5,494 research outputs found
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
Post‐traumatic stress disorder\u27s relation with positive and negative emotional avoidance: The moderating role of gender
Post‐traumatic stress disorder (PTSD) is characterized by avoidance of trauma‐related emotions. Research indicates that this avoidance may extend to any emotional experience that elicits distress, including those that are unrelated to the trauma. Literature in this area has been limited in its exclusive focus on negative emotions. Despite evidence of gender differences in PTSD and emotional avoidance separately, no studies to date have examined gender as a moderator of their association. The goal of the current study was to extend research by exploring the moderating role of gender in the relation between PTSD symptom severity and positive and negative emotional avoidance. Participants were 276 trauma‐exposed individuals (65.9% female, 65.6% White, Mage = 19.24) from a university in the north‐eastern United States. Moderation results indicated a main effect for PTSD symptom severity on both positive (b = 0.07, p \u3c .001) and negative (b = 0.04, p = .03) emotional avoidance. The interaction of gender and PTSD symptom severity was significant for positive emotion avoidance (b = 0.97, p = .01). Analysis of simple slopes revealed that PTSD symptom severity was significantly associated with positive emotional avoidance for males (b = 0.13, p \u3c .001) but not females (b = 0.03, p = .08). Results suggest the importance of gender‐sensitive recommendations for assessment and treatment of emotional avoidance in PTSD
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 mechanical Carnot engine
A cyclic thermodynamic heat engine runs most efficiently if it is reversible.
Carnot constructed such a reversible heat engine by combining adiabatic and
isothermal processes for a system containing an ideal gas. Here, we present an
example of a cyclic engine based on a single quantum-mechanical particle
confined to a potential well. The efficiency of this engine is shown to equal
the Carnot efficiency because quantum dynamics is reversible. The quantum heat
engine has a cycle consisting of adiabatic and isothermal quantum processes
that are close analogues of the corresponding classical processes.Comment: 10 page
Fundamental Limits on the Speed of Evolution of Quantum States
This paper reports on some new inequalities of
Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution
between two orthogonal pure states. The clear determinant of the qualitative
behavior of this time scale is the statistics of the energy spectrum. An
often-overlooked correspondence between the real-time behavior of a quantum
system and the statistical mechanics of a transformed (imaginary-time)
thermodynamic system appears promising as a source of qualitative insights into
the quantum dynamics.Comment: 6 pages, 1 eps figur
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
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
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 and for any density operator
on a finite dimensional Hilbert space with the orthogonal projection onto
the range of there holds the estimate \Tr(\Pi \rme^{-\rmi ht}\rho
\rme^{\rmi ht}) \geq\cos^{2}((\Delta h)_{\rho}t) for all real with
We show that equality either holds for all
or it does not hold for a single with All the density operators saturating the bound for
all i.e. the mixed intelligent states, are determined.Comment: 12 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
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
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