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A novel methodology is presented for reconstructing the Eulerian number density field of dispersed gas-droplet flows modelled using the Fully Lagrangian Approach (FLA). In this work, the nonparametric framework of kernel regression is used to accumulate the FLA number density contributions of individual droplets in accordance with the spatial structure of the dispersed phase. The high variation which is observed in the droplet number density field for unsteady flows is accounted for by using the Eulerian-Lagrangian transformation tensor, which is central to the FLA, to specify the size and shape of the kernel associated with each droplet. This procedure enables a high level of structural detail to be retained, and it is demonstrated that far fewer droplets have to be tracked in order to reconstruct a faithful Eulerian representation of the dispersed phase. Furthermore, the kernel regression procedure is easily extended to higher dimensions, and inclusion of the droplet radius within the phase space description using the generalised Fully Lagrangian Approach (gFLA) additionally enables statistics of the droplet size distribution to be determined for polydisperse flows. The developed methodology is applied to a range of one-dimensional and two-dimensional steady-state and transient flows, for both monodisperse and polydisperse droplets, and it is shown that kernel regression performs well across this variety of cases. A comparison is made against conventional direct trajectory methods to determine the saving in computational expense which can be gained, and it is found that $10^3$ times fewer droplet realisations are needed to reconstruct a qualitatively similar representation of the number density field., Comment: 35 pages, 13 figures

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium., Comment: 5 pages, 3 figures

A nanoscale device consisting of a metal nanowire, a dielectric, and a gate is proposed. A combination of quantum and thermal stochastic effects enable the device to have multiple functionalities, serving alternately as a transistor, a variable resistor, or a simple resistive element with $I-V$ characteristics that can switch between ohmic and non-ohmic. By manipulating the gate voltage, stochastic transitions between different conducting states of the nanowire can be induced, with a switching time as short as picoseconds. With an appropriate choice of dielectric, the transconductance of the device can significantly exceed the conductance quantum $G_0=2e^2/h$, a remarkable figure of merit for a device at this lengthscale., Comment: 6 pages, 7 figures

We calculate transmission eigenvalue distributions for Pt-benzene-Pt and Pt-butadiene-Pt junctions using realistic state-of-the-art many-body techniques. An effective field theory of interacting $\pi$-electrons is used to include screening and van der Waals interactions with the metal electrodes. We find that the number of dominant transmission channels in a molecular junction is equal to the degeneracy of the molecular orbital closest to the metal Fermi level., Comment: 9 pages, 8 figures

A brief review of the nanoscale free-electron model of metal nanowires is presented. This continuum description of metal nanostructures allows for a unified treatment of cohesive and conducting properties. Conductance channels act as delocalized chemical bonds whose breaking is responsible for jumps in the conductance and force oscillations. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of a nanowire, and much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing factors. A linear stability analysis reveals a sequence of ``magic'' conductance values for which the underlying nanowire geometry is exceptionally stable. The stable configurations include Jahn-Teller deformed wires of broken axial symmetry. The model naturally explains the experimentally observed shell and supershell structures., Comment: To appear in "Handbook of Nanophysics" (ed. K.Sattler) (Taylor & Francis 2010)

Electron spin relaxation rate (eSR) is investigated on several organic semiconductors of different morphologies and molecular structures, using avoided level crossing muon spectroscopy as a local spin probe. We find that two functionalized acenes (polycrystalline tri(isopropyl)silyl-pentacene and amorphous 5,6,11,12-tetraphenyltetracene) exhibit eSRs with an Arrhenius-like temperature dependence, each with two characteristic energy scales similar to those expected from vibrations. Polycrystalline tris(8-hydroxyquinolate)gallium shows a similar behavior. The observed eSR for these molecules is no greater than 0.85 MHz at 300 K. The variety of crystal structures and transport regimes that these molecules possess, as well as the local nature of the probe, strongly suggest an intra-molecular phenomenon general to many organic semiconductors, contrasting the commonly assumed spin relaxation models based on inter-molecular charge carrier transport.

