Long-Range Energy-Level Interaction in Small Metallic Particles

We consider the energy level statistics of non-interacting electrons which diffuse in a $d$-dimensional disordered metallic conductor of characteristic Thouless energy $E_c.$ We assume that the level distribution can be written as the Gibbs distribution of a classical one-dimensional gas of fictitious particles with a pairwise additive interaction potential $f(\varepsilon ).$ We show that the interaction which is consistent with the known correlation function of pairs of energy levels is a logarithmic repulsion for level separations $\varepsilon <E_c,$ in agreement with Random Matrix Theory. When $\varepsilon >E_c,$ $f(\varepsilon )$ vanishes as a power law in $\varepsilon /E_c$ with exponents $-{1 \over 2},-2,$ and $-{3 \over 2}$ for $d=1,2,$ and 3, respectively. While for $d=1,2$ the energy-level interaction is always repulsive, in three dimensions there is long-range level attraction after the short-range logarithmic repulsion.Comment: Saclay-s93/014 Email: [email protected] [2017: missing figure included

Universal Quantum Signatures of Chaos in Ballistic Transport

The conductance of a ballistic quantum dot (having chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's circular ensemble. General formulas are obtained for the mean and variance of transport properties in the orthogonal (beta=1), unitary (beta=2), and symplectic (beta=4) symmetry class. Applications include universal conductance fluctuations, weak localization, sub-Poissonian shot noise, and normal-metal-superconductor junctions. The complete distribution P(g) of the conductance g is computed for the case that the coupling to the reservoirs occurs via two quantum point contacts with a single transmitted channel. The result P(g)=g^(-1+beta/2) is qualitatively different in the three symmetry classes. ***Submitted to Europhysics Letters.****Comment: 4 pages, REVTeX-3.0, INLO-PUB-94032

Shot noise in the chaotic-to-regular crossover regime

We investigate the shot noise for phase-coherent quantum transport in the chaotic-to-regular crossover regime. Employing the Modular Recursive Green's Function Method for both ballistic and disordered two-dimensional cavities we find the Fano factor and the transmission eigenvalue distribution for regular systems to be surprisingly similar to those for chaotic systems. We argue that in the case of regular dynamics in the cavity, diffraction at the lead openings is the dominant source of shot noise. We also explore the onset of the crossover from quantum to classical transport and develop a quasi-classical transport model for shot noise suppression which agrees with the numerical quantum data.Comment: 4 pages, 3 figures, submitted to Phys.Rev.Let

Isolated resonances in conductance fluctuations in ballistic billiards

We study numerically quantum transport through a billiard with a classically mixed phase space. In particular, we calculate the conductance and Wigner delay time by employing a recursive Green's function method. We find sharp, isolated resonances with a broad distribution of resonance widths in both the conductance and the Wigner time, in contrast to the well-known smooth conductance fluctuations of completely chaotic billiards. In order to elucidate the origin of the isolated resonances, we calculate the associated scattering states as well as the eigenstates of the corresponding closed system. As a result, we find a one-to-one correspondence between the resonant scattering states and eigenstates of the closed system. The broad distribution of resonance widths is traced to the structure of the classical phase space. Husimi representations of the resonant scattering states show a strong overlap either with the regular regions in phase space or with the hierarchical parts surrounding the regular regions. We are thus lead to a classification of the resonant states into regular and hierarchical, depending on their phase space portrait.Comment: 2 pages, 5 figures, to be published in J. Phys. Soc. Jpn., proceedings Localisation 2002 (Tokyo, Japan

Embedding method for the scattering phase in strongly correlated quantum dots

The embedding method for the calculation of the conductance through interacting systems connected to single channel leads is generalized to obtain the full complex transmission amplitude that completely characterizes the effective scattering matrix of the system at the Fermi energy. We calculate the transmission amplitude as a function of the gate potential for simple diamond-shaped lattice models of quantum dots with nearest neighbor interactions. In our simple models we do not generally observe an interaction dependent change in the number of zeroes or phase lapses that depend only on the symmetry properties of the underlying lattice. Strong correlations separate and reduce the widths of the resonant peaks while preserving the qualitative properites of the scattering phase.Comment: 11 pages, 3 figures. Proceedings of the Workshop on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Serie

The Łojasiewicz exponent over a field of arbitrary characteristic

Let K be an algebraically closed field and let K((XQ)) denote the field of generalized series with coefficients in K. We propose definitions of the local Łojasiewicz exponent of F = ( f1, . . . , fm) ∈ K[[X, Y ]]m as well as of the Łojasiewicz exponent at infinity of F = ( f1, . . . , fm) ∈ K[X, Y ]m, which generalize the familiar case of K = C and F ∈ C{X, Y }m (resp. F ∈ C[X, Y ]m), see Cha˛dzy´nski and Krasi´nski (In: Singularities, 1988; In: Singularities, 1988; Ann Polon Math 67(3):297–301, 1997; Ann Polon Math 67(2):191–197, 1997), and prove some basic properties of such numbers. Namely, we show that in both cases the exponent is attained on a parametrization of a component of F (Theorems 6 and 7), thus being a rational number. To this end, we define the notion of the Łojasiewicz pseudoexponent of F ∈ (K((XQ))[Y ])m for which we give a description of all the generalized series that extract the pseudoexponent, in terms of their jets. In particular, we show that there exist only finitely many jets of generalized series giving the pseudoexponent of F (Theorem 5). The main tool in the proofs is the algebraic version of Newton’s Polygon Method. The results are illustrated with some explicit examples

Growth and optical properties of GaN/AlN quantum wells

We demonstrate the growth of GaN/AlN quantum well structures by plasma-assisted molecular-beam epitaxy by taking advantage of the surfactant effect of Ga. The GaN/AlN quantum wells show photoluminescence emission with photon energies in the range between 4.2 and 2.3 eV for well widths between 0.7 and 2.6 nm, respectively. An internal electric field strength of $9.2\pm 1.0$ MV/cm is deduced from the dependence of the emission energy on the well width.Comment: Submitted to AP

Universal Parametric Correlations of Conductance Peaks in Quantum Dots

We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a symmetric dot we show that this correlation function is affected by breaking time-reversal symmetry but is independent of the details of the channels in the external leads. We derive a new scaling which depends on the eigenfunctions alone and can be extracted directly from the conductance peak heights. Our results are in excellent agreement with model simulations of a disordered quantum dot.Comment: 12 pages, RevTex, 2 Postscript figure

Mesoscopic Fluctuations of Elastic Cotunneling in Coulomb Blockaded Quantum Dots

We report measurements of mesoscopic fluctuations of elastic cotunneling in Coulomb blockaded quantum dots. Unlike resonant tunneling on Coulomb peaks, cotunneling in the valleys is sensitive to charging effects. We observe a larger magnetic field scale for the cotunneling (valley) fluctuations compared to the peaks, as well as an absence of "weak localization" (reduced conductance at B = 0) in valleys. Cotunneling fluctuations remain correlated over several valleys while peak conductance correlations decreases quickly.Comment: 9 pages, postscript (includes 4 figs). To be published in PR