82 research outputs found
On the quantisation of the angular momentum
When a hydrogen-like atom is treated as a two dimensional system whose
configuration space is multiply connected, then in order to obtain the same
energy spectrum as in the Bohr model the angular momentum must be
half-integral.Comment: Latex, 5 page
Rectified voltage induced by a microwave field in a confined two-dimensional electron gas with a mesoscopic static vortex
We investigate the effect of a microwave field on a confined two dimensional
electron gas which contains an insulating region comparable to the Fermi
wavelength. The insulating region causes the electron wave function to vanish
in that region. We describe the insulating region as a static vortex. The
vortex carries a flux which is determined by vanishing of the charge density of
the electronic fluid due to the insulating region. The sign of the vorticity
for a hole is opposite to the vorticity for adding additional electrons. The
vorticity gives rise to non-commuting kinetic momenta. The two dimensional
electron gas is described as fluid with a density which obeys the Fermi-Dirac
statistics. The presence of the confinement potential gives rise to vanishing
kinetic momenta in the vicinity of the classical turning points. As a result,
the Cartesian coordinate do not commute and gives rise to a Hall current which
in the presence of a modified Fermi-Surface caused by the microwave field
results in a rectified voltage. Using a Bosonized formulation of the two
dimensional gas in the presence of insulating regions allows us to compute the
rectified current. The proposed theory may explain the experimental results
recently reported by J. Zhang et al.Comment: 14 pages, 2 figure
Quantum Zeno Effect and Light-Dark Periods for a Single Atom
The quantum Zeno effect (QZE) predicts a slow-down of the time development of
a system under rapidly repeated ideal measurements, and experimentally this was
tested for an ensemble of atoms using short laser pulses for non-selective
state measurements. Here we consider such pulses for selective measurements on
a single system. Each probe pulse will cause a burst of fluorescence or no
fluorescence. If the probe pulses were strictly ideal measurements, the QZE
would predict periods of fluorescence bursts alternating with periods of no
fluorescence (light and dark periods) which would become longer and longer with
increasing frequency of the measurements. The non-ideal character of the
measurements is taken into account by incorporating the laser pulses in the
interaction, and this is used to determine the corrections to the ideal case.
In the limit, when the time between the laser pulses goes to zero, no freezing
occurs but instead we show convergence to the familiar macroscopic light and
dark periods of the continuously driven Dehmelt system. An experiment of this
type should be feasible for a single atom or ion in a trapComment: 16 pages, LaTeX, a4.sty; to appear in J. Phys.
Progress in Classical and Quantum Variational Principles
We review the development and practical uses of a generalized Maupertuis
least action principle in classical mechanics, in which the action is varied
under the constraint of fixed mean energy for the trial trajectory. The
original Maupertuis (Euler-Lagrange) principle constrains the energy at every
point along the trajectory. The generalized Maupertuis principle is equivalent
to Hamilton's principle. Reciprocal principles are also derived for both the
generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis
Principle is the classical limit of Schr\"{o}dinger's variational principle of
wave mechanics, and is also very useful to solve practical problems in both
classical and semiclassical mechanics, in complete analogy with the quantum
Rayleigh-Ritz method. Classical, semiclassical and quantum variational
calculations are carried out for a number of systems, and the results are
compared. Pedagogical as well as research problems are used as examples, which
include nonconservative as well as relativistic systems
From least action in electrodynamics to magnetomechanical energy -- a review
The equations of motion for electromechanical systems are traced back to the
fundamental Lagrangian of particles and electromagnetic fields, via the Darwin
Lagrangian. When dissipative forces can be neglected the systems are
conservative and one can study them in a Hamiltonian formalism. The central
concepts of generalized capacitance and inductance coefficients are introduced
and explained. The problem of gauge independence of self-inductance is
considered. Our main interest is in magnetomechanics, i.e. the study of systems
where there is exchange between mechanical and magnetic energy. This throws
light on the concept of magnetic energy, which according to the literature has
confusing and peculiar properties. We apply the theory to a few simple
examples: the extension of a circular current loop, the force between parallel
wires, interacting circular current loops, and the rail gun. These show that
the Hamiltonian, phase space, form of magnetic energy has the usual property
that an equilibrium configuration corresponds to an energy minimum.Comment: 29 pages, 9 figures, 65 reference
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