62 research outputs found
Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers
Free energies and other thermodynamical quantities are investigated in
canonical and grand canonical ensembles of statistical mechanics involving
unstable states which are described by the generalized eigenstates with complex
energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is
applied to the systems containing parabolic potential barriers (PPB's). The
entropy and energy productions from PPB systems are studied. An equilibrium for
a chemical process described by reactions is also
discussed.Comment: 14 pages, AmS-LaTeX, no figur
Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier
We investigate the resonant states for the parabolic potential barrier known
also as inverted or reversed oscillator. They correspond to the poles of
meromorphic continuation of the resolvent operator to the complex energy plane.
As a byproduct we establish an interesting relation between parabolic cylinder
functions (representing energy eigenfunctions of our system) and a class of
Gel'fand distributions used in our recent paper.Comment: 14 page
Stationary Flows of the Parabolic Potential Barrier in Two Dimensions
In the two-dimensional isotropic parabolic potential barrier , though it is a model of an unstable system in quantum
mechanics, we can obtain the stationary states corresponding to the real energy
eigenvalue . Further, they are infinitely degenerate. For the first few
eigenstates, we will find the stationary flows round a right angle that are
expressed by the complex velocity potentials .Comment: 12 pages, AmS-LaTeX, 4 figure
On the upper bound of the electronic kinetic energy in terms of density functionals
We propose a simple density functional expression for the upper bound of the
kinetic energy for electronic systems. Such a functional is valid in the limit
of slowly varying density, its validity outside this regime is discussed by
making a comparison with upper bounds obtained in previous work. The advantages
of the functional proposed for applications to realistic systems is briefly
discussed.Comment: 10 pages, no figure
Vortices and chirality of magnetostatic modes in quasi-2D ferrite disk particles
In this paper we show that the vortex states can be created not only in
magnetically soft "small" (with the dipolar and exchange energy competition)
cylindrical dots, but also in magnetically saturated "big" (when the exchange
is neglected) cylindrical dots. A property associated with a vortex structure
becomes evident from an analysis of confinement phenomena of magnetic
oscillations in a ferrite disk with a dominating role of magnetic-dipolar
(non-exchange-interaction) spectra. In this case the scalar
(magnetostatic-potential) wave functions may have a phase singularity in a
center of a dot. A non-zero azimuth component of the flow velocity demonstrates
the vortex structure. The vortices are guaranteed by the chiral edge states of
magnetic-dipolar modes in a quasi-2D ferrite disk
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