931 research outputs found
Experimental and Theoretical Studies in Planetary Aeronomy Quarterly Progress Report, 24 May - 31 Aug. 1968
Determining absorption and photoionization cross sections of planetary gases - planetary aeronomy researc
Quantum Systems and Alternative Unitary Descriptions
Motivated by the existence of bi-Hamiltonian classical systems and the
correspondence principle, in this paper we analyze the problem of finding
Hermitian scalar products which turn a given flow on a Hilbert space into a
unitary one. We show how different invariant Hermitian scalar products give
rise to different descriptions of a quantum system in the Ehrenfest and
Heisenberg picture.Comment: 18 page
Definition Research Study
Data were complied on the physical behavior and characteristics of plasma gas and/or dust in the context of how they relate to the self-contamination of manned orbiting vehicles. A definition is given of a systematic experimental program designed to yield the required empirical data on the plasma, neutral gas, and/or the particulate matter surrounding the orbiting vehicles associated with shuttle missions. Theoretical analyses were completed on the behavior of materials to be released from the orbiting or subsatellite shuttle vehicles. The results were used to define some general experimental design recommendations directly applicable to the space shuttle program requirement. An on-board laser probe technique is suggested for measuring the dynamic behavior, inventory, and physical characteristics of particulates in the vicinity of an orbiting spacecraft. Laser probing of cometary photodissociation is also assessed
Quantum Bi-Hamiltonian Systems
We define quantum bi-Hamiltonian systems, by analogy with the classical case,
as derivations in operator algebras which are inner derivations with respect to
two compatible associative structures. We find such structures by means of the
associative version of Nijenhuis tensors. Explicit examples, e.g. for the
harmonic oscillator, are given.Comment: 14 pages; the paper is posted for archival purpose
Contractions: Nijenhuis and Saletan tensors for general algebraic structures
Generalizations in many directions of the contraction procedure for Lie
algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature,
not necessarily Lie brackets, are considered on sections of finite-dimensional
vector bundles. Saletan contractions of such infinite-dimensional algebras are
obtained via a generalization of the Nijenhuis tensor approach. In particular,
this procedure is applied to Lie algebras, Lie algebroids, and Poisson
structures. There are also results on contractions of n-ary products and
coproducts.Comment: 25 pages, LateX, corrected typo
Alternative structures and bi-Hamiltonian systems on a Hilbert space
We discuss transformations generated by dynamical quantum systems which are
bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an
infinite-dimensional complex Hilbert space. We introduce the notion of
Hermitian structures in generic relative position. We provide few necessary and
sufficient conditions for two Hermitian structures to be in generic relative
position to better illustrate the relevance of this notion. The group of
bi-unitary transformations is considered in both the generic and non-generic
case. Finally, we generalize the analysis to real Hilbert spaces and extend to
infinite dimensions results already available in the framework of
finite-dimensional linear bi-Hamiltonian systems.Comment: 11 page
The nonlinear superposition principle and the Wei-Norman method
Group theoretical methods are used to study some properties of the Riccati
equation, which is the only differential equation admitting a nonlinear
superposition principle. The Wei-Norman method is applied to obtain the
associated differential equation in the group . The superposition
principle for first order differential equation systems and Lie-Scheffers
theorem are also analysed from this group theoretical perspective. Finally, the
theory is applied in the solution of second order differential equations like
time-independent Schroedinger equatio
Dynamical Aspects of Lie--Poisson Structures
Quantum Groups can be constructed by applying the quantization by deformation
procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to
develop an understanding of these structures by investigating dynamical systems
which are associated with this bracket. We look at and , as
submanifolds of a 4--dimensional phase space with constraints, and deal with
two classes of problems. In the first set of examples we consider some
hamiltonian systems associated with Lie-Poisson structures and we investigate
the equations of the motion. In the second set of examples we consider systems
which preserve the chosen bracket, but are dissipative. However in this
approach, they survive the quantization procedure.Comment: 17 pages, figures not include
Alternative Algebraic Structures from Bi-Hamiltonian Quantum Systems
We discuss the alternative algebraic structures on the manifold of quantum
states arising from alternative Hermitian structures associated with quantum
bi-Hamiltonian systems. We also consider the consequences at the level of the
Heisenberg picture in terms of deformations of the associative product on the
space of observables.Comment: Accepted for publication in Int. J. Geom. Meth. Mod. Phy
- …