Resonant tunneling through a C60 molecular junction in liquid environment

We present electronic transport measurements through thiolated C$_{60}$ molecules in liquid environment. The molecules were placed within a mechanically controllable break junction using a single anchoring group per molecule. When varying the electrode separation of the C$_{60}$-modified junctions, we observed a peak in the conductance traces. The shape of the curves is strongly influenced by the environment of the junction as shown by measurements in two distinct solvents. In the framework of a simple resonant tunneling model, we can extract the electronic tunneling rates governing the transport properties of the junctions.Comment: 13 pages, 4 figures. To appear in Nanotechnolog

Effective interaction between molecules in the BEC regime of a superfluid Fermi gas

We investigate the effective interaction between Cooper-pair molecules in the st rong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analy sis of fluctuations in a single-channel model. We show that a physical cutoff en ergy $\omega_c$ originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work t hus clarifies recent results by showing that $a_{\rm M}=2a_{\rm F}$ is a {\it ba re} molecular scattering length while $a_{\rm M}=(0.6\sim0.75) a_{\rm F}$ is the low energy molecular scattering length renormalized to include high-energy scat tering up to $\omega_c$ (here $a_{\rm F}$ is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that $a_{\rm M}$ is strongly dependent on temperature, vanishing at $T_{\rm c}$, consistent with the earlier Bose gas results of Bijlsma and Stoof.Comment: 10 pages, 3 figure

The transition temperature of the dilute interacting Bose gas

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.Comment: 4 pages, Revtex, to be published in Physical Review Letter

The effect of disorder on the critical temperature of a dilute hard sphere gas

We have performed Path Integral Monte Carlo (PIMC) calculations to determine the effect of quenched disorder on the superfluid density of a dilute 3D hard sphere gas. The disorder was introduced by locating set of hard cylinders randomly inside the simulation cell. Our results indicate that the disorder leaves the superfluid critical temperature basically unchanged. Comparison to experiments of helium in Vycor is made.Comment: 4 pages, 4 figure

Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates

We formulate a conserving gapless mean-field theory for Bose-Einstein condensates on the basis of a Luttinger-Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$ and s-wave scattering length $a$ to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $\Delta T_c$ from the ideal-gas result $T_{0}$ is positive and given to the leading order by $\Delta T_c = 2.33a n^{1/3}T_0$, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.Comment: Minor errors remove

Self-consistent equation for an interacting Bose gas

We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential $V(r)$ such that 0<\int d\br V(r) = a<\infty. Expressing the partition function by the Feynman-Kac functional integral yields a classical-like polymer representation of the quantum gas. With Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation $\rho (\mu)=F(\mu-a\rho(\mu))$ between the density $\rho$ and the chemical potential $\mu$, valid in the range of convergence of Mayer series. The function $F$ is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in the mean-field limit $\gamma\to 0$ only tree diagrams contribute and function $F$ reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of Mayer series (vicinity of Bose-Einstein condensation) and study dominant corrections to mean field. At lowest order, the form of function $F$ is shown to depend on single polymer partition function for which we derive lower and upper bounds and on the resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.

Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor

Shot noise suppression at room temperature in atomic-scale Au junctions

Shot noise encodes additional information not directly inferable from simple electronic transport measurements. Previous measurements in atomic-scale metal junctions at cryogenic temperatures have shown suppression of the shot noise at particular conductance values. This suppression demonstrates that transport in these structures proceeds via discrete quantum channels. Using a high frequency technique, we simultaneously acquire noise data and conductance histograms in Au junctions at room temperature and ambient conditions. We observe noise suppression at up to three conductance quanta, with possible indications of current-induced local heating and $1/f$ noise in the contact region at high biases. These measurements demonstrate the quantum character of transport at room temperature at the atomic scale. This technique provides an additional tool for studying dissipation and correlations in nanodevices.Comment: 15 pages, 4 figures + supporting information (6 pages, 6 figures

The density dependence of the transition temperature in a homogenous Bose flui

Transition temperature data obtained as a function of particle density in the $^4$He-Vycor system are compared with recent theoretical calculations for 3D Bose condensed systems. In the low density dilute Bose gas regime we find, in agreement with theory, a positive shift in the transition temperature of the form $\Delta T/T_0 = \gamma(na^{3})^{1/3}$. At higher densities a maximum is found in the ratio of $T_c /T_0$ for a value of the interaction parameter, na$^3$, that is in agreement with path-integral Monte Carlo calculations.Comment: 4 pages, 3 figure

Index estimates for free boundary minimal hypersurfaces

We show that the Morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of its first relative homology group (which is at least as big as the number of its boundary components, minus one). In ambient dimension three, this implies a lower bound for the index of a free boundary minimal surface which is linear both with respect to the genus and the number of boundary components. Thereby, the compactness theorem by Fraser and Li implies a strong compactness theorem for the space of free boundary minimal surfaces with uniformly bounded Morse index inside a convex domain. Our estimates also imply that the examples constructed, in the unit ball, by Fraser–Schoen and Folha–Pacard–Zolotareva have arbitrarily large index. Extensions of our results to more general settings (including various classes of positively curved Riemannian manifolds and other convexity assumptions) are discussed