We predict an enormous order-dependent quantum enhancement of thermoelectric effects in the vicinity of a higher-order `supernode' in the transmission spectrum of a nanoscale junction. Single-molecule junctions based on 3,3'-biphenyl and polyphenyl ether (PPE) are investigated in detail. The nonequilibrium thermodynamic efficiency and power output of a thermoelectric heat engine based on a 1,3-benzene junction are calculated using many-body theory, and compared to the predictions of the figure-of-merit ZT., Comment: 5 pages, 6 figures

Coherent electronic transport in single-molecule junctions is investigated in the Coulomb blockade regime. Both the transmission phase and probability are calculated for junctions with various contact symmetries. A dramatic suppression of the Coulomb blockade peaks is predicted for junctions where multiple atomic orbitals of the molecule couple to a single electrode although the charging steps are unaffected., Comment: 6 pages, 4 figures

A many-body theory of molecular junction transport based on nonequilibrium Green's functions is developed, which treats coherent quantum effects and Coulomb interactions on an equal footing. The central quantity of the many-body theory is the Coulomb self-energy matrix $\Sigma_{\rm C}$ of the junction. $\Sigma_{\rm C}$ is evaluated exactly in the sequential tunneling limit, and the correction due to finite tunneling width is evaluated self-consistently using a conserving approximation based on diagrammatic perturbation theory on the Keldysh contour. Our approach reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously in a single unified transport theory. As a first application of our theory, we have calculated the thermoelectric power and differential conductance spectrum of a benzenedithiol-gold junction using a semi-empirical $\pi$-electron Hamiltonian that accurately describes the full spectrum of electronic excitations of the molecule up to 8--10eV., Comment: 13 pages, 7 figures

An asymptotically exact quantum mechanical calculation of the matrix elements for tunneling through an asymmetric barrier is combined with the two-state statistical model for decay out of superdeformed bands to determine the energy barrier (as a function of spin) separating the superdeformed and normal-deformed wells for several nuclei in the 190 and 150 mass regions. The spin-dependence of the barrier leading to sudden decay out is shown to be consistent with the decrease of a centrifugal barrier with decreasing angular momentum. Values of the barrier frequency in the two mass regions are predicted., Comment: v1: 4 pages, 1 figure, 1 table. v2: 5 pages, 1 figure, 1 table; minor corrections and clarifications

A nanoscale variable resistor consisting of a metal nanowire (active element), a dielectric, and a gate, is proposed. By means of the gate voltage, stochastic transitions between different conducting states of the nanowire can be induced, with a switching time as fast as picoseconds. With an appropriate choice of dielectric, the transconductance of the device, which may also be considered an ``electromechanical transistor,'' is shown to significantly exceed the conductance quantum G_0=2e^2/h, a remarkable figure of merit for a nanoscale device., Comment: 6 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version will be superseded

We develop a theoretical approach to quantum transport through single conjugated organic molecules that accurately accounts for all molecular excited and ground states via a semi-empirical many-body molecular Hamiltonian. We then calculate the linear and non-linear transport properties of a benzenedithiol molecule covalently bonded to two gold electrodes at room temperature, eliminating all free parameters by comparing the calculated thermopower and linear-conductance with experiment. The resulting `molecular diamond' structure exhibits experimentally observed many-body effects inaccessible to mean-field approaches., Comment: A revised and significantly expanded treatment is given in arXiv:0812.0867

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier., Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev. E

We report experiments on aluminum nanowires in ultra-high vacuum at room temperature that reveal a periodic spectrum of exceptionally stable structures. Two "magic" series of stable structures are observed: At low conductance, the formation of stable nanowires is governed by electronic shell effects whereas for larger contacts atomic packing dominates. The crossover between the two regimes is found to be smooth. A detailed comparison of the experimental results to a theoretical stability analysis indicates that while the main features of the observed electron-shell structure are similar to those of alkali and noble metals, a sequence of extremely stable wires plays a unique role in Aluminum. This series appears isolated in conductance histograms and can be attributed to "superdeformed" non-axisymmetric nanowires., Comment: 15 pages, 9 figures

Superdeformed nuclei in the 190 mass region exhibit a striking universality in their decay-out profiles. We show that this universality can be explained in the two-level model of superdeformed decay as related to a strong separation of energy scales: a higher scale related to the nuclear interactions, and a lower scale caused by electromagnetic decay. Furthermore, we present the results of the two-level model for all decays for which sufficient data are known, including statistical extraction of the matrix element for tunneling through the potential barrier., Comment: 7 pages, 3 figures. v2: some minor clarifications, minor correction to Fig. 2

