Effects of interaction on an adiabatic quantum electron pump

We study the effects of inter-electron interactions on the charge pumped through an adiabatic quantum electron pump. The pumping is through a system of barriers, whose heights are deformed adiabatically. (Weak) interaction effects are introduced through a renormalisation group flow of the scattering matrices and the pumped charge is shown to {\it always} approach a quantised value at low temperatures or long length scales. The maximum value of the pumped charge is set by the number of barriers and is given by $Q_{\rm max} = n_b -1$. The correlation between the transmission and the charge pumped is studied by seeing how much of the transmission is enclosed by the pumping contour. The (integer) value of the pumped charge at low temperatures is determined by the number of transmission maxima enclosed by the pumping contour. The dissipation at finite temperatures leading to the non-quantised values of the pumped charge scales as a power law with the temperature ($Q-Q_{\rm int} \propto T^{2\alpha}$), or with the system size ($Q-Q_{\rm int} \propto L_s^{-2\alpha}$), where $\alpha$ is a measure of the interactions and vanishes at $T=0 ~(L_s=\infty)$. For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.Comment: 9 pages, 9 figures, better quality figures available on request from author

Tunneling through two resonant levels: fixed points and conductances

We study point contact tunneling between two leads of a Tomonaga-Luttinger liquid through two degenerate resonant levels in parallel. This is one of the simplest cases of a quantum junction problem where the Fermi statistics of the electrons plays a non-trivial role through the Klein factors appearing in bosonization. Using a mapping to a `generalized Coulomb model' studied in the context of the dissipative Hofstadter model, we find that any asymmetry in the tunneling amplitudes from the two leads grows at low temperatures, so that ultimately there is no conductance across the system. For the symmetric case, we identify a non-trivial fixed point of this model; the conductance at that point is generally different from the conductance through a single resonant level.Comment: 6 pages, 3 figure

PPARα-targeted mitochondrial bioenergetics mediate repair of intestinal barriers at the host-microbe intersection during SIV infection.

Chronic gut inflammatory diseases are associated with disruption of intestinal epithelial barriers and impaired mucosal immunity. HIV-1 (HIV) causes depletion of mucosal CD4+ T cells early in infection and disruption of gut epithelium, resulting in chronic inflammation and immunodeficiency. Although antiretroviral therapy (ART) is effective in suppressing viral replication, it is incapable of restoring the "leaky gut," which poses an impediment for HIV cure efforts. Strategies are needed for rapid repair of the epithelium to protect intestinal microenvironments and immunity in inflamed gut. Using an in vivo nonhuman primate intestinal loop model of HIV/AIDS, we identified the pathogenic mechanism underlying sustained disruption of gut epithelium and explored rapid repair of gut epithelium at the intersection of microbial metabolism. Molecular, immunological, and metabolomic analyses revealed marked loss of peroxisomal proliferator-activated receptor-α (PPARα) signaling, predominant impairment of mitochondrial function, and epithelial disruption both in vivo and in vitro. To elucidate pathways regulating intestinal epithelial integrity, we introduced probiotic Lactobacillus plantarum into Simian immunodeficiency virus (SIV)-inflamed intestinal lumen. Rapid recovery of the epithelium occurred within 5 h of L. plantarum administration, independent of mucosal CD4+ T cell recovery, and in the absence of ART. This intestinal barrier repair was driven by L. plantarum-induced PPARα activation and restoration of mitochondrial structure and fatty acid β-oxidation. Our data highlight the critical role of PPARα at the intersection between microbial metabolism and epithelial repair in virally inflamed gut and as a potential mitochondrial target for restoring gut barriers in other infectious or gut inflammatory diseases

Transport through quasi-ballistic quantum wires: the role of contacts

We model one-dimensional transport through each open channel of a quantum wire by a Luttinger liquid with three different interaction parameters for the leads, the contact regions and the wire, and with two barriers at the contacts. We show that this model explains several features of recent experiments, such as the flat conductance plateaux observed even at finite temperatures and for different lengths, and universal conductance corrections in different channels. We discuss the possibility of seeing resonance-like structures of a fully open channel at very low temperatures.Comment: revtex, 5 pages, 1 eps figure; clarifications added in light of new experiment

