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

Minimal long-term neurobehavioral impairments after endovascular perforation subarachnoid hemorrhage in mice

AbstractCognitive deficits are among the most severe and pervasive consequences of aneurysmal subarachnoid hemorrhage (SAH). A critical step in developing therapies targeting such outcomes is the characterization of experimentally-tractable pre-clinical models that exhibit multi-domain neurobehavioral deficits similar to those afflicting humans. We therefore searched for neurobehavioral abnormalities following endovascular perforation induction of SAH in mice, a heavily-utilized model. We instituted a functional screen to manage variability in injury severity, then assessed acute functional deficits, as well as activity, anxiety-related behavior, learning and memory, socialization, and depressive-like behavior at sub-acute and chronic time points (up to 1 month post-injury). Animals in which SAH was induced exhibited reduced acute functional capacity and reduced general activity to 1 month post-injury. Tests of anxiety-related behavior including central area time in the elevated plus maze and thigmotaxis in the open field test revealed increased anxiety-like behavior at subacute and chronic time-points, respectively. Effect sizes for subacute and chronic neurobehavioral endpoints in other domains, however, were small. In combination with persistent variability, this led to non-significant effects of injury on all remaining neurobehavioral outcomes. These results suggest that, with the exception of anxiety-related behavior, alternate mouse models are required to effectively analyze cognitive outcomes after SAH.</jats:p

Scalar Quantum Field Theory with Cubic Interaction

In this paper it is shown that an i phi^3 field theory is a physically acceptable field theory model (the spectrum is positive and the theory is unitary). The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.Comment: Corrected expressions in equations (20) and (21

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

Intruder States and their Local Effect on Spectral Statistics

The effect on spectral statistics and on the revival probability of intruder states in a random background is analysed numerically and with perturbative methods. For random coupling the intruder does not affect the GOE spectral statistics of the background significantly, while a constant coupling causes very strong correlations at short range with a fourth power dependence of the spectral two-point function at the origin.The revival probability is significantly depressed for constant coupling as compared to random coupling.Comment: 18 pages, 10 Postscript figure

modCHIMERA: A novel murine closed-head model of moderate traumatic brain injury

AbstractTraumatic brain injury is a major source of global disability and mortality. Preclinical TBI models are a crucial component of therapeutic investigation. We report a tunable, monitored model of murine non-surgical, diffuse closed-head injury—modCHIMERA—characterized by impact as well as linear and rotational acceleration. modCHIMERA is based on the Closed-Head Impact Model of Engineered Rotational Acceleration (CHIMERA) platform. We tested this model at 2 energy levels: 1.7 and 2.1 Joules—substantially higher than previously reported for this system. Kinematic analysis demonstrated linear acceleration exceeding injury thresholds in humans, although outcome metrics tracked impact energy more closely than kinematic parameters. Acute severity metrics were consistent with a complicated-mild or moderate TBI, a clinical population characterized by high morbidity but potentially reversible pathology. Axonal injury was multifocal and bilateral, neuronal death was detected in the hippocampus, and microglial neuroinflammation was prominent. Acute functional analysis revealed prolonged post-injury unconsciousness, and decreased spontaneous behavior and stimulated neurological scores. Neurobehavioral deficits were demonstrated in spatial learning/memory and socialization at 1-month. The overall injury profile of modCHIMERA corresponds with the range responsible for a substantial portion of TBI-related disability in humans. modCHIMERA should provide a reliable platform for efficient analysis of TBI pathophysiology and testing of treatment modalities.</jats:p

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

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

Spectral statistics of the k-body random-interaction model

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.Comment: 17 pages, no figure

Nuclear Structure Calculations with Low-Momentum Potentials in a Model Space Truncation Approach

We have calculated the ground-state energy of the doubly magic nuclei 4He, 16O and 40Ca within the framework of the Goldstone expansion starting from various modern nucleon-nucleon potentials. The short-range repulsion of these potentials has been renormalized by constructing a low-momentum potential V-low-k. We have studied the connection between the cutoff momemtum Lambda and the size of the harmonic oscillator space employed in the calculations. We have found a fast convergence of the results with a limited number of oscillator quanta.Comment: 6 pages, 8 figures, to be published on Physical Review