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 $V_0$ is studied as a function of the concentration of the gas $n$ and magnetic field $B$ in the presence of the Feshbach resonance. We find the zero temperature phase diagrams in the plane ($B,n$) at a given $V_0$ and in the plane $(V_0, n)$ at a given $B$. 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 10$^{17-18}$cm$^{-3}$ 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.