We consider a system of charged one-dimensional spin-$frac{1}{2}$ fermions at low temperature. We study how the energy of a highly-excited quasiparticle (or hole) relaxes toward the chemical potential in the regime of weak interactions. The dominant
relaxation processes involve collisions with two other fermions. We find a dramatic enhancement of the relaxation rate at low energies, with the rate scaling as the inverse sixth power of the excitation energy. This behavior is caused by the long-range nature of the Coulomb interaction.
We study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In t
he absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.
We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxati
on rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions.
We have developed a Monte Carlo simulation for ion transport in hot background gases, which is an alternative way of solving the corresponding Boltzmann equation that determines the distribution function of ions. We consider the limit of low ion dens
ities when the distribution function of the background gas remains unchanged due to collision with ions. A special attention has been paid to properly treat the thermal motion of the host gas particles and their influence on ions, which is very important at low electric fields, when the mean ion energy is comparable to the thermal energy of the host gas. We found the conditional probability distribution of gas velocities that correspond to an ion of specific velocity which collides with a gas particle. Also, we have derived exact analytical formulas for piecewise calculation of the collision frequency integrals. We address the cases when the background gas is monocomponent and when it is a mixture of different gases. The developed techniques described here are required for Monte Carlo simulations of ion transport and for hybrid models of non-equilibrium plasmas. The range of energies where it is necessary to apply the technique has been defined. The results we obtained are in excellent agreement with the existing ones obtained by complementary methods. Having verified our algorithm, we were able to produce calculations for Ar$^+$ ions in Ar and propose them as a new benchmark for thermal effects. The developed method is widely applicable for solving the Boltzmann equation that appears in many different contexts in physics.
We develop a theory of thermal transport of weakly interacting electrons in quantum wires. Unlike higher-dimensional systems, a one-dimensional electron gas requires three-particle collisions for energy relaxation. The fastest relaxation is provided
by the intrabranch scattering of comoving electrons which establishes a partially equilibrated form of the distribution function. The thermal conductance is governed by the slower interbranch processes which enable energy exchange between counterpropagating particles. We derive an analytic expression for the thermal conductance of interacting electrons valid for arbitrary relation between the wire length and electron thermalization length. We find that in sufficiently long wires the interaction-induced correction to the thermal conductance saturates to an interaction-independent value.
We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons
at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter K and the deviation from the resonance condition is obtained. For weak dissipation and 1/2<K<1, the conduction shows a non-monotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.
We consider a thin superconducting film with a magnetic dot with permanent magnetization (normal to the film) placed on it by a method based on London-Maxwell equations. For sufficiently high dot magnetization a single vortex appears in the ground st
ate. Further increase of magnetization is accompanied with the appearance of antivortices and more vortices in the film. We study analytically conditions for the appearance of a vortex--antivortex pair for a range of parameters. The phase diagram with diversity of vortex--antivortex states is calculated numerically. When appear in the ground state, antivortices are at distances comparable to the dot radius. For not too large dot radii the total vorticity in the ground state is predominantly zero or one. Magnetic field due to the dot and vortices everywhere in space is calculated analytically.
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigri
d method with respect to the number of grid points allowed us to use $256times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids(the initial solution on $256times 256$ grid was extrapolated steady solution from $128times 128$ grid which allowed using long integration time steps). The fluid solver may be used as the basis for hybrid codes for DC discharges.
We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $eta$ the weak link is always a relevant perturbation which suppresses transport strongl
y. At zero temperature the current voltage relation of the link is $Isim exp(-E_0/eV)$ where $E_0simeta/kappa$ and $kappa$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $exp(-sqrt{{cal C}E_0/k_BT})$. The decay of Friedel oscillation saturates for distance larger than $L_{eta}sim 1/eta $ from the impurity.
