220 research outputs found
Exact solutions of the radial Schrodinger equation for some physical potentials
By using an ansatz for the eigenfunction, we have obtained the exact
analytical solutions of the radial Schrodinger equation for the pseudoharmonic
and Kratzer potentials in two dimensions. The energy levels of all the bound
states are easily calculated from this eigenfunction ansatz. The normalized
wavefunctions are also obtained.Comment: 13 page
Most probable transition path in an overdamped system for a finite transition time
The most probable transition path in a one-dimensional overdamped system is
rigorously proved to possess less than two turning points. The proof is valid
for any potentials, transition times, initial and final transition points
Present Status of Neutrino Mixing
A short review of the status of neutrino mixing and neutrino oscillations is
given. The basics of neutrino mixing and oscillations is discussed. The latest
evidences of neutrino oscillations obtained in the Super-Kamiokande and the SNO
solar neutrino experiments and in the Super-Kamiokande atmospheric neutrino
experiment are considered. The results of solar and atmospheric neutrino
experiments are discussed from the point of view of the three-neutrino mixing.Comment: 20 pages, Proceedings of the Advanced Study Institute "Symmetries and
Spin", Praha-Spin-2001, Czech Republic, July 15-28, 200
Rotational and vibrational spectra of quantum rings
One can confine the two-dimensional electron gas in semiconductor
heterostructures electrostatically or by etching techniques such that a small
electron island is formed. These man-made ``artificial atoms'' provide the
experimental realization of a text-book example of many-particle physics: a
finite number of quantum particles in a trap. Much effort was spent on making
such "quantum dots" smaller and going from the mesoscopic to the quantum
regime. Far-reaching analogies to the physics of atoms, nuclei or metal
clusters were obvious from the very beginning: The concepts of shell structure
and Hund's rules were found to apply -- just as in real atoms! In this Letter,
we report the discovery that electrons confined in ring-shaped quantum dots
form rather rigid molecules with antiferromagnetic order in the ground state.
This can be seen best from an analysis of the rotational and vibrational
excitations
Differential probability for surface and volume electronic excitations in Fe, Pd and Pt
The normalized differential mean free path for volume scattering and the
differential surface excitation probability for medium energy electrons
travelling in Fe, Pd and Pt are extracted from Reflection Electron Energy Loss
Spectra (REELS). This was achieved by means of a recently introduced procedure
in which two REELS spectra taken under different experimental conditions are
simultaneously deconvoluted. In this way, it is possible to obtain the unique
reconstruction for the surface and volume single scattering loss distribution.
The employed method is compared with a procedure that is frequently used for
this purpose [Tougaard and Chorkendorff, Phys. Rev. B 35(1987)6570]. It is
shown, both theoretically and through analysis of model spectra as well as
experimental data that this method does not result in a {\em single} scattering
loss distribution. Rather, it gives a mixture of surface, bulk and mixed
scattering of any order
Splitting of Landau levels of a 2D electron due to electron-phonon interactions
We show that in a very strong magnetic field electron-phonon interaction
gives rise to a splitting of Landau levels of a 2D electron into a series of
infinitely degenerate sublevels. We provide both qualitative and quantitative
description of this phenomenon. The cases of interaction with acoustic and
polar optical phonons are considered. The energy distance between nearest
sublevels in both cases tends to zero as at large .Comment: 4 pages, LaTe
Delay Equations and Radiation Damping
Starting from delay equations that model field retardation effects, we study
the origin of runaway modes that appear in the solutions of the classical
equations of motion involving the radiation reaction force. When retardation
effects are small, we argue that the physically significant solutions belong to
the so-called slow manifold of the system and we identify this invariant
manifold with the attractor in the state space of the delay equation. We
demonstrate via an example that when retardation effects are no longer small,
the motion could exhibit bifurcation phenomena that are not contained in the
local equations of motion.Comment: 15 pages, 1 figure, a paragraph added on page 5; 3 references adde
Bell's inequalities for states with positive partial transpose
We study violations of n particle Bell inequalities (as developed by Mermin
and Klyshko) under the assumption that suitable partial transposes of the
density operator are positive. If all transposes with respect to a partition of
the system into p subsystems are positive, the best upper bound on the
violation is 2^((n-p)/2). In particular, if the partial transposes with respect
to all subsystems are positive, the inequalities are satisfied. This is
supporting evidence for a recent conjecture by Peres that positivity of partial
transposes could be equivalent to existence of local classical models.Comment: 4 pages, REVTe
Scaling analysis of electron transport through metal-semiconducting carbon nanotube interfaces: Evolution from the molecular limit to the bulk limit
We present a scaling analysis of electronic and transport properties of
metal-semiconducting carbon nanotube interfaces as a function of the nanotube
length within the coherent transport regime, which takes fully into account
atomic-scale electronic structure and three-dimensional electrostatics of the
metal-nanotube interface using a real-space Green's function based
self-consistent tight-binding theory. As the first example, we examine devices
formed by attaching finite-size single-wall carbon nanotubes (SWNT) to both
high- and low- work function metallic electrodes through the dangling bonds at
the end. We analyze the nature of Schottky barrier formation at the
metal-nanotube interface by examining the electrostatics, the band lineup and
the conductance of the metal-SWNT molecule-metal junction as a function of the
SWNT molecule length and metal-SWNT coupling strength. We show that the
confined cylindrical geometry and the atomistic nature of electronic processes
across the metal-SWNT interface leads to a different physical picture of band
alignment from that of the planar metal-semiconductor interface. We analyze the
temperature and length dependence of the conductance of the SWNT junctions,
which shows a transition from tunneling- to thermal activation-dominated
transport with increasing nanotube length. The temperature dependence of the
conductance is much weaker than that of the planar metal-semiconductor
interface due to the finite number of conduction channels within the SWNT
junctions. We find that the current-voltage characteristics of the metal-SWNT
molecule-metal junctions are sensitive to models of the potential response to
the applied source/drain bias voltages.Comment: Minor revision to appear in Phys. Rev. B. Color figures available in
the online PRB version or upon request to: [email protected]
Some peculiarities of motion of neutral and charged test particles in the field of a spherically symmetric charged object in General Relativity
We propose the method of investigation of radial motions for charged and
neutral test particles in the Reissner-Nordstr\"{o}m field by means of mass
potential. In this context we analyze special features of interaction of
charges and their motions in General Relativity and construct the radial motion
classification. For test particles and a central source with charges and
, respectively, the conditions of attraction (when ) and repulsion
(when ) are obtained. The conditions of motionless test particle states
with respect to the central source are investigated and, in addition, stability
conditions for such static equilibrium states are found. It is shown that
stable states are possible only for the bound states of weakly charged
particles in the field of a naked singularity. Frequencies of small
oscillations of test particles near their equilibrium positions are also found.Comment: 15 pages, 9 figure
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