Interaction-induced backscattering in short quantum wires

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.Comment: 10 pages, 4 figure

Resistivity of inhomogeneous quantum wires

We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, non-uniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.Comment: 4 pages, 1 figur

Conductance of a helical edge liquid coupled to a magnetic impurity

Transport in an ideal two-dimensional quantum spin Hall device is dominated by the counterpropagating edge states of electrons with opposite spins, giving the universal value of the conductance, $2e^2/h$. We study the effect on the conductance of a magnetic impurity, which can backscatter an electron from one edge state to the other. In the case of isotropic Kondo exchange we find that the correction to the electrical conductance caused by such an impurity vanishes in the dc limit, while the thermal conductance does acquire a finite correction due to the spin-flip backscattering.Comment: 5 pages, 2 figure

Skewed Sudakov Regime, Harmonic Numbers, and Multiple Polylogarithms

On the example of massless QED we study an asymptotic of the vertex when only one of the two virtualities of the external fermions is sent to zero. We call this regime the skewed Sudakov regime. First, we show that the asymptotic is described with a single form factor, for which we derive a linear evolution equation. The linear operator involved in this equation has a discrete spectrum. Its eigenfunctions and eigenvalues are found. The spectrum is a shifted sequence of harmonic numbers. With the spectrum found, we represent the expansion of the asymptotic in the fine structure constant in terms of multiple polylogarithms. Using this representation, the exponentiation of the doubly logarithmic corrections of the Sudakov form factor is recovered. It is pointed out that the form factor of the skewed Sudakov regime is growing with the virtuality of a fermion decreasing at a fixed virtuality of another fermion.Comment: 6 page

Spectral functions of strongly interacting isospin-1/2 bosons in one dimension

We study a system of one-dimensional (iso)spin-1/2 bosons in the regime of strong repulsive interactions. We argue that the low-energy spectrum of the system consists of acoustic density waves and the spin excitations described by an effective ferromagnetic spin chain with a small exchange constant J. We use this description to compute the dynamic spin structure factor and the spectral functions of the system.Comment: reference adde

Renormalization of impurity scattering in one-dimensional interacting electron systems in magnetic field

We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On the contrary, we show that in a strong magnetic field the interaction may suppress the backscattering of majority-spin electrons by the impurity potential in the vicinity of the weak-potential fixed point. This implies that in a certain temperature range the impurity becomes almost transparent for the majority-spin electrons while it is impenetrable for the minority-spin ones. The impurity potential can thus have a strong spin-filtering effect.Comment: 11 pages, 2 figures; v2: a typo corrected and a reference added; v3: published version, Sec.II revised with an additional explanatory subsection, comments on the case of more than half-filling added, typos corrected, a reference update

Sub-Hz line width diode lasers by stabilization to vibrationally and thermally compensated ULE Fabry-Perot cavities

We achieved a 0.5 Hz optical beat note line width with ~ 0.1 Hz/s frequency drift at 972 nm between two external cavity diode lasers independently stabilized to two vertically mounted Fabry-Perot (FP) reference cavities. Vertical FP reference cavities are suspended in mid-plane such that the influence of vertical vibrations to the mirror separation is significantly suppressed. This makes the setup virtually immune for vertical vibrations that are more difficult to isolate than the horizontal vibrations. To compensate for thermal drifts the FP spacers are made from Ultra-Low-Expansion (ULE) glass which possesses a zero linear expansion coefficient. A new design using Peltier elements in vacuum allows operation at an optimal temperature where the quadratic temperature expansion of the ULE could be eliminated as well. The measured linear drift of such ULE FP cavity of 63 mHz/s was due to material aging and the residual frequency fluctuations were less than 40 Hz during 16 hours of measurement. Some part of the temperature-caused drift is attributed to the thermal expansion of the mirror coatings. High-frequency thermal fluctuations that cause vibrations of the mirror surfaces limit the stability of a well designed reference cavity. By comparing two similar laser systems we obtain an Allan instability of 2*10-15 between 0.1 and 10 s averaging time, which is close to the theoretical thermal noise limit.Comment: submitted to Applied Physics

Asymmetric Zero-Bias Anomaly for Strongly Interacting Electrons in One Dimension

We study a system of one-dimensional electrons in the regime of strong repulsive interactions, where the spin exchange coupling J is small compared with the Fermi energy, and the conventional Tomonaga-Luttinger theory does not apply. We show that the tunneling density of states has a form of an asymmetric peak centered near the Fermi level. In the spin-incoherent regime, where the temperature is large compared to J, the density of states falls off as a power law of energy \epsilon measured from the Fermi level, with the prefactor at positive energies being twice as large as that at the negative ones. In contrast, at temperatures below J the density of states forms a split peak with most of the weight shifted to negative \epsilon.Comment: 4 pages, 2 figure

The Challenge of Light-Front Quantisation: Recent Results

We explain what is the challenge of light-front quantisation, and how we can now answer it because of recent progress in solving the problem of zero modes in the case of non-Abelian gauge theories. We also give a description of the light-front Hamiltonian for SU(2) finite volume gluodynamics resulting from this recent solution to the problem of light-front zero modes.Comment: 17 pages, lecture delivered by GBP at the XXXIV PNPI Winter School, Repino, St.Petersburg, Russia, February 14-20, 2000, version to appear in the Proceeding