27 research outputs found
Derivation of the transverse force on a moving vortex in a superfluid
We describe an exact derivation of the total nondissipative transverse force
acting on a quantized vortex moving in a uniform background. The derivation is
valid for neutral boson or fermion superfluids, provided the order parameter is
a complex scalar quantity. The force is determined by the one-particle density
matrix far away from the vortex core, and is found to be the Magnus force
proportional to the superfluid density.Comment: Latex, 6 page
Paraxial propagation of a quantum charge in a random magnetic field
The paraxial (parabolic) theory of a near forward scattering of a quantum
charged particle by a static magnetic field is presented. From the paraxial
solution to the Aharonov-Bohm scattering problem the transverse transfered
momentum (the Lorentz force) is found. Multiple magnetic scattering is
considered for two models: (i) Gaussian -correlated random magnetic
field; (ii) a random array of the Aharonov-Bohm magnetic flux line. The
paraxial gauge-invariant two-particle Green function averaged with respect to
the random field is found by an exact evaluation of the Feynman integral. It is
shown that in spite of the anomalous character of the forward scattering, the
transport properties can be described by the Boltzmann equation. The Landau
quantization in the field of the Aharonov-Bohm lines is discussed.Comment: Figures and references added. Many typos corrected. RevTex, 25 pages,
9 figure
Iordanskii Force and the Gravitational Aharonov-Bohm effect for a Moving Vortex
I discuss the scattering of phonons by a vortex moving with respect to a
superfluid condensate. This allows us to test the compatibility of the
scattering-theory derivation of the Iordanskii force with the galilean
invariance of the underlying fluid dynamics. In order to obtain the correct
result we must retain terms in the sound-wave equation, and this
reinforces the interpretation, due to Volovik, of the Iordanskii force as an
analogue of the gravitational Bohm-Aharonov effect.Comment: 20 pages, LaTe
Friction force on a vortex due to the scattering of superfluid excitations in helium II
The longitudinal friction acting on a vortex line in superfluid He is
investigated within a simple model based on the analogy between such vortex
dynamics and that of the quantal Brownian motion of a charged point particle in
a uniform magnetic field. The scattering of superfluid quasiparticle
excitations by the vortex stems from a translationally invariant interaction
potential which, expanded to first order in the vortex velocity operator, gives
rise to vortex transitions between nearest Landau levels. The corresponding
friction coefficient is shown to be, in the limit of elastic scattering
(vanishing cyclotron frequency), equivalent to that arising from the Iordanskii
formula. Proposing a simple functional form for the scattering amplitude, with
only one adjustable parameter whose value is set in order to get agreement to
the Iordanskii result for phonons, an excellent agreement is also found with
the values derived from experimental data up to temperatures about 1.5 K.
Finite values of the cyclotron frequency arising from recent theories are shown
to yield similar results. The incidence of vortex-induced quasiparticle
transitions on the friction process is estimated to be, in the roton dominated
regime, about 50 % of the value of the friction coefficient, 8 % of which
corresponds to roton-phonon transitions and 42 % to roton
ones.Comment: 15 pages, 4 figures; typos corrected, to be published in PR
A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field
A single model is presented which represents both of the two apparently
unrelated localisation problems of the title. The phase diagram of this model
is examined using scaling ideas and numerical simulations. It is argued that
the localisation length in a spin-degenerate Landau level diverges at two
distinct energies, with the same critical behaviour as in a spin-split Landau
level, and that all states of a charged particle moving in two dimensions, in a
random magnetic field with zero average, are localised.Comment: 7 pages (RevTeX 3.0) plus 4 postscript figure
Experimental study of weak antilocalization effect in a high mobility InGaAs/InP quantum well
The magnetoresistance associated with quantum interference corrections in a
high mobility, gated InGaAs/InP quantum well structure is studied as a function
of temperature, gate voltage, and angle of the tilted magnetic field.
