6,877 research outputs found
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
Conidial germination in scon\u3csup\u3ec\u3c/sup\u3e
Conidial germination in scon
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
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
On the dominance of J(P)=0(+) ground states in even-even nuclei from random two-body interactions
Recent calculations using random two-body interactions showed a preponderance
of J(P)=0(+) ground states, despite the fact that there is no strong pairing
character in the force. We carry out an analysis of a system of identical
particles occupying orbits with j=1/2, 3/2 and 5/2 and discuss some general
features of the spectra derived from random two-body interactions. We show that
for random two-body interactions that are not time-reversal invariant the
dominance of 0(+) states in this case is more pronounced, indicating that
time-reversal invariance cannot be the origin of the 0(+) dominance.Comment: 8 pages, 3 tables and 3 figures. Phys. Rev. C, in pres
Inferring Networks of Substitutable and Complementary Products
In a modern recommender system, it is important to understand how products
relate to each other. For example, while a user is looking for mobile phones,
it might make sense to recommend other phones, but once they buy a phone, we
might instead want to recommend batteries, cases, or chargers. These two types
of recommendations are referred to as substitutes and complements: substitutes
are products that can be purchased instead of each other, while complements are
products that can be purchased in addition to each other.
Here we develop a method to infer networks of substitutable and complementary
products. We formulate this as a supervised link prediction task, where we
learn the semantics of substitutes and complements from data associated with
products. The primary source of data we use is the text of product reviews,
though our method also makes use of features such as ratings, specifications,
prices, and brands. Methodologically, we build topic models that are trained to
automatically discover topics from text that are successful at predicting and
explaining such relationships. Experimentally, we evaluate our system on the
Amazon product catalog, a large dataset consisting of 9 million products, 237
million links, and 144 million reviews.Comment: 12 pages, 6 figure
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
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
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