Magnetoconductance oscillations in quasiballistic multimode nanowires

We calculate the conductance of quasi-one-dimensional nanowires with electronic states confined to a surface charge layer, in the presence of a uniform magnetic field. Two-terminal magnetoconductance (MC) between two leads deposited on the nanowire via tunnel barriers is dominated by density-of-states (DOS) singularities, when the leads are well apart. There is also a mesoscopic correction due to a higher-order coherent tunneling between the leads for small lead separation. The corresponding MC structure depends on the interference between electron propagation via different channels connecting the leads, which in the simplest case, for the magnetic field along the wire axis, can be crudely characterized by relative winding numbers of paths enclosing the magnetic flux. In general, the MC oscillations are aperiodic, due to the Zeeman splitting, field misalignment with the wire axis, and a finite extent of electron distribution across the wire cross section, and are affected by spin-orbit coupling. The quantum-interference MC traces contain a wealth of information about the electronic structure of multichannel wires, which would be complimentary to the DOS measurements. We propose a four-terminal configuration to enhance the relative contribution of the higher-order tunneling processes and apply our results to realistic InAs nanowires carrying several quantum channels in the surface charge-accumulation layer.Comment: 11 pages, 8 figure

A General Precipitation-Limited L_X-T-R Relation Among Early-Type Galaxies

The relation between X-ray luminosity (L_X) and ambient gas temperature (T) among massive galactic systems is an important cornerstone of both observational cosmology and galaxy-evolution modeling. In the most massive galaxy clusters, the relation is determined primarily by cosmological structure formation. In less massive systems, it primarily reflects the feedback response to radiative cooling of circumgalactic gas. Here we present a simple but powerful model for the L_X-T relation as a function of physical aperture R within which those measurements are made. The model is based on the precipitation framework for AGN feedback and assumes that the circumgalactic medium is precipitation-regulated at small radii and limited by cosmological structure formation at large radii. We compare this model with many different data sets and show that it successfully reproduces the slope and upper envelope of the L_X-T-R relation over the temperature range from ~0.2 keV through >10 keV. Our findings strongly suggest that the feedback mechanisms responsible for regulating star formation in individual massive galaxies have much in common with the precipitation-triggered feedback that appears to regulate galaxy-cluster cores.Comment: Submitted to ApJ, 9 pages, 3 figures (v2 fixes a few small typos

Quasi-Particles in Two-Dimensional Hubbard Model: Splitting of Spectral Weight

It is shown that the energy $(\varepsilon)$ and momentum $(k)$ dependences of the electron self-energy function $\Sigma (k, \varepsilon + i0) \equiv \Sigma^{R}(k, \varepsilon)$ are, ${\rm Im} \Sigma^{R} (k, \varepsilon) = -a\varepsilon^{2}|\varepsilon - \xi_{k}|^{- \gamma (k)}$ where $a$ is some constant, $\xi_{k} = \varepsilon(k)-\mu, \varepsilon(k)$ being the band energy, and the critical exponent $\gamma(k)$, which depends on the curvature of the Fermi surface at $k$, satisfies, $0 \leq \gamma(k) \leq 1$. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $\varepsilon, \xi_{k} \rightarrow 0$ but for $\xi_{k} \neq 0$ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.Comment: 8 pages (LaTeX) 4 figures available upon request will be sent by air mail. KomabaCM-preprint-O

Spectral sum rules for the Tomonaga-Luttinger model

In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution photoemission spectra of quasi-one-dimensional conductors. It is shown that the limit of infinite frequency and band cut\-off do not commute. Our result for arbitrary shape of the interaction potential generalizes an earlier discussion by Suzumura. A general analytical expression for the spectral function for wave vectors far from the Fermi wave vector $k_{F}$ is presented. Numerical spectra are shown to illustrate the sum rules.Comment: 9 pages, REVTEX 3.0, 2 figures added as postscript file

Nonuniversal spectral properties of the Luttinger model

The one electron spectral functions for the Luttinger model are discussed for large but finite systems. The methods presented allow a simple interpretation of the results. For finite range interactions interesting nonunivesal spectral features emerge for momenta which differ from the Fermi points by the order of the inverse interaction range or more. For a simplified model with interactions only within the branches of right and left moving electrons analytical expressions for the spectral function are presented which allows to perform the thermodynamic limit. As in the general spinless model and the model including spin for which we present mainly numerical results the spectral functions do not approach the noninteracting limit for large momenta. The implication of our results for recent high resolution photoemission measurements on quasi one-dimensional conductors are discussed.Comment: 19 pages, Revtex 2.0, 5 ps-figures, to be mailed on reques

Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap

Using an asymptotic phase representation of the particle density operator $\hat{\rho}(z)$ in the one-dimensional harmonic trap, the part $\delta \hat{\rho}_F(z)$ which describes the Friedel oscillations is extracted. The expectation value $$ with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent $\nu = (K+1)/2$ away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.Comment: Revised version to appear in Journal of Physics B: Atomic, Molecular and Optical Physic

