Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.Comment: 12 page

Gauge fields - strings duality and the loop equation

We explore gauge fields - strings duality by means of the loop equations and the zigzag symmetry. The results are striking and incomplete. Striking - because we find that the string ansatz proposed in [A.M. Polyakov, hep-th/9711002] satisfies gauge theory Schwinger-Dyson equations precisely at the critical dimension D=4. Incomplete - since we get these results only in the WKB approximation and only for a special class of contours. The ways to go beyond these limitations and in particular the OPE for operators defined on the loop are also discussed.Comment: 23 pages, 3 references added, minor change

Many-body delocalization transition and relaxation in a quantum dot

We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state", a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.Comment: 16+6 pages, 2 figures; comments, additional explanations, references, and Supplemental Material adde

Large-scale Ferrofluid Simulations on Graphics Processing Units

We present an approach to molecular-dynamics simulations of ferrofluids on graphics processing units (GPUs). Our numerical scheme is based on a GPU-oriented modification of the Barnes-Hut (BH) algorithm designed to increase the parallelism of computations. For an ensemble consisting of one million of ferromagnetic particles, the performance of the proposed algorithm on a Tesla M2050 GPU demonstrated a computational-time speed-up of four order of magnitude compared to the performance of the sequential All-Pairs (AP) algorithm on a single-core CPU, and two order of magnitude compared to the performance of the optimized AP algorithm on the GPU. The accuracy of the scheme is corroborated by comparing the results of numerical simulations with theoretical predictions

Ultranarrow resonance in Coulomb drag between quantum wires at coinciding densities

We investigate the influence of the chemical potential mismatch $\Delta$ (different electron densities) on Coulomb drag between two parallel ballistic quantum wires. For pair collisions, the drag resistivity $\rho_{\rm D}(\Delta)$ shows a peculiar anomaly at $\Delta=0$ with $\rho_{\rm D}$ being finite at $\Delta=0$ and vanishing at any nonzero $\Delta$. The "bodyless" resonance in $\rho_{\rm D}(\Delta)$ at zero $\Delta$ is only broadened by processes of multi-particle scattering. We analyze Coulomb drag for finite $\Delta$ in the presence of both two- and three-particle scattering within the kinetic equation framework, focusing on a Fokker-Planck picture of the interaction-induced diffusion in momentum space of the double-wire system. We describe the dependence of $\rho_{\rm D}$ on $\Delta$ for both weak and strong intrawire equilibration due to three-particle scattering.Comment: 21 pages (+2.5 pages Suppl. Mat.), 2 figures; additional explanation

Aharonov-Bohm conductance through a single-channel quantum ring: Persistent-current blockade and zero-mode dephasing

We study the effect of electron-electron interaction on transport through a tunnel-coupled single-channel ring. We find that the conductance as a function of magnetic flux shows a series of interaction-induced resonances that survive thermal averaging. The period of the series is given by the interaction strength $\alpha$. The physics behind this behavior is the blocking of the tunneling current by the circular current. The main mechanism of dephasing is due to circular-current fluctuations. The dephasing rate is proportional to the tunneling rate and does not depend on $\alpha$.Comment: 7 pages, 1 figure, typos corrected, appendix adde