987 research outputs found
An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations
A novel recipe for exactly solving in finite terms a class of special
differential Riccati equations is reported. Our procedure is entirely based on
a successful resolution strategy quite recently applied to quantum dynamical
time-dependent SU(2) problems. The general integral of exemplary differential
Riccati equations, not previously considered in the specialized literature, is
explicitly determined to illustrate both mathematical usefulness and easiness
of applicability of our proposed treatment. The possibility of exploiting the
general integral of a given differential Riccati equation to solve an SU(2)
quantum dynamical problem, is succinctly pointed out.Comment: 10 page
Zero energy resonance and the logarithmically slow decay of unstable multilevel systems
The long time behavior of the reduced time evolution operator for unstable
multilevel systems is studied based on the N-level Friedrichs model in the
presence of a zero energy resonance.The latter means the divergence of the
resolvent at zero energy. Resorting to the technique developed by Jensen and
Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is
characterized by the zero energy eigenstate that does not belong to the Hilbert
space. It is then shown that for some kinds of the rational form factors the
logarithmically slow decay of the reduced time evolution operator can be
realized.Comment: 31 pages, no figure
Probing the Equation of State of Nuclear Matter via Neutron Star Asteroseismology
We general relativistically calculate the frequency of fundamental torsional
oscillations of neutron star crusts, where we focus on the crystalline
properties obtained from macroscopic nuclear models in a way depending on the
equation of state of nuclear matter. We find that the calculated frequency is
sensitive to the density dependence of the symmetry energy, but almost
independent of the incompressibility of symmetric nuclear matter. By
identifying the lowest-frequency quasi-periodic oscillation in giant flares
observed from soft gamma-ray repeaters as the fundamental torsional mode and
allowing for the dependence of the calculated frequency on stellar models, we
provide a lower limit of the density derivative of the symmetry energy as
MeV.Comment: 4 pages, 4 figure
Purification through Zeno-like Measurements
A series of frequent measurements on a quantum system (Zeno-like
measurements) is shown to result in the ``purification'' of another quantum
system in interaction with the former. Even though the measurements are
performed on the former system, their effect drives the latter into a pure
state, irrespectively of its initial (mixed) state, provided certain conditions
are satisfied.Comment: REVTeX4, 4 pages, 1 figure; to be published in Phys. Rev. Lett.
(2003
Lymphoma and hypercalcemia in a pediatric orthotopic liver transplant patient
We present a case report of a pediatric orthotopic liver transplant recipient who developed lymphoma with hypercalcemia on cyclosporine and prednisone immunosuppression. This is the first reported posttransplant lymphoproliferative disorder complicated by hypercalcemia, with a finding of an elevated 1,25 dihydroxyl vitamin D state, suggesting that it has a role in the pathophysiology of this B cell lymphoma hypercalcemia. The clinical course and management of this disorder with a 31-month follow-up are described. © 1989 by Williams & Wilkins
Macroscopic limit of a solvable dynamical model
The interaction between an ultrarelativistic particle and a linear array made
up of two-level systems (^^ ^^ AgBr" molecules) is studied by making use of
a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes
between the particle and the molecules are properly taken into account, and the
evolution of the total system is calculated exactly both when the array is
initially in the ground state and in a thermal state. In the macroscopic limit
(), the system remains solvable and leads to interesting
connections with the Jaynes-Cummings model, that describes the interaction of a
particle with a maser. The visibility of the interference pattern produced by
the two branch waves of the particle is computed, and the conditions under
which the spin array in the limit behaves as a ^^ ^^
detector" are investigated. The behavior of the visibility yields good insights
into the issue of quantum measurements: It is found that, in the
thermodynamical limit, a superselection-rule space appears in the description
of the (macroscopic) apparatus. In general, an initial thermal state of the ^^
^^ detector" provokes a more substantial loss of quantum coherence than an
initial ground state. It is argued that a system decoheres more as the
temperature of the detector increases. The problem of ^^ ^^ imperfect
measurements" is also shortly discussed.Comment: 30 pages, report BA-TH/93-13
Exponential behavior of a quantum system in a macroscopic medium
An exponential behavior at all times is derived for a solvable dynamical
model in the weak-coupling, macroscopic limit. Some implications for the
quantum measurement problem are discussed, in particular in connection with
dissipation.Comment: 8 pages, report BA-TH/94-17
Reflection and Transmission in a Neutron-Spin Test of the Quantum Zeno Effect
The dynamics of a quantum system undergoing frequent "measurements", leading
to the so-called quantum Zeno effect, is examined on the basis of a
neutron-spin experiment recently proposed for its demonstration. When the
spatial degrees of freedom are duely taken into account, neutron-reflection
effects become very important and may lead to an evolution which is totally
different from the ideal case.Comment: 26 pages, 6 figure
Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
The long-time behavior of the survival probability for unstable multilevel
systems that follows the power-decay law is studied based on the N-level
Friedrichs model, and is shown to depend on the initial population in unstable
states. A special initial state maximizing the asymptote of the survival
probability at long times is found and examined by considering the spontaneous
emission process for the hydrogen atom interacting with the electromagnetic
field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.
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