281 research outputs found
Existence of Optimal Control for a Nonlinear-Viscous Fluid Model
We consider the optimal control problem for a mathematical model describing steady flows of a nonlinear-viscous incompressible fluid in a bounded three-dimensional (or a two-dimensional) domain with impermeable solid walls. The control parameter is the surface force at a given part of the flow domain boundary. For a given bounded set of admissible controls, we construct generalized (weak) solutions that minimize a given cost functional
Slow relaxation of conductance of amorphous hopping insulators
We discuss memory effects in the conductance of hopping insulators due to
slow rearrangements of structural defects leading to formation of polarons
close to the electron hopping states. An abrupt change in the gate voltage and
corresponding shift of the chemical potential change populations of the hopping
sites, which then slowly relax due to rearrangements of structural defects. As
a result, the density of hopping states becomes time dependent on a scale
relevant to rearrangement of the structural defects leading to the excess time
dependent conductivity.Comment: 6 pages, 1 figur
Superfluid-insulator transition and BCS-BEC crossover in dirty ultracold Fermi gas
Superfluid-insulator transition in an ultracold Fermi gas in the external
disorder potential of the amplitude is studied as a function of the
concentration of the gas and magnetic field in the presence of the
Feshbach resonance. We find the zero temperature phase diagrams in the plane
() at a given and in the plane at a given . Our
results for BEC side of the diagram are also valid for the superfluid-insulator
transition in a Bose gas.Comment: Reference added, typos correcte
Density of States and Conductivity of Granular Metal or Array of Quantum Dots
The conductivity of a granular metal or an array of quantum dots usually has
the temperature dependence associated with variable range hopping within the
soft Coulomb gap of density of states. This is difficult to explain because
neutral dots have a hard charging gap at the Fermi level. We show that
uncontrolled or intentional doping of the insulator around dots by donors leads
to random charging of dots and finite bare density of states at the Fermi
level. Then Coulomb interactions between electrons of distant dots results in
the a soft Coulomb gap. We show that in a sparse array of dots the bare density
of states oscillates as a function of concentration of donors and causes
periodic changes in the temperature dependence of conductivity. In a dense
array of dots the bare density of states is totally smeared if there are
several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are
dropped. Some small changes are given to improve the organizatio
Statistics of the Charging Spectrum of a Two-Dimensional Coulomb Glass Island
The fluctuations of capacitance of a two-dimensional island are studied in
the regime of low electron concentration and strong disorder, when electrons
can be considered classical particles. The universal capacitance distribution
is found, with the dispersion being of the order of the average. This
distribution is shown to be closely related to the shape of the Coulomb gap in
the one-electron density of states of the island. Behavior of the the
capacitance fluctuations near the metal - insulator transition is discussed.Comment: 4 pages, LaTex, 4 Postscript figures are included Discussion of the
situation with screening by metallic gate is adde
Interacting quantum rotors in oxygen-doped germanium
We investigate the interaction effect between oxygen impurities in
crystalline germanium on the basis of a quantum rotor model. The dipolar
interaction of nearby oxygen impurities engenders non-trivial low-lying
excitations, giving rise to anomalous behaviors for oxygen-doped germanium
(Ge:O) below a few degrees Kelvin. In particular, it is theoretically predicted
that Ge:O samples with oxygen-concentration of 10cm show (i)
power-law specific heats below 0.1 K, and (ii) a peculiar hump in dielectric
susceptibilities around 1 K. We present an interpretation for the power-law
specific heats, which is based on the picture of local double-well potentials
randomly distributed in Ge:O samples.Comment: 13 pages, 11 figures; to be published in Phys. Rev.
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