27,850 research outputs found
Statistical Properties of Many Particle Eigenfunctions
Wavefunction correlations and density matrices for few or many particles are
derived from the properties of semiclassical energy Green functions. Universal
features of fixed energy (microcanonical) random wavefunction correlation
functions appear which reflect the emergence of the canonical ensemble as the
number of particles approaches infinity. This arises through a little known
asymptotic limit of Bessel functions. Constraints due to symmetries,
boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure
Nonperiodic Orbit Sums in Weyl's Expansion for Billiards
Weyl's expansion for the asymptotic mode density of billiards consists of the
area, length, curvature and corner terms. The area term has been associated
with the so-called zero-length orbits. Here closed nonperiodic paths
corresponding to the length and corner terms are constructed.Comment: 8 pages, 2 figure
Aerothermal modeling program, phase 1
Aerothermal submodels used in analytical combustor models are analyzed. The models described include turbulence and scalar transport, gaseous full combustion, spray evaporation/combustion, soot formation and oxidation, and radiation. The computational scheme is discussed in relation to boundary conditions and convergence criteria. Also presented is the data base for benchmark quality test cases and an analysis of simple flows
Geometric phases and anholonomy for a class of chaotic classical systems
Berry's phase may be viewed as arising from the parallel transport of a
quantal state around a loop in parameter space. In this Letter, the classical
limit of this transport is obtained for a particular class of chaotic systems.
It is shown that this ``classical parallel transport'' is anholonomic ---
transport around a closed curve in parameter space does not bring a point in
phase space back to itself --- and is intimately related to the Robbins-Berry
classical two-form.Comment: Revtex, 11 pages, no figures
Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions
Eigenvalues and eigenfunctions of Mathieu's equation are found in the short
wavelength limit using a uniform approximation (method of comparison with a
`known' equation having the same classical turning point structure) applied in
Fourier space. The uniform approximation used here relies upon the fact that by
passing into Fourier space the Mathieu equation can be mapped onto the simpler
problem of a double well potential. The resulting eigenfunctions (Bloch waves),
which are uniformly valid for all angles, are then used to describe the
semiclassical scattering of waves by potentials varying sinusoidally in one
direction. In such situations, for instance in the diffraction of atoms by
gratings made of light, it is common to make the Raman-Nath approximation which
ignores the motion of the atoms inside the grating. When using the
eigenfunctions no such approximation is made so that the dynamical diffraction
regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important
references to existing work on uniform approximations, such as Olver's method
applied to the modified Mathieu equation. It is emphasised that the paper
presented here pertains to Fourier space uniform approximation
A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling
We present a new dimensional scaling transformation of the Schrodinger
equation for the two electron bond. This yields, for the first time, a good
description of the two electron bond via D-scaling. There also emerges, in the
large-D limit, an intuitively appealing semiclassical picture, akin to a
molecular model proposed by Niels Bohr in 1913. In this limit, the electrons
are confined to specific orbits in the scaled space, yet the uncertainty
principle is maintained because the scaling leaves invariant the
position-momentum commutator. A first-order perturbation correction,
proportional to 1/D, substantially improves the agreement with the exact ground
state potential energy curve. The present treatment is very simple
mathematically, yet provides a strikingly accurate description of the potential
energy curves for the lowest singlet, triplet and excited states of H_2. We
find the modified D-scaling method also gives good results for other molecules.
It can be combined advantageously with Hartree-Fock and other conventional
methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter
Civil tiltrotor missions and applications. Phase 2: The commercial passenger market
The commercial passenger market for the civil tiltrotor was examined in phase 2. A market responsive commercial tiltrotor was found to be technically feasible, and a significant worldwide market potential was found to exist for such an aircraft, especially for relieving congestion in urban area-to-urban area service and for providing cost effective hub airport feeder service. Potential technical obstacles of community noise, vertiport area navigation, surveillance, and control, and the pilot/aircraft interface were determined to be surmountable. Nontechnical obstacles relating to national commitment and leadership and development of ground and air infrastructure were determined to be more difficult to resolve; an innovative public/private partnership is suggested to allow coordinated development of an initial commercial tiltrotor network to relieve congestion in the crowded US Northeast corridor by the year 2000
Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)
A quantal guiding center theory allowing to systematically study the
separation of the different time scale behaviours of a quantum charged spinning
particle moving in an external inhomogeneous magnetic filed is presented. A
suitable set of operators adapting to the canonical structure of the problem
and generalizing the kinematical momenta and guiding center operators of a
particle coupled to a homogenous magnetic filed is constructed. The Pauli
Hamiltonian rewrites in this way as a power series in the magnetic length making the problem amenable to a perturbative analysis. The
first two terms of the series are explicitly constructed. The effective
adiabatic dynamics turns to be in coupling with a gauge filed and a scalar
potential. The mechanism producing such magnetic-induced geometric-magnetism is
investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include
Geometric phases and hidden local gauge symmetry
The analysis of geometric phases associated with level crossing is reduced to
the familiar diagonalization of the Hamiltonian in the second quantized
formulation. A hidden local gauge symmetry, which is associated with the
arbitrariness of the phase choice of a complete orthonormal basis set, becomes
explicit in this formulation (in particular, in the adiabatic approximation)
and specifies physical observables. The choice of a basis set which specifies
the coordinate in the functional space is arbitrary in the second quantization,
and a sub-class of coordinate transformations, which keeps the form of the
action invariant, is recognized as the gauge symmetry. We discuss the
implications of this hidden local gauge symmetry in detail by analyzing
geometric phases for cyclic and noncyclic evolutions. It is shown that the
hidden local symmetry provides a basic concept alternative to the notion of
holonomy to analyze geometric phases and that the analysis based on the hidden
local gauge symmetry leads to results consistent with the general prescription
of Pancharatnam. We however note an important difference between the geometric
phases for cyclic and noncyclic evolutions. We also explain a basic difference
between our hidden local gauge symmetry and a gauge symmetry (or equivalence
class) used by Aharonov and Anandan in their definition of generalized
geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published
in Phys. Rev.
Topological properties of Berry's phase
By using a second quantized formulation of level crossing, which does not
assume adiabatic approximation, a convenient formula for geometric terms
including off-diagonal terms is derived. The analysis of geometric phases is
reduced to a simple diagonalization of the Hamiltonian in the present
formulation. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial for any
finite time interval . The topological interpretation of Berry's phase such
as the topological proof of phase-change rule thus fails in the practical
Born-Oppenheimer approximation, where a large but finite ratio of two time
scales is involved.Comment: 9 pages. A new reference was added, and the abstract and the
presentation in the body of the paper have been expanded and made more
precis
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