Vibrational absorption sidebands in the Coulomb blockade regime of single-molecule transistors

Current-driven vibrational non-equilibrium induces vibrational sidebands in single-molecule transistors which arise from tunneling processes accompanied by absorption of vibrational quanta. Unlike conventional sidebands, these absorption sidebands occur in a regime where the current is nominally Coulomb blockaded. Here, we develop a detailed and analytical theory of absorption sidebands, including current-voltage characteristics as well as shot noise. We discuss the relation of our predictions to recent experiments.Comment: 7 pages, 6 figures; revised discussion of relation to experimen

Distribution of level curvatures for the Anderson model at the localization-delocalization transition

We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators $P(k)$ has a logarithmically-normal form. At the Anderson localization-delocalization transition $P(k)$ fits very well the proposed novel distribution $P(k)\propto (1+k^{\mu})^{3/\mu}$ with $\mu \approx 1.58$, which approaches the RMT result for large $k$ and is non-analytical at small $k$. We ascribe such a non-analiticity to the spatial multifractality of the critical wave functions.Comment: 4 ReVTeX pages and 4(.epsi)figures included in one uuencoded packag

On the critical level-curvature distribution

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.Comment: 4 pages, 3 figure

Orbital Magnetism in Ensembles of Parabolic Potentials

We study the magnetic susceptibility of an ensemble of non-interacting electrons confined by parabolic potentials and subjected to a perpendicular magnetic field at finite temperatures. We show that the behavior of the average susceptibility is qualitatively different from that of billiards. When averaged over the Fermi energy the susceptibility exhibits a large paramagnetic response only at certain special field values, corresponding to comensurate classical frequencies, being negligible elsewhere. We derive approximate analytical formulae for the susceptibility and compare the results with numerical calculations.Comment: 4 pages, 4 figures, REVTE

Persistent Currents in Quantum Chaotic Systems

The persistent current of ballistic chaotic billiards is considered with the help of the Gutzwiller trace formula. We derive the semiclassical formula of a typical persistent current $I^{typ}$ for a single billiard and an average persistent current $$ for an ensemble of billiards at finite temperature. These formulas are used to show that the persistent current for chaotic billiards is much smaller than that for integrable ones. The persistent currents in the ballistic regime therefore become an experimental tool to search for the quantum signature of classical chaotic and regular dynamics.Comment: 4 pages (RevTex), to appear in Phys. Rev. B, No.59, 12256-12259 (1999

Universality in quantum parametric correlations

We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations. Under certain general conditions we show that this procedure is unique. The approach is illustrated with the particular case of the distribution of eigenvalue curvatures. We also derive a semiclassical formula for the non-universal scaling factor, and give an explicit expression valid for arbitrary deformations of a billiard system.Comment: LaTeX, 10 pages, 2 figures. Revised version, to appear in PR

Two interacting particles in a random potential

We study the scaling of the localization length of two interacting particles in a one-dimensional random lattice with the single particle localization length. We obtain several regimes, among them one interesting weak Fock space disorder regime. In this regime we derive a weak logarithmic scaling law. Numerical data support the absence of any strong enhancement of the two particle localization length

Strongly correlated Fermi-Bose mixtures in disordered optical lattices

We investigate theoretically the low-temperature physics of a two-component ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson-boson and the boson-fermion interactions, the tunneling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and we show that it corresponds to the formation of Fermi glasses, spin glasses, and quantum percolation regimes.Comment: Proceedings of the 3rd International Workshop on `Theory of Quantum Gases and Quantum Coherence

Semiclassical Quantisation Using Diffractive Orbits

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we construct the corresponding zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the diffractive zeta function.Comment: Revtex document. Submitted to PRL. Figures available on reques