29,771 research outputs found
Quantum stochastic integrals as operators
We construct quantum stochastic integrals for the integrator being a
martingale in a von Neumann algebra, and the integrand -- a suitable process
with values in the same algebra, as densely defined operators affiliated with
the algebra. In the case of a finite algebra we allow the integrator to be an
--martingale in which case the integrals are --martingales too
An Ostrowski Type Inequality for Mappings Whose Second Derivatives are Bounded and Applications
An integral inequality of Ostrowski's type for mappings whose second derivatives are bounded is proved. Applications in Numerical Integration and for special means are pointed out
On the Perturbed Trapezoid Formula
Some inequalities related to the perturbed trapezoid formula are given. An application for the expectation of a random variable is also pointed out
Retrodiction with two-level atoms: atomic previvals
In the Jaynes-Cummings model a two-level atom interacts with a single-mode
electromagnetic field. Quantum mechanics predicts collapses and revivals in the
probability that a measurement will show the atom to be excited at various
times after the initial preparation of the atom and field. In retrodictive
quantum mechanics we seek the probability that the atom was prepared in a
particular state given the initial state of the field and the outcome of a
later measurement on the atom. Although this is not simply the time reverse of
the usual predictive problem, we demonstrate in this paper that retrodictive
collapses and revivals also exist. We highlight the differences between
predictive and retrodictive evolutions and describe an interesting situation
where the prepared state is essentially unretrodictable.Comment: 15 pages, 3 (5) figure
Rabi Oscillations in Systems with Small Anharmonicity
When a two-level quantum system is irradiated with a microwave signal, in
resonance with the energy difference between the levels, it starts Rabi
oscillation between those states. If there are other states close, in energy,
to the first two, the Rabi signal will also induce transition to those. Here,
we study the probability of transition to the third state, in a three-level
system, while a Rabi oscillation between the first two states is performed. We
investigate the effect of pulse shaping on the probability and suggest methods
for optimizing pulse shapes to reduce transition probability.Comment: 7 pages, 7 figure
The response function of modulated grid Faraday cup plasma instruments
Modulated grid Faraday cup plasma analyzers are a very useful tool for making in situ measurements of space plasmas. One of their great attributes is that their simplicity permits their angular response function to be calculated theoretically. An expression is derived for this response function by computing the trajectories of the charged particles inside the cup. The Voyager Plasma Science (PLS) experiment is used as a specific example. Two approximations to the rigorous response function useful for data analysis are discussed. The theoretical formulas were tested by multi-sensor analysis of solar wind data. The tests indicate that the formulas represent the true cup response function for all angles of incidence with a maximum error of only a few percent
Murdoch has had too many favours
Long-standing proposals to update media ownership policies need to be implemented, particularly in relation to 21st Century Fox impending bid for Sky
Retrodiction as a tool for micromaser field measurements
We use retrodictive quantum theory to describe cavity field measurements by
successive atomic detections in the micromaser. We calculate the state of the
micromaser cavity field prior to detection of sequences of atoms in either the
excited or ground state, for atoms that are initially prepared in the excited
state. This provides the POM elements, which describe such sequences of
measurements.Comment: 20 pages, 4(8) figure
Frictional quantum decoherence
The dynamics associated with a measurement-based master equation for quantum
Brownian motion are investigated. A scheme for obtaining time evolution from
general initial conditions is derived. This is applied to analyze dissipation
and decoherence in the evolution of both a Gaussian and a Schr\"{o}dinger cat
initial state. Dependence on the diffusive terms present in the master equation
is discussed with reference to both the coordinate and momentum
representations.Comment: 18 pages, 7 figure
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