Particular attention is paid to the experimental extraction of phase-breaking
and spin-orbit scattering times when weak anti- localization effects are
prominent. Compared with metals and low mobility semiconductors the
characteristic magnetic field in high mobility
samples is very small and the experimental dependencies of the interference
effects extend to fields several hundreds of times larger. Fitting experimental
results under these conditions therefore requires theories valid for arbitrary
magnetic field. It was found, however, that such a theory was unable to fit the
experimental data without introducing an extra, empirical, scale factor of
about 2. Measurements in tilted magnetic fields and as a function of
temperature established that both the weak localization and the weak
anti-localization effects have the same, orbital origin. Fits to the data
confirmed that the width of the low field feature, whether a weak localization
or a weak anti-localization peak, is determined by the phase-breaking time and
also established that the universal (negative) magnetoresistance observed in
the high field limit is associated with a temperature independent spin-orbit
scattering time.Comment: 13 pages including 10 figure
Activation Energy in a Quantum Hall Ferromagnet and Non-Hartree-Fock Skyrmions
The energy of Skyrmions is calculated with the help of a technique based on
the excitonic representation: the basic set of one-exciton states is used for
the perturbation-theory formalism instead of the basic set of one-particle
states. We use the approach, at which a skyrmion-type excitation (at zero Lande
factor) is considered as a smooth non-uniform rotation in the 3D spin space.
The result within the framework of an excitonically diagonalized part of the
Coulomb Hamiltonian can be obtained by any ratio [where is the typical Coulomb
energy ( being the magnetic length); is the cyclotron
frequency], and the Landau-level mixing is thereby taken into account. In
parallel with this, the result is also found exactly, to second order in terms
of the (if supposing to be small) with use of the
total Hamiltonian. When extrapolated to the region , our
calculations show that the skyrmion gap becomes substantially reduced in
comparison with the Hartree-Fock calculations. This fact brings the theory
essentially closer to the available experimental data.Comment: 14 pages, 1 figure. to appear in Phys. Rev. B, Vol. 65 (Numbers ~
19-22), 200
Travelling waves for the Gross-Pitaevskii equation II
The purpose of this paper is to provide a rigorous mathematical proof of the
existence of travelling wave solutions to the Gross-Pitaevskii equation in
dimensions two and three. Our arguments, based on minimization under
constraints, yield a full branch of solutions, and extend earlier results,
where only a part of the branch was built. In dimension three, we also show
that there are no travelling wave solutions of small energy.Comment: Final version accepted for publication in Communications in
Mathematical Physics with a few minor corrections and added remark
Magnetoresistance and dephasing in a two-dimensional electron gas at intermediate conductances
We study, both theoretically and experimentally, the negative
magnetoresistance (MR) of a two-dimensional (2D) electron gas in a weak
transverse magnetic field . The analysis is carried out in a wide range of
zero- conductances (measured in units of ), including the range
of intermediate conductances, . Interpretation of the experimental
results obtained for a 2D electron gas in GaAs/InGaAs/GaAs single
quantum well structures is based on the theory which takes into account terms
of higher orders in , stemming from both the interference contribution and
the mutual effect of weak localization (WL) and Coulomb interaction. We
demonstrate that at intermediate conductances the negative MR is described by
the standard WL "digamma-functions" expression, but with a reduced prefactor
. We also show that at not very high the second-loop corrections
dominate over the contribution of the interaction in the Cooper channel, and
therefore appear to be the main source of the lowering of the prefactor,
. We further analyze the regime of a "weak insulator",
when the zero- conductance is low due to the localization at low
, whereas the Drude conductance is high, In this regime, while the
MR still can be fitted by the digamma-functions formula, the experimentally
obtained value of the dephasing rate has nothing to do with the true one. The
corresponding fitting parameter in the low- limit is determined by the
localization length and may therefore saturate at , even though the
true dephasing rate vanishes.Comment: 36 pages, 16 figure
Vortex Dynamics and the Hall-Anomaly: a Microscopic Analysis
We present a microscopic derivation of the equation of motion for a vortex in
a superconductor. A coherent view on vortex dynamics is obtained, in which {\it
both} hydrodynamics {\it and} the vortex core contribute to the forces acting
on a vortex. The competition between these two provides an interpretation of
the observed sign change in the Hall angle in superconductors with mean free
path of the order of the coherence length in terms of broken
particle-hole symmetry, which is related to details of the microscopic
mechanism of superconductivity.Comment: 12 pages, late