30,806 research outputs found
Von Neumann spin measurements with Rashba fields
We show that dynamics in spin-orbit coupling field simulates the von Neumann
measurement of a particle spin. We demonstrate how the measurement influences
the spin and coordinate evolution of a particle by comparing two examples of
such a procedure. First example is a simultaneous measurement of spin
components, and , corresponding to non-commuting
operators, which cannot be accurately obtained together at a given time instant
due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a
spatial walk such a procedure determines measurement-time averages of and , which already can be precisely evaluated in a single
short-time measurement. The other, qualitatively different, example is the spin
of a one-dimensional particle in a magnetic field. Here the outcome depends on
the angle between the spin-orbit coupling and magnetic fields. These results
can be applied to studies of spin-orbit coupled cold atoms and electrons in
solids.Comment: 6 figure
Density Functional Theory versus the Hartree Fock Method: Comparative Assessment
We compare two different approaches to investigations of many-electron
systems. The first is the Hartree-Fock (HF) method and the second is the
Density Functional Theory (DFT). Overview of the main features and peculiar
properties of the HF method are presented. A way to realize the HF method
within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this
is impossible without including a specific correlation energy, which is defined
by the difference between the sum of the kinetic and exchange energies of a
system considered within KS and HF, respectively. It is the nonlocal exchange
potential entering the HF equations that generates this correlation energy. We
show that the total correlation energy of a finite electron system, which has
to include this correlation energy, cannot be obtained from considerations of
uniform electron systems. The single-particle excitation spectrum of
many-electron systems is related to the eigenvalues of the corresponding KS
equations. We demonstrate that this spectrum does not coincide in general with
the eigenvalues of KS or HF equations.Comment: 16 pages, Revtex, no figure
Absolute Continuity Theorem for Random Dynamical Systems on
In this article we provide a proof of the so called absolute continuity
theorem for random dynamical systems on which have an invariant
probability measure. First we present the construction of local stable
manifolds in this case. Then the absolute continuity theorem basically states
that for any two transversal manifolds to the family of local stable manifolds
the induced Lebesgue measures on these transversal manifolds are absolutely
continuous under the map that transports every point on the first manifold
along the local stable manifold to the second manifold, the so-called
Poincar\'e map or holonomy map. In contrast to known results, we have to deal
with the non-compactness of the state space and the randomness of the random
dynamical system.Comment: 46 page
Angular distributions of secondary electrons in fast particle-atom scattering
We present the angular distribution of electrons knocked out from an atom in
a fast charge particle collision at small momentum transfer. It is determined
not only by dipole but also by quadrupole transitions, the contribution of
which can be considerably enhanced as compared to the case of photoionization.
There the non-dipole parameters are suppressed as compared to the dipole ones
by the parameter \omega R/c << 1, where is the photon energy, R is the ionized
shell radius and c is the speed of light. This suppression in fast
electron-atom collisions can be considerably reduced: the corresponding
expansion parameter \omega R/ \nu << 1 is much bigger than in photoionization,
since the speed of the incoming electron is much smaller than c. In formation
of the angular distribution it is decisively important that the ionizing field
in collision process is longitudinal, while in photoionization - it is
transversal.
We illustrate the general formulas by concrete results for outer s-, p-, and
some nd-subshells of multi-electron noble gas atoms Ar, Kr and Xe, at several
transferred momentum values: q=0.0, 0.1, 1.1, 2.1. Even for very small
transferred momentum q, i.e. in the so-called optical limit, the deviations
from the photoionization case are prominent.Comment: arXiv admin note: substantial text overlap with arXiv:1012.5465 and
arXiv:1108.101
The -structures on complex line bundles and explicit Riemannian metrics with SU(4)-holonomy
We completely explore the system of ODE's which is equivalent to the
existence of a parallel -structure on the cone over a 7-dimensional
3-Sasakian manifold. The one-dimensional family of solutions of this system is
constructed. The solutions of this family correspond to metrics with holonomy
SU(4) which generalize the Calabi metrics.Comment: 11 page
Quantum Teleportation Using Quantum Non-Demolition Technique
We propose a new scheme and protocol for quantum teleportation of a
single-mode field state, based on entanglement produced by quantum
non-demolition interaction. We show that the recently attained results in QND
technique allow to perform the teleportation in quantum regime. We also show
that applying QND coupling to squeezed fields will significantly improve the
quality of teleportation for a given degree of squeezing.Comment: 4 pages RevTeX, 2 figure
Motion of a Vector Particle in a Curved Space-time. IV. Asymptotical shape of caustic
The studies of influence of spin on a photon motion in a Schwartzschild
spacetime is continued. In the previous paper [2] the first order correction to
the geodesic motion is reduced to a non-uniform linear ordinary differential
equation and the equation obtained has been solved by the standard method of
integration of the Green function. If each photon draws a world line specified
by this solution then light rays from infinitely distant source form a caustic
which does not appear without the spin-gravity interaction. The goal of the
present work is to obtain explicit form of caustic.Comment: 6 page
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