Crossover of magnetoconductance autocorrelation for a ballistic chaotic quantum dot

The autocorrelation function C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)= \langle \delta g(\varphi,\,\eps)\, \delta g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle ($\varphi$ and \eps are rescaled magnetic flux and energy) for the magnetoconductance of a ballistic chaotic quantum dot is calculated in the framework of the supersymmetric non-linear $\sigma$-model. The Hamiltonian of the quantum dot is modelled by a Gaussian random matrix. The particular form of the symmetry breaking matrix is found to be relevant for the autocorrelation function but not for the average conductance. Our results are valid for the complete crossover from orthogonal to unitary symmetry and their relation with semiclassical theory and an $S$-matrix Brownian motion ensemble is discussed.Comment: 7 pages, no figures, accepted for publication in Europhysics Letter

Correlation functions of one-dimensional Bose-Fermi mixtures

We calculate the asymptotic behaviour of correlation functions as a function of the microscopic parameters for a Bose-Fermi mixture with repulsive interaction in one dimension. For two cases, namely polarized and unpolarized fermions the singularities of the momentum distribution functions are characterized as a function of the coupling constant and the relative density of bosons.Comment: RevTeX 4, 10 pages, 2 figure

Breit-Wigner width for two interacting particles in one-dimensional random potential

For two interacting particles (TIP) in one-dimensional random potential the dependence of the Breit-Wigner width $\Gamma$, the local density of states and the TIP localization length on system parameters is determined analytically. The theoretical predictions for $\Gamma$ are confirmed by numerical simulations.Comment: 10 pages Latex, 4 figures included. New version with extended numerical results and discussions of earlier result

Analytical Results for Random Band Matrices with Preferential Basis

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a random band matrix with a strongly fluctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of random band matrices with preferential basis. Our analytical results are in good agreement with (but more general than) recent numerical findings by Jacquod and Shepelyansky.Comment: 8 pages RevTex and 1 Figure, both uuencode

Anderson-like impurity in the one-dimensional t-J model: formation of local states and magnetic behaviour

We consider an integrable model describing an Anderson-like impurity coupled to an open $t$--$J$ chain. Both the hybridization (i.e. its coupling to bulk chain) and the local spectrum can be controlled without breaking the integrability of the model. As the hybridization is varied, holon and spinon bound states appear in the many body ground state. Based on the exact solution we study the state of the impurity and its contribution to thermodynamic quantities as a function of an applied magnetic field. Kondo behaviour in the magnetic response of the impurity can be observed provided that its parameters have been adjusted properly to the energy scales of the holon and spinon excitations of the one-dimensional bulk.Comment: 32 pages, 11 figure

Theory of quasi-one dimensional imbalanced Fermi gases

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D `tubes') with spin imbalance, where strong intratube quantum fluctuations invalidate mean field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against inter-tube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.Comment: new expanded version, 8 pages, updated reference

Conductance length autocorrelation in quasi one-dimensional disordered wires

Employing techniques recently developed in the context of the Fokker--Planck approach to electron transport in disordered systems we calculate the conductance length correlation function $$ for quasi 1d wires. Our result is valid for arbitrary lengths L and $\Delta L$. In the metallic limit the correlation function is given by a squared Lorentzian. In the localized regime it decays exponentially in both L and $\Delta L$. The correlation length is proportional to L in the metallic regime and saturates at a value approximately given by the localization length $\xi$ as $L\gg\xi$.Comment: 23 pages, Revtex, two figure

Diffusion-weighted magnetic resonance imaging (MRI) without susceptibility artifacts: single-shot stimulated echo acquisition mode (STEAM) MRI with iterative reconstruction and spatial regularization

This work describes a new method for diffusion-weighted (DW) magnetic resonance imaging (MRI) without susceptibility artifacts. The technique combines a DW spin-echo module and a single-shot stimulated echo acquisition mode (STEAM) MRI readout with undersampled radial trajectories and covers a volume by a gapless series of cross-sectional slices. In a first step, optimal coil sensitivities for all slices are obtained from a series of non-DW acquisitions by nonlinear inverse reconstruction with regularization to the image and coil sensitivities of a directly neighboring slice. In a second step, these coil sensitivities are used to compute all series of non-DW and DW images by linear inverse reconstruction with spatial regularization to a neighboring image. Proof-of-principle applications to the brain (51 sections) and prostate (31 sections) of healthy subjects were realized for a protocol with two b-values and 6 gradient directions at 3 T. Including averaging the measuring times for studies of the brain at 1.0×1.0×3.0 mm3 resolution (b =1,000 s mm−2) and prostate at 1.4×1.4×3.0 mm3 resolution (b =600 s mm-2) were 2.5 min and 4.5 min, respectively. All reconstructions were accomplished online with use of a multi-GPU computer integrated into the MRI system. The resulting non-DW images, mean DW images averaged across directions and maps of the apparent diffusion coefficient confirm the absence of geometric distortions or false signal alterations and demonstrate diagnostic image quality. The novel method for DW STEAM MRI of a volume without susceptibility artifacts warrants extended clinical trials

Localized to extended states transition for two interacting particles in a two-dimensional random potential

We show by a numerical procedure that a short-range interaction $u$ induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by an scaling analysis of the renormalized decay length of the bars. For $u=1$, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected.Comment: 4 two-column pages, 4 eps figures, Revtex, to be published in Europhys. Let