Transport in quantum wires

With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic systems, we discuss some recent experimental puzzles in these systems, which include reduction of quantised conductances and an interesting {\it odd-even} effect in the presence of an in-plane magnetic field. We then discuss a recent non-homogeneous Luttinger liquid model proposed by us, which addresses and gives an explanation for the reduced conductances and the {\it odd-even} effect. We end with a brief summary and discussion of future projects.Comment: Talk presented at the International Discussion Meeting on Mesoscopic and Disordered systems, December, 2000, 16 pages, 2 figure

Renormalization group study of the conductances of interacting quantum wire systems with different geometries

We examine the effect of interactions between the electrons on the conductances of some systems of quantum wires with different geometries. The systems include a wire with a stub in the middle, a wire containing a ring which can enclose a magnetic flux, and a system of four wires which are connected in the middle through a fifth wire. Each of the wires is taken to be a weakly interacting Tomonaga-Luttinger liquid, and scattering matrices are introduced at all the junctions. Using a renormalization group method developed recently for studying the flow of scattering matrices for interacting systems in one dimension, we compute the conductances of these systems as functions of the temperature and the wire lengths. We present results for all three regimes of interest, namely, high, intermediate and low temperature. These correspond respectively to the thermal coherence length being smaller than, comparable to and larger than the smallest wire length in the different systems, i.e., the length of the stub or each arm of the ring or the fifth wire. The renormalization group procedure and the formulae used to compute the conductances are different in the three regimes. We present a phenomenologically motivated formalism for studying the conductances in the intermediate regime where there is only partial coherence. At low temperatures, we study the line shapes of the conductances versus the electron energy near some of the resonances; the widths of the resonances go to zero with decreasing temperature. Our results show that the conductances of various systems of experimental interest depend on the temperature and lengths in a non-trivial way when interactions are taken into account.Comment: Revtex, 17 pages including 15 figure

Renormalization group study of the Kondo problem at a junction of several Luttinger wires

We study a system consisting of a junction of N quantum wires, where the junction is characterized by a scalar S-matrix, and an impurity spin is coupled to the electrons close to the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group equations for the Kondo couplings of the spin to the electronic modes on different wires, and analyze the renormalization group flows and fixed points for different values of the initial Kondo couplings and of the junction S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We generally find that the Kondo couplings flow towards large and antiferromagnetic values in one of two possible ways. For the Griffiths S-matrix, we study one of the strong coupling flows by a perturbative expansion in the inverse of the Kondo coupling; we find that at large distances, the system approaches the ferromagnetic fixed point of the decoupled S-matrix. For the decoupled S-matrix with antiferromagnetic Kondo couplings and weak inter-electron interactions, the flows are to one of two strong coupling fixed points in which all the channels are strongly coupled to each other through the impurity spin. But strong inter-electron interactions, with K_\rho < N/(N+2), stabilize a multi-channel fixed point in which the coupling between different channels goes to zero. We have also studied the temperature dependence of the conductance at the decoupled and Griffiths S-matrices.Comment: Revtex4, 16 pages including 6 figure

Junction of several weakly interacting quantum wires: a renormalization group study

We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range density-density interaction, and they encounter a general scattering matrix at the junction. We derive the renormalization group equations satisfied by the S-matrix, and we identify its fixed points and their stabilities. The conductance between any pair of wires is then studied as a function of physical parameters such as temperature. We discuss the possibility of observing the effects of junctions in present day experiments, such as the four-terminal conductance of a quantum wire and crossed quantum wires.Comment: RevTeX, 13 pages, including 4 eps figure

Field Theories of Frustrated Heisenberg Antiferromagnets

We study the Heisenberg antiferromagnetic chain with both dimerization and frustration. The classical ground state has three phases: a Neel phase, a spiral phase and a colinear phase. In each phase, we discuss a non-linear sigma model field theory governing the low energy excitations. We study the theory in the spiral phase in detail using the renormalization group. The field theory, based on an $SO(3)$ matrix-valued field, becomes $SO(3) \times SO(3)$ and Lorentz invariant at long distances where the elementary excitation is analytically known to be a massive spin-$1/2$ doublet. The field theory supports $Z_2 ~$ solitons which lead to a double degeneracy in the spectrum for half-integer spins (when there is no dimerization).Comment: Latex, 12 pages, 2 figures (gzipped and uuencoded