1,402 research outputs found
On the temperature dependence of ballistic Coulomb drag in nanowires
We have investigated within the theory of Fermi liquid dependence of Coulomb
drag current in a passive quantum wire on the applied voltage across an
active wire and on the temperature for any values of . We assume
that the bottoms of the 1D minibands in both wires almost coincide with the
Fermi level. We come to conclusions that 1) within a certain temperature
interval the drag current can be a descending function of the temperature ;
2) the experimentally observed temperature dependence of the drag
current can be interpreted within the framework of Fermi liquid theory; 3) at
relatively high applied voltages the drag current as a function of the applied
voltage saturates; 4) the screening of the electron potential by metallic gate
electrodes can be of importance.Comment: 7 pages, 1 figur
Whitham systems and deformations
We consider the deformations of Whitham systems including the "dispersion
terms" and having the form of Dubrovin-Zhang deformations of Frobenius
manifolds. The procedure is connected with B.A. Dubrovin problem of
deformations of Frobenius manifolds corresponding to the Whitham systems of
integrable hierarchies. Under some non-degeneracy requirements we suggest a
general scheme of the deformation of the hyperbolic Whitham systems using the
initial non-linear system. The general form of the deformed Whitham system
coincides with the form of the "low-dispersion" asymptotic expansions used by
B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius
manifolds.Comment: 27 pages, Late
Analytic model for a frictional shallow-water undular bore
We use the integrable Kaup-Boussinesq shallow water system, modified by a
small viscous term, to model the formation of an undular bore with a steady
profile. The description is made in terms of the corresponding integrable
Whitham system, also appropriately modified by friction. This is derived in
Riemann variables using a modified finite-gap integration technique for the
AKNS scheme. The Whitham system is then reduced to a simple first-order
differential equation which is integrated numerically to obtain an asymptotic
profile of the undular bore, with the local oscillatory structure described by
the periodic solution of the unperturbed Kaup-Boussinesq system. This solution
of the Whitham equations is shown to be consistent with certain jump conditions
following directly from conservation laws for the original system. A comparison
is made with the recently studied dissipationless case for the same system,
where the undular bore is unsteady.Comment: 24 page
Bilinear identities on Schur symmetric functions
A series of bilinear identities on the Schur symmetric functions is obtained
with the use of Pluecker relations.Comment: Accepted to Journal of Nonlinear Mathematical Physics. A reference to
a connected result is adde
Giant Oscillations of Acoustoelectric Current in a Quantum Channel
A theory of d.c. electric current induced in a quantum channel by a
propagating surface acoustic wave (acoustoelectric current) is worked out. The
first observation of the acoustoelectric current in such a situation was
reported by J. M. Shilton et al., Journ. Phys. C (to be published). The authors
observed a very specific behavior of the acoustoelectric current in a
quasi-one-dimensional channel defined in a GaAs-AlGaAs heterostructure by a
split-gate depletion -- giant oscillations as a function of the gate voltage.
Such a behavior was qualitatively explained by an interplay between the
energy-momentum conservation law for the electrons in the upper transverse mode
with a finite temperature splitting of the Fermi level. In the present paper, a
more detailed theory is developed, and important limiting cases are considered.Comment: 7 pages, 2 Postscript figures, RevTeX 3.
Weyl approach to representation theory of reflection equation algebra
The present paper deals with the representation theory of the reflection
equation algebra, connected with a Hecke type R-matrix. Up to some reasonable
additional conditions the R-matrix is arbitrary (not necessary originated from
quantum groups). We suggest a universal method of constructing finite
dimensional irreducible non-commutative representations in the framework of the
Weyl approach well known in the representation theory of classical Lie groups
and algebras. With this method a series of irreducible modules is constructed
which are parametrized by Young diagrams. The spectrum of central elements
s(k)=Tr_q(L^k) is calculated in the single-row and single-column
representations. A rule for the decomposition of the tensor product of modules
into the direct sum of irreducible components is also suggested.Comment: LaTeX2e file, 27 pages, no figure
Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
Dynamics of interacting cold atomic gases have recently become a focus of
both experimental and theoretical studies. Often cold atom systems show
hydrodynamic behavior and support the propagation of nonlinear dispersive
waves. Although this propagation depends on many details of the system, a great
insight can be obtained in the rather universal limit of weak nonlinearity,
dispersion and dissipation (WNDD). In this limit, using a reductive
perturbation method we map some of the hydrodynamic models relevant to cold
atoms to well known chiral one-dimensional equations such as KdV, Burgers,
KdV-Burgers, and Benjamin-Ono equations. These equations have been thoroughly
studied in literature. The mapping gives us a simple way to make estimates for
original hydrodynamic equations and to study the interplay between
nonlinearity, dissipation and dispersion which are the hallmarks of nonlinear
hydrodynamics.Comment: 18 pages, 3 figures, 1 tabl
Field-induced transition from parallel to perpendicular parametric pumping for a microstrip transducer
Microstrip transducers used for the excitation of spin waves in magnetic
films possess two characteristic properties: high spatial localization of the
microwave magnetic field and the presence of field components parallel and
perpendicular to the bias field.
Here, the effects of these features on the process of parametric pumping are
presented. By microwave measurements of the spin-wave instability threshold a
transition from parallel pumping to perpendicular pumping at the critical field
with the minimal threshold is observed. This transition is
accompanied by a sharp threshold increase above the critical field due to the
spatial confinement of the pump region.Comment: 4 pages, 2 figure
Coulomb drag between ballistic one-dimensional electron systems
The presence of pronounced electronic correlations in one-dimensional systems
strongly enhances Coulomb coupling and is expected to result in distinctive
features in the Coulomb drag between them that are absent in the drag between
two-dimensional systems. We review recent Fermi and Luttinger liquid theories
of Coulomb drag between ballistic one-dimensional electron systems, and give a
brief summary of the experimental work reported so far on one-dimensional drag.
Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a
maximum of the drag resistance R_D when the one-dimensional subbands of the two
quantum wires are aligned and the Fermi wave vector k_F is small, and also an
exponential decay of R_D with increasing inter-wire separation, both features
confirmed by experimental observations. A crucial difference between the two
theoretical models emerges in the temperature dependence of the drag effect.
Whereas the FL theory predicts a linear temperature dependence, the LL theory
promises a rich and varied dependence on temperature depending on the relative
magnitudes of the energy and length scales of the systems. At higher
temperatures, the drag should show a power-law dependence on temperature, R_D
\~ T^x, experimentally confirmed in a narrow temperature range, where x is
determined by the Luttinger liquid parameters. The spin degree of freedom plays
an important role in the LL theory in predicting the features of the drag
effect and is crucial for the interpretation of experimental results.Comment: 25 pages, 14 figures, to appear in Semiconductor Science and
Technolog
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