Isoperimetric-type inequalities for iterated Brownian motion in R^n

We extend generalized isoperimetric-type inequalities to iterated Brownian motion over several domains in \RR{R}^{n}. These kinds of inequalities imply in particular that for domains of finite volume, the exit distribution and moments of the first exit time for iterated Brownian motion are maximized with the ball $D^{*}$ centered at the origin, which has the same volume as $D$Comment: 10 page

Discretized Thermal Green's Functions

We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free energy. A conformal transformation is used to analytically continue the periodized Matsubara Green's function to the continuous real axis in a way that conserves the discontinuity at t=0 of the corresponding real-time Green's function. For given discretization the method allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation as we decrease the discretization interval. The ideas are tested on Dynamical Mean Field Theory calculations of the paramagnetic Hubbard model

Spin symmetry and spin current of helicity eigenstates of the Luttinger Hamiltonian

A general spin symmetry argument is proposed for spin currents in semiconductors. In particular, due to the symmetry with respect to spin polarization of the helicity eigenstates of the Luttinger Hamiltonian for a hole-doped semiconductor, the spin polarized flux from a single helicity eigenstate induced by an external electric field, is canceled exactly when all such contributions from eigenstates that are degenerate in energy are summed. Thus, the net spin current predicted by Murakami et al, Science 301, 1348 (2003), cannot be produced by such a Hamiltonian. Possible symmetry breaking mechanisms which may generate a spin current are discussed

Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large $U$. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.Comment: 4 pages, 2 figure

Generalized conductance sum rule in atomic break junctions

When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels (valence orbitals of the junction atom) undergo strong variations. We propose a microscopic explanation of this phenomenon, based on Coulomb correlation effects between electrons in valence orbitals of the junction atom. The resulting approximate conductance quantization is closely related to the Friedel sum rule.Comment: 4 pages, 1 figure, appears in Proceedings of the NATO Advanced Research Workshop ``Size dependent magnetic scattering'', Pecs, Hungary, May 28 - June 1, 200

Transport in Luttinger Liquids

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry exactly solvable Luttinger-like model.Comment: Latex file, 15 pages, four eps figure

Non-Fermi Liquid Effective Field Theory of Dense QCD Matter

We review an effective field theory for the non-Fermi liquid regime of dense QCD matter. Non-Fermi liquid effects arise due the presence of unscreened magnetic gluon exchanges. We show that there is a systematic low energy expansion in fractional powers and logarithms of energy. We discuss the validity of some standard theorems of Fermi liquid theory.Comment: 4 pages; Contribution to the proceedings of the International Conference on Strong & Electroweak Matter 2006, Brookhaven National Laboratory, Upton, NY, May 200

Oscillatory Tunneling between Quantum Hall Systems

Electron tunneling between quantum Hall systems on the same two dimensional plane separated by a narrow barrier is studied. We show that in the limit where inelastic scattering time is much longer than the tunneling time, which can be achieved in practice, electrons can tunnel back and forth through the barrier continously, leading to an oscillating current in the absence of external drives. The oscillatory behavior is dictated by a tunneling gap in the energy spectrum. We shall discuss ways to generate oscillating currents and the phenomenon of natural ``dephasing" between the tunneling currents of edge states. The noise spectra of these junctions are also studied. They contain singularites reflecting the existence of tunneling gaps as well as the inherent oscillation in the system. (Figures will be given upon requests).Comment: 20 pages, OS

Structure and transport in multi-orbital Kondo systems

We consider Kondo impurity systems with multiple local orbitals, such as rare earth ions in a metallic host or multi--level quantum dots coupled to metallic leads. It is shown that the multiplet structure of the local orbitals leads to multiple Kondo peaks above the Fermi energy $E_F$, and to ``shadow'' peaks below $E_F$. We use a slave boson mean field theory, which recovers the strong coupling Fermi liquid fixed point, to calculate the Kondo peak positions, widths, and heights analytically at T=0, and NCA calculations to fit the temperature dependence of high--resolution photoemission spectra of Ce compounds. In addition, an approximate conductance quantization for transport through multi--level quantum dots or single--atom transistors in the Kondo regime due to a generalized Friedel sum rule is demonstrated.Comment: 4 pages, 3 figures. Invited article, 23rd International Conference on Low Temperature Physics LT23, Hiroshima, Japan 200