We experimentally investigated the decay behavior with time t of resonances near and at exceptional points, where two complex eigenvalues and also the associated eigenfunctions coalesce. The measurements were performed with a dissipative microwave billiard, whose shape depends on two parameters. The t^2-dependence predicted at the exceptional point on the basis of a two-state matrix model could be verified. Outside the exceptional point the predicted Rabi oscillations, also called quantum echoes in this context, were detected. To our knowledge this is the first time that quantum echoes related to exceptional points were observed experimentally., Comment: 10 pages, 3 figures

The Peierls instability in multi-channel metal nanowires is investigated. Hyperscaling relations are established for the finite-size-, temperature-, and wavevector-scaling of the electronic free energy. It is shown that the softening of surface modes at wavevector $q=2k_{F,\nu}$ leads to critical fluctuations of the wire's radius at zero temperature, where $k_{F,\nu}$ is the Fermi wavevector of the highest occupied channel. This Peierls charge density wave emerges as the system size becomes comparable to the channel correlation length. Although the Peierls instability is weak in metal nanowires, in the sense that the correlation length is exponentially long, we predict that nanowires fabricated by current techniques can be driven into the charge-density-wave regime under strain., Comment: 8 pages, 5 figures

A general linear stability analysis of simple metal nanowires is presented using a continuum approach which correctly accounts for material-specific surface properties and electronic quantum-size effects. The competition between surface tension and electron-shell effects leads to a complex landscape of stable structures as a function of diameter, cross section, and temperature. By considering arbitrary symmetry-breaking deformations, it is shown that the cylinder is the only generically stable structure. Nevertheless, a plethora of structures with broken axial symmetry is found at low conductance values, including wires with quadrupolar, hexapolar and octupolar cross sections. These non-integrable shapes are compared to previous results on elliptical cross sections, and their material-dependent relative stability is discussed., Comment: 12 pages, 4 figures

In a recent Letter [Appl. Phys. Lett. 87, 103104 (2005)], Yoshida et al. report that nonlinearities in current-voltage curves of gold quantum point contacts occur as a result of a shortening of the distance between electrodes at finite bias, presumably due to thermal expansion. For short wires, the electrode displacement induces a thickening of the wire, as well as nonlinearities of the IV curve, while the radius of long wires is left unchanged, thus resulting in a linear IV curve. We argue here that electron shell effects, which favor wires with certain "magic radii," prevent the thickening of long wires under compression, but have little effect on wires below a critical length., Comment: Version accepted for publication in Applied Physics Letters

The history and importance of superdeformation in nuclei is briefly discussed. A simple two-level model is then employed to obtain an elegant expression for the branching ratio for the decay via the E1 process in the normal-deformed band of superdeformed nuclei. From this expression, the spreading width Gamma^downarrow for superdeformed decay is found to be determined completely by experimentally known quantities. The accuracy of the two-level approximation is verified by considering the effects of other normal-deformed states. Furthermore, by using a statistical model of the energy levels in the normal-deformed well, we can obtain a probabilistic expression for the tunneling matrix element V., Comment: 8 pages, 3 figures, from a talk given at the conference Blueprints for the Nucleus: From First Principles to Collective Motion, May 17-22, 2004, Feza Gursey Institute, Istanbul, Turkey, A Festschrift in honor of Professor Bruce Barrett, http://www.physics.sdsu.edu/Istanbul/

We investigate multi-terminal quantum transport through single monocyclic aromatic annulene molecules, and their derivatives, using the nonequilibrium Green function approach in the self-consistent Hartree-Fock approximation. A new device concept, the Quantum Interference Effect Transistor (QuIET) is proposed, exploiting perfect destructive interference stemming from molecular symmetry, and controlling current flow by introducing decoherence and/or elastic scattering that break the symmetry. This approach overcomes the fundamental problems of power dissipation and environmental sensitivity that beset many nanoscale device proposals., Comment: 4 pages, 5 figures

