles each of which undergo isospin measurements at spacelike separated locations. The equations of motion take the form of stochastic differential equations. These equations are solved explicitly in terms of random variables with a priori known probability distribution in the physical probability measure. In the course of solving these equations a correspondence is made between the state reduction process and the problem of classical nonlinear filtering. It is shown that the solution is covariant, violates Bell inequalities, and does not permit superluminal signaling. It is demonstrated that the model is not governed by the Free Will Theorem and it is argued that the claims of Conway and Kochen, that there can be no relativistic theory providing a mechanism for state reduction, are false.Comment: 19 pages, 3 figure

The EPR experiment in the energy-based stochastic reduction framework

We consider the EPR experiment in the energy-based stochastic reduction framework. A gedanken set up is constructed to model the interaction of the particles with the measurement devices. The evolution of particles' density matrix is analytically derived. We compute the dependence of the disentanglement rate on the parameters of the model, and study the dependence of the outcome probabilities on the noise trajectories. Finally, we argue that these trajectories can be regarded as non-local hidden variables.Comment: 11 pages, 5 figure

Hidden variable interpretation of spontaneous localization theory

The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine the dynamics of the distribution of particles conditional on this noisy information and consistency with the GRW wavefunction dynamics is demonstrated. Viewing this development as a hybrid BM-GRW theory, it is argued that, besides helping to clarify the relationship between the GRW theory and BM, its merits make it worth considering in its own right.Comment: 13 page

Martingale Models for Quantum State Reduction

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations experienced by the expectation of the observable during the course of the reduction process and an upper bound is established for the ensemble average of the greatest fluctuations incurred. We consider the general projection postulate of L\"uders applicable in the case of a possibly degenerate eigenvalue spectrum, and derive this result rigorously from the underlying stochastic dynamics for state reduction in the case of both a pure and a mixed initial state. We also analyse the associated Lindblad equation for the evolution of the density matrix, and obtain an exact time-dependent solution for the state reduction that explicitly exhibits the transition from a general initial density matrix to the L\"uders density matrix. Finally, we apply Girsanov's theorem to derive a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.Comment: 30 pages LaTeX. Submitted to Journal of Physics

Fleming's bound for the decay of mixed states

Fleming's inequality is generalized to the decay function of mixed states. We show that for any symmetric hamiltonian $h$ and for any density operator $\rho$ on a finite dimensional Hilbert space with the orthogonal projection $\Pi$ onto the range of $\rho$ there holds the estimate \Tr(\Pi \rme^{-\rmi ht}\rho \rme^{\rmi ht}) \geq\cos^{2}((\Delta h)_{\rho}t) for all real $t$ with $(\Delta h)_{\rho}| t| \leq\pi/2.$ We show that equality either holds for all $t\in\mathbb{R}$ or it does not hold for a single $t$ with $0<(\Delta h)_{\rho}| t| \leq\pi/2.$ All the density operators saturating the bound for all $t\in\mathbb{R},$ i.e. the mixed intelligent states, are determined.Comment: 12 page

Research on nonlinear optical materials: an assessment. IV. Photorefractive and liquid crystal materials

This panel considered two separate subject areas: photorefractive materials used for nonlinear optics and liquid crystal materials used in light valves. Two related subjects were not considered due to lack of expertise on the panel: photorefractive materials used in light valves and liquid crystal materials used in nonlinear optics. Although the inclusion of a discussion of light valves by a panel on nonlinear optical materials at first seems odd, it is logical because light valves and photorefractive materials perform common functions

On observability of Renyi's entropy

Despite recent claims we argue that Renyi's entropy is an observable quantity. It is shown that, contrary to popular belief, the reported domain of instability for Renyi entropies has zero measure (Bhattacharyya measure). In addition, we show the instabilities can be easily emended by introducing a coarse graining into an actual measurement. We also clear up doubts regarding the observability of Renyi's entropy in (multi--)fractal systems and in systems with absolutely continuous PDF's.Comment: 18 pages, 1 EPS figure, REVTeX, minor changes, accepted to Phys. Rev.