Kelly R. Patton

Thermal transport through a mesoscopic weak link

We calculate the rate of energy flow between two macroscopic bodies, each in thermodynamic equilibrium at a different temperature, and joined by a weak mechanical link. The macroscopic solids are assumed to be electrically insulating, so that thermal energy is carried only by phonons. To leading order in the strength of the weak link, modeled here by a harmonic spring, the thermal current is determined by a product of the local vibrational density-of-states of the two bodies at the points of connection. Our general expression for the thermal current can be regarded as a thermal analog of the well-known formula for the electrical current through a resistive barrier. It is also related to the thermal Landauer formula in the weak-tunneling limit. Implications for heat transport experiments on dielectric quantum point-contacts are discussed.

Phonons in a nanoparticle mechanically coupled to a substrate

The discrete nature of the vibrational modes of an isolated nanometer-scale solid dramatically modifies its low-energy electron and phonon dynamics from that of a bulk crystal. However, nanocrystals are usually coupled\char22{}even if only weakly so\char22{}to an environment consisting of other nanocrystals, a support matrix, or a solid substrate, and this environmental interaction will modify the vibrational properties at low frequencies. In this paper we investigate the modification of the vibrational modes of a spherical insulating nanoparticle caused by a weak mechanical coupling to a semi-infinite substrate. The phonons of the bulk substrate act as a bath of harmonic oscillators, and the coupling to this reservoir shifts and broadens the nanoparticles modes. The vibrational density of states in the nanoparticle is obtained by solving the Dyson equation for the phonon propagator, and we show that environmental interaction is especially important at low frequencies. As a probe of the modified phonon spectrum, we consider nonradiative energy relaxation of a localized electronic impurity state in the nanoparticle, for which good agreement with a recent experiment is found.

Theory of electron-phonon dynamics in insulating nanoparticles

We discuss the rich vibrational dynamics of nanometer-scale semiconducting and insulating crystals as probed by localized electronic impurity states, with an emphasis on nanoparticles that are only weakly coupled to their environment. Two principal regimes of electron-phonon dynamics are distinguished, and a brief survey of vibrational-mode broadening mechanisms is presented. Recent work on the effects of mechanical interaction with the environment is discussed.

Phonon spectrum in a nanoparticle mechanically coupled to a substrate

Abstract We calculate the vibrational density-of-states in an insulating nanoparticle that is in weak mechanical contact with a semi-infinite substrate. The work is motivated by a recent experiment by Yang et al., where the low-energy phonon density-of-states of Y2O3 nanoparticles doped with Eu3+ was measured. Preliminary results presented here, based on the conventional quasiparticle-pole approximation for the phonon propagator, are in reasonable agreement with experiment.

Thermodynamic equivalence of certain ideal Bose and Fermi gases

It has been established recently that there is an interesting thermodynamic “equivalence” between noninteracting Bose and spinless Fermi gases in two dimensions, and between one-dimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble. These are known to be special cases of a larger class of equivalences of noninteracting systems having an energy-independent single-particle density of states (DOS). Furthermore, the thermodynamic equivalence has also been established for any noninteracting quantum gas with a discrete ladder-type spectrum in the canonical ensemble. Here we investigate the intriguing possibility that the equivalence for systems with a constant DOS is a special case of a more general equivalence between noninteracting Bose and Fermi gases with a discrete ladder-type spectrum in the grand-canonical ensemble, which reduces to the constant-DOS case when the level-spacing approaches zero. By direct numerical calculation of the Bose and Fermi grand-canonical free energies, we conclude that the grand-canonical equivalence does not apply to the ladder-spectrum case.

Infrared catastrophe and tunneling into strongly correlated electron systems : Beyond the x-ray edge limit

We develop a nonperturbative method to calculate the electron propagator in low-dimensional and strongly correlated electron systems. The method builds on our earlier work using a HubbardStratonovich transformation to map the tunneling problem to the x-ray edge problem, which accounts for the infrared catastrophe caused by the sudden introduction of a new electron into a conductor during a tunneling event. Here we use a cumulant expansion to include fluctuations about this x-ray edge limit. We find that the dominant effect of electron-electron interaction at low energies is to correct the noninteracting Green’s function by a factor e , where S can be interpreted as the Euclidean action for a density field describing the time-dependent charge distribution of the newly added electron. Initially localized, this charge distribution spreads in time as the electron is accommodated by the host conductor, and during this relaxation process action is accumulated according to classical electrostatics with a screened interaction. The theory applies to lattice or continuum models of any dimensionality, with or without translational invariance. In one dimension the method correctly predicts a power-law density of states (DOS) for electrons with short-range interaction and no disorder, and when applied to the solvable Tomonaga-Luttinger model, the exact DOS is obtained.

Mesoscopic thermal transport