Thermally induced conductance jumps of metal nanowires are modeled using stochastic Ginzburg-Landau field theories. Changes in radius are predicted to occur via the nucleation of surface kinks at the wire ends, consistent with recent electron microscopy studies. The activation rate displays nontrivial dependence on nanowire length, and undergoes first- or second-order-like transitions as a function of length. The activation barriers of the most stable structures are predicted to be universal, i.e., independent of the radius of the wire, and proportional to the square root of the surface tension. The reduction of the activation barrier under strain is also determined., Comment: 5 pages, 3 figures

This article presents a brief review of the nanoscale free-electron model, which provides a continuum description of metal nanostructures. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of metal nanowires, and that much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing factors. A linear stability analysis reveals that metal nanocylinders with certain magic conductance values G=1, 3, 6, 12, 17, 23, 34, 42, 51, 67, 78, 96, ... times the conductance quantum are exceptionally stable. A nonlinear dynamical simulation of nanowire structural evolution reveals a universal equilibrium shape consisting of a magic cylinder suspended between unduloidal contacts. The lifetimes of these metastable structures are also computed., Comment: 8 pages, 6 figures

We propose a new type of molecular transistor, the Quantum Interference Effect Transistor (QuIET), based on tunable current suppression due to quantum interference. We show that any aromatic hydrocarbon ring has two-lead configurations for which current at small voltages is suppressed by destructive interference. A transistor can be created by providing phase relaxation or decoherence at a site on the ring. We propose several molecules which could tunably introduce the necessary dephasing or decoherence, as well as a proof of principle using a scanning tunneling microscope tip. Within the self-consistent Hartree-Fock approximation, the QuIET is shown to have characteristics strikingly similar to those of conventional field effect and bipolar junction transistors., Comment: A provisional patent application has been filed for this invention

We develop a generalized grand canonical potential for the ballistic nonequilibrium electron distribution in a metal nanowire with a finite applied bias voltage. Coulomb interactions are treated in the self-consistent Hartree approximation, in order to ensure gauge invariance. Using this formalism, we investigate the stability and cohesive properties of metallic nanocylinders at ultrahigh current densities. A linear stability analysis shows that metal nanowires with certain {\em magic conductance values} can support current densities up to 10^11 A/cm^2, which would vaporize a macroscopic piece of metal. This finding is consistent with experimental studies of gold nanowires. Interestingly, our analysis also reveals the existence of reentrant stability zones--geometries that are stable only under an applied bias., Comment: 12 pages, 6 figures, version published in PRB

Experimental conductance histograms for Na nanowires are analyzed in detail and compared to recent theoretical results on the stability of cylindrical and elliptical nanowires, using the free-electron model. We find a one-to-one correspondence between the peaks in the histograms and the most stable nanowire geometries, indicating that several of the commonly observed nanowires have elliptical cross sections.

We introduce a continuum approach to studying the lifetimes of monovalent metal nanowires. By modelling the thermal fluctuations of cylindrical nanowires through the use of stochastic Ginzburg-Landau classical field theories, we construct a self-consistent approach to the fluctuation-induced `necking' of nanowires. Our theory provides quantitative estimates of the lifetimes for alkali metal nanowires in the conductance range 10 < G/G_0 < 100 (where G_0=2e^2/h is the conductance quantum), and allows us to account for qualitative differences in the conductance histograms of alkali vs. noble metal nanowires.

A stability analysis of metal nanowires shows that a Jahn-Teller deformation breaking cylindrical symmetry can be energetically favorable, leading to stable nanowires with elliptic cross sections. The sequence of stable cylindrical and elliptical nanowires allows for a consistent interpretation of experimental conductance histograms for alkali metals, including both the shell and supershell structures. It is predicted that for gold, elliptical nanowires are even more likely to form since their eccentricity is smaller than for alkali metals. The existence of certain metastable ``superdeformed'' nanowires is also predicted.