Record Statistics for Multiple Random Walks

We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance \sigma^2 of the jump distribution is finite and (II) when \sigma^2 is divergent as in the case of L\'evy flights with index 0 < \mu < 2. In both cases we find that the mean record number grows universally as \sim \alpha_N \sqrt{n} for large n, but with a very different behavior of the amplitude \alpha_N for N > 1 in the two cases. We find that for large N, \alpha_N \approx 2 \sqrt{\log N} independently of \sigma^2 in case I. In contrast, in case II, the amplitude approaches to an N-independent constant for large N, \alpha_N \approx 4/\sqrt{\pi}, independently of 0<\mu<2. For finite \sigma^2 we argue, and this is confirmed by our numerical simulations, that the full distribution of (R_{n,N}/\sqrt{n} - 2 \sqrt{\log N}) \sqrt{\log N} converges to a Gumbel law as n \to \infty and N \to \infty. In case II, our numerical simulations indicate that the distribution of R_{n,N}/\sqrt{n} converges, for n \to \infty and N \to \infty, to a universal nontrivial distribution, independently of \mu. We discuss the applications of our results to the study of the record statistics of 366 daily stock prices from the Standard & Poors 500 index.Comment: 25 pages, 8 figure

Spectroscopic signatures of spin-charge separation in the quasi-one-dimensional organic conductor TTF-TCNQ

The electronic structure of the quasi-one-dimensional organic conductor TTF-TCNQ is studied by angle-resolved photoelectron spectroscopy (ARPES). The experimental spectra reveal significant discrepancies to band theory. We demonstrate that the measured dispersions can be consistently mapped onto the one-dimensional Hubbard model at finite doping. This interpretation is further supported by a remarkable transfer of spectral weight as function of temperature. The ARPES data thus show spectroscopic signatures of spin-charge separation on an energy scale of the conduction band width.Comment: 4 pages, 4 figures; to appear in PR

Dynamic scaling in the vicinity of the Luttinger liquid fixed point

We calculate the single-particle spectral function A (k, omega) of a one-dimensional Luttinger liquid by means of a functional renormalization group (RG) approach. Given an infrared energy cutoff Lambda = Lambda_0 e^{- l}, our approach yields the spectral function in the scaling form, A_{\Lambda} (k_F + p, omega) = tau Z_l tilde{A}_l (p xi, omega tau), where k_F is the Fermi momentum, Z_l is the wave-function renormalization factor, tau = 1 / \Lambda is the time scale and xi = v_F / \Lambda is the length scale associated with Lambda. At the Luttinger liquid fixed point (l rightarrow infty) our RG result for A (k, omega) exhibits the correct anomalous scaling properties, and for k = \pm k_F agrees exactly with the well-known bosonization result at weak coupling. Our calculation demonstrates that the field rescaling is essential for obtaining the crossover from Fermi liquid behavior to Luttinger liquid behavior from a truncation of the hierarchy of exact RG flow equations as the infrared cutoff is reduced.Comment: 15 pages, 5 figure

A Very Hot, High Redshift Cluster of Galaxies: More Trouble for Omega_0 = 1

We have observed the most distant (z=0.829) cluster of galaxies in the Einstein Extended Medium Sensitivity Survey, with the ASCA and ROSAT satellites. We find an X-ray temperature of 12.3 +3.1/-2.2 keV for this cluster, and the ROSAT map reveals significant substructure. The high temperature of MS1054-0321 is consistent with both its approximate velocity dispersion, based on the redshifts of 12 cluster members we have obtained at the Keck and the Canada-France-Hawaii telescopes, and with its weak lensing signature. The X-ray temperature of this cluster implies a virial mass ~ 7.4 x 10^14 h^-1 solar masses, if the mean matter density in the universe equals the critical value, or larger if Omega_0 < 1. Finding such a hot, massive cluster in the EMSS is extremely improbable if clusters grew from Gaussian perturbations in an Omega_0 = 1 universe. Combining the assumptions that Omega_0 = 1 and that the intial perturbations were Gaussian with the observed X-ray temperature function at low redshift, we show that the probability of this cluster occurring in the volume sampled by the EMSS is less than a few times 10^{-5}. Nor is MS1054-0321 the only hot cluster at high redshift; the only two other $z > 0.5$ EMSS clusters already observed with ASCA also have temperatures exceeding 8 keV. Assuming again that the initial perturbations were Gaussian and Omega_0 = 1, we find that each one is improbable at the < 10^{-2} level. These observations, along with the fact that these luminosities and temperatures of the high-$z$ clusters all agree with the low-z L_X-T_X relation, argue strongly that Omega_0 < 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.Comment: 20 pages, 4 figures, To appear in 1 Aug 1998 ApJ (heavily revised version of original preprint