819 research outputs found
Universal Local symmetries and non-superposition in classical mechanics
In the Hilbert space formulation of classical mechanics (CM), pioneered by
Koopman and von Neumann (KvN), there are potentially more observables that in
the standard approach to CM. In this paper we show that actually many of those
extra observables are not invariant under a set of universal local symmetries
which appear once the KvN is extended to include the evolution of differential
forms. Because of their non-invariance, those extra observables have to be
removed. This removal makes the superposition of states in KvN, and as a
consequence also in CM, impossible
Dislocation screening in crystals with spherical topology
Whereas disclination defects are energetically prohibitive in two-dimensional
flat crystals, their existence is necessary in crystals with spherical
topology, such as viral capsids, colloidosomes or fullerenes. Such a
geometrical frustration gives rise to large elastic stresses, which render the
crystal unstable when its size is significantly larger than the typical lattice
spacing. Depending on the compliance of the crystal with respect to stretching
and bending deformations, these stresses are alleviated by either a local
increase of the intrinsic curvature in proximity of the disclinations or by the
proliferation of excess dislocations, often organized in the form of
one-dimensional chains known as "scars". The associated strain field of the
scars is such to counterbalance the one resulting from the isolated
disclinations. Here, we develop a continuum theory of dislocation screening in
two-dimensional closed crystals with genus one. Upon modeling the flux of scars
emanating from a given disclination as an independent scalar field, we
demonstrate that the elastic energy of closed two-dimensional crystals with
various degrees of asphericity can be expressed as a simple quadratic function
of the screened topological charge of the disclinations, both at zero and
finite temperature. This allows us to predict the optimal density of the excess
dislocations as well as the minimal stretching energy attained by the crystal
INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION
It is shown that the existence of a time operator in the Liouville space
representation of both classical and quantum evolution provides a mechanism for
effective entropy change of physical states. In particular, an initially
effectively pure state can evolve under the usual unitary evolution to an
effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at
[email protected] (internet)
Quantum dynamics and statistics of two coupled down-conversion processes
In the framework of Heisenberg-Langevin theory the dynamical and statistical
effects arising from the linear interaction of two nondegenerate
down-conversion processes are investigated. Using the strong-pumping
approximation the analytical solution of equations of motion is calculated. The
phenomena reminiscent of Zeno and anti-Zeno effects are examined. The
possibility of phase-controlled and mismatch-controlled switching is
illustrated.Comment: 17 pages, 7 figure
Comparison of analytical functions used to describe topside electron density profiles with satellite data
Electron density models of the ionosphere use different analytical formulations for the electron density vertical
profile in the topside. The present paper compares some single-layer topside analytical descriptions (Chapman,
Epstein, modified Epstein used in the NeQuick model) with experimental topside profiles obtained from measurements
of IK19 and ISIS2 satellites. The limits of height range and shape for each formulation are described
and analyzed and suggestions for the use of multiple layers solution to reproduce experimental results are given
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
Quantum Zeno effect in a probed downconversion process
The distorsion of a spontaneous downconvertion process caused by an auxiliary
mode coupled to the idler wave is analyzed. In general, a strong coupling with
the auxiliary mode tends to hinder the downconversion in the nonlinear medium.
On the other hand, provided that the evolution is disturbed by the presence of
a phase mismatch, the coupling may increase the speed of downconversion. These
effects are interpreted as being manifestations of quantum Zeno or anti-Zeno
effects, respectively, and they are understood by using the dressed modes
picture of the device. The possibility of using the coupling as a nontrivial
phase--matching technique is pointed out.Comment: 11 pages, 4 figure
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