A new expression for the branching ratio for the decay via the E1 process in the normal-deformed band of superdeformed nuclei is given within a simple two-level model. Using this expression, the spreading or tunneling width Gamma^downarrow for superdeformed decay can be expressed entirely in terms of experimentally known quantities. We show how to determine the tunneling matrix element V from the measured value of Gamma^downarrow and a statistical model of the energy levels. The accuracy of the two-level approximation is verified by considering the effects of the other normal-deformed states., Comment: 4 pages, 4 figures

The conducting and thermodynamic properties of ballistic metallic nanocontacts with smooth shapes are investigated. All properties are related to the electronic scattering matrix, which is evaluated in the WKB approximation for independent electrons and in the self-consistent Hartree approximation for interacting electrons. Mesoscopic oscillations of order 1nN in the cohesive force and of order e in the contact charge are predicted when a metallic nanocontact is pulled apart, which are synchronized with quantized jumps in the conductance., Comment: 5 pages, 1 figure; corrected spelling of one author name on abstract page (paper is unchanged)

The surface dynamics and thermodynamics of metal nanowires are investigated in a continuum model. Competition between surface tension and electron-shell effects leads to a rich stability diagram, with fingers of stability extending to extremely high temperatures for certain magic conductance values. The linearized dynamics of the nanowire's surface are investigated, including both acoustic surface phonons and surface self-diffusion of atoms. On the stability boundary, the surface exhibits critical fluctuations, and the nanowire becomes inhomogeneous. Some stability fingers coalesce at higher temperatures, or exhibit overhangs, leading to reentrant behavior. The nonlinear surface dynamics of unstable nanowires are also investigated in a single-mode approximation. We find evidence that some unstable nanowires do not break, but rather neck down to the next stable radius., Comment: 9 pages, 5 figures, expanded version

When a macroscopic metallic wire is subject to tensile stress, it necks down smoothly as it elongates. We show that nanowires with radii comparable to the Fermi wavelength display remarkably different behavior. Using concepts from fluid dynamics, a PDE for nanowire shape evolution is derived from a semiclassical energy functional that includes electron-shell effects. A rich dynamics involving movement and interaction of kinks connecting locally stable radii is found, and a new class of universal equilibrium shapes is predicted., Comment: 4 pages, 3 postscript figures. New result on universal equilibrium shapes

Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green's function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent., Comment: 5 pages, 2 figures, presented at Pan-American Advanced Studies Institute (PASI) 2001: Physics and Technology at the Nanometer Scale

A remarkably quantitative understanding of the electrical and mechanical properties of metal wires with a thickness on the scale of a nanometer has been obtained within the free-electron model using semiclassical techniques. Convergent trace formulas for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, are derived. Mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force, whose amplitude depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1nN, in agreement with experiments on gold nanowires. A linear stability analysis shows that the classical instability of a long wire under surface tension can be completely suppressed by quantum effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the conductance quantum, in accord with recent results on alkali metal nanowires., Comment: 14 pages, 11 figures, lecture given at the Symposium on 30 Years of the Gutzwiller Trace Formula, German Physical Society Meeting, Hamburg, March 28, 2001

Metal nanowires exhibit a number of interesting properties: their electrical conductance is quantized, their shot-noise is suppressed by the Pauli principle, and they are remarkably strong and stable. We show that many of these properties can be understood quantitatively using a nanoscale generalization of the free-electron model. Possible technological applications of nanowires are also discussed., Comment: 8 pages, 5 postscript figures, lectures given at Pan-American Advanced Studies Institute on Physics and Technology at the Nanometer Scale

Experimental conductance histograms built from several thousand successive breakings of sodium nanowires exhibit peaks up to rather high conductance values (100 x 2e^2/h). In this paper, we present results from a disordered free-electron model of a metallic nanowire, which was previously successful in describing both conductance histograms and shot noise measurements in gold nanocontacts with much lower conductances. We find in particular that, with a modification of the model of disorder, the conductance histogram can be understood as an interplay of conductance quantization and disorder for low conductances (G < 10 x 2e^2/h), while peaks corresponding to higher conductance are actually a combination of several ``quantized conductance peaks''. We also predict a saturation of the shot noise at high conductance to about 1/10 of its classical value 2eI., Comment: 4 pages, 1 figure, to be published in the proceedings of the XXXVI Rencontres de Moriond

We study the persistent currents induced by both the Aharonov-Bohm and Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a side-branch quantum dot at Kondo resonance. For privileged values of the Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic Aharonov-Bohm flux, we find that the presence of the quantum dot has no effect on the persistent current. In contrast, the Kondo resonance interferes with the spin-dependent Aharonov-Casher effect to induce a current which, in the strong-coupling limit, is independent of the number of electrons in the ring., Comment: Replaced with published version; 5 pages

A linear stability analysis of metallic nanowires is performed in the free-electron model using quantum chaos techniques. It is found that the classical instability of a long wire under surface tension can be completely suppressed by electronic shell effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the quantum of conductance. Our results are quantitatively consistent with recent experiments with alkali metal nanowires., Comment: 10 pages, 5 eps figures, updated and expanded, accepted for publication in "Nonlinearity"

We study the influence of a magnetic impurity or ultrasmall quantum dot on the charge persistent current of a mesoscopic ring. The system consists of electrons in a one-dimensional ring threaded by spin-dependent Aharonov-Bohm/Casher fluxes, coupled via an antiferromagnetic exchange interaction to a localized electron. By passing to a basis of electron states with definite parities, the problem is mapped onto a Kondo model for the even-parity channel plus free electrons in the odd-parity channel. States of opposite parities decouple for values of the flux corresponding to periodic or antiperiodic boundary conditions. For these special cases, the model is solved exactly by a Bethe ansatz, allowing for an exact calculation of the charge persistent current. In particular we show that the charge stiffness in the special case of spin-independent fluxes is insensitive to the presence of the magnetic impurity/quantum dot., Comment: To appear in the Proceedings from "Electron Transport in Mesoscopic Physics", J. Low Temp. Phys. (in press); 5 pages

In a recent Letter, Nakamura et al. [Phys. Rev. Lett. 82, 1538 (1999)] described first principles calculations for a breaking Na nanocontact. Their system consists of a periodic one-dimensional array of supercells, each of which contains 39 Na atoms, originally forming a straight, crystalline wire with a length of 6 atoms. The system is elongated by increasing the length of the unit cell. At each step, the atomic configuration is relaxed to a new local equilibrium, and the tensile force is evaluated from the change of the total energy with elongation. Aside from a discontinuity of the force occuring at the transition from a crytalline to an amorphous configuration during the early stages of elongation, they were unable to identify any simple correlations between the force and the number of electronic modes transmitted through the contact. An important question is whether their model is realistic, i.e., whether it can be compared to experimental results obtained for a single nanocontact between two macroscopic pieces of metal. In this Comment, we demonstrate that with such a small unit cell, the interference effects between neighboring contacts are of the same size as the force oscillations in a single nanocontact., Comment: 1 page

In a recent letter (Phys.Rev.Lett. 82, 1526 (1999)), van den Brom and van Ruitenbeek found a pronounced suppression of the shot noise in atom-size gold contacts with conductances near integer multiples of $G_0=2e^2/h$, revealing unambiguously the quantized nature of the electronic transport. However, the ad hoc model they introduced to describe the contribution of partially-open conductance channels to the shot noise is unable to fit either the maxima or minima of their shot noise data. Here we point out that a model of quantum-confined electrons with disorder quantitatively reproduces their measurements., Comment: 1 page, 1 figure, submitted to Phys. Rev. Lett

Convergent semiclassical trace formulae for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, are derived. It is shown that mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force: the amplitude of the oscillations depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1 nano-Newton, in agreement with recent experiments. Interestingly, quantum tunneling is shown to be described quantitatively in terms of the instability of the classical periodic orbits., Comment: corrects spelling of one author name on abstract page (paper is unchanged)

Recent theoretical investigations of the decay mechanism out of a superdeformed nuclear band have yielded qualitatively different results, depending on the relative values of the relevant decay widths. We present a simple two-level model for the dynamics of the tunneling between the superdeformed and normal-deformed bands, which treats decay and tunneling processes on an equal footing. The previous theoretical results are shown to correspond to coherent and incoherent limits of the full tunneling dynamics. Our model accounts for experimental data in both the A~150 mass region, where the tunneling dynamics is coherent, and in the A~190 mass region, where the tunneling dynamics is incoherent., Comment: 4 pages

The cohesion and conductance of a point contact in a two-dimensional metallic nanowire are investigated in an independent-electron model with hard-wall boundary conditions. All properties of the nanowire are related to the Green's function of the electronic scattering problem, which is solved exactly via a modified recursive Green's function algorithm. Our results confirm the validity of a previous approach based on the WKB approximation for a long constriction, but find an enhancement of cohesion for shorter constrictions. Surprisingly, the cohesion persists even after the last conductance channel has been closed. For disordered nanowires, a statistical analysis yields well-defined peaks in the conductance histograms even when individual conductance traces do not show well-defined plateaus. The shifts of the peaks below integer multiples of $2e^2/h$, as well as the peak heights and widths, are found to be in excellent agreement with predictions based on random matrix theory, and are similar to those observed experimentally. Thus abrupt changes in the wire geometry are not necessary for reproducing the observed conductance histograms. The effect of disorder on cohesion is found to be quite strong and very sensitive to the particular configuration of impurities at the center of the constriction., Comment: 10 pages, 7 figures, submitted to Phys. Rev. B, discussions of the equilibrium geometry and of the effects of disorder on the cohesion have been modified

The conducting and mechanical properties of a metallic nanowire formed at the junction between two macroscopic metallic electrodes are investigated. Both two- and three-dimensional wires with a W(ide)-N(arrow)-W(ide) geometry are modelled in the free-electron approximation with hard-wall boundary conditions. Tunneling and quantum-size effects are treated exactly using the scattering matrix formalism. Oscillations of order E_F/lambda_F in the tensile force are found when the wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance. The force and conductance are shown to be essentially independent of the width of the wide sections (electrodes). The exact results are compared with an adiabatic approximation; the later is found to overestimate the effects of tunneling, but still gives qualitatively reasonable results for nanowires of length L>>lambda_F, even for this abrupt geometry. In addition to the force and conductance, the net charge of the nanowire is calculated and the effects of screening are included within linear response theory. Mesoscopic charge fluctuations of order e are predicted which are strongly correlated with the mesoscopic force fluctuations. The local density of states at the Fermi energy exhibits nontrivial behavior which is correlated with fine structure in the force and conductance, showing the importance of treating the whole wire as a mesoscopic system rather than treating only the narrow part., Comment: 23 pages, 8 figures

The ground state persistent current and electron addition spectrum in two-dimensional quantum dot arrays and one-dimensional quantum dot rings, pierced by an external magnetic flux, are investigated using the extended Hubbard model. The collective multidot problem is shown to map exactly into the strong field noninteracting finite-size Hofstadter butterfly problem at the spin polarization transition. The finite size Hofstadter problem is discussed, and an analytical solution for limiting values of flux is obtained. In weak fields we predict novel flux periodic oscillations in the spin component along the quantization axis with a periodicity given by $\nu h/e$ ($\nu \le 1$). The sensitivity of the calculated persistent current to interaction and disorder is shown to reflect the intricacies of various Mott-Hubbard quantum phase transitions in two- dimensional systems: the persistent current is suppressed in the antiferromagnetic Mott-insulating phase governed by intradot Coulomb interactions; the persistent current is maximized at the spin density wave - charge density wave transition driven by the nearest neighbor interdot interaction; the Mott-insulating phase persistent current is enhanced by the long-range interdot interactions to its noninteracting value; the strong suppression of the noninteracting current in the presence of random disorder is seen only at large disorder strengths; at half filling even a relatively weak intradot Coulomb interaction enhances the disordered noninteracting system persistent current; in general, the suppression of the persistent current by disorder is less significant in the presence of the long-range interdot Coulomb interaction., Comment: 50 pages, 21 figures, 3 tables

Coherent resonant tunneling through an artificial molecule of quantum dots in an inhomogeneous magnetic field is investigated using an extended Hubbard model. Both the multiterminal conductance of an array of quantum dots and the persistent current of a quantum dot molecule embedded in an Aharanov-Bohm ring are calculated. The conductance and persistent current are calculated analytically for the case of a double quantum dot and numerically for larger arrays using a multi-terminal Breit-Wigner type formula, which allows for the explicit inclusion of inelastic processes. Cotunneling corrections to the persistent current are also investigated, and it is shown that the sign of the persistent current on resonance may be used to determine the spin quantum numbers of the ground state and low-lying excited states of an artificial molecule. An inhomogeneous magnetic field is found to strongly suppress transport due to pinning of the spin-density-wave ground state of the system, and giant magnetoresistance is predicted to result from the ferromagnetic transition induced by a uniform external magnetic field., Comment: 23 pages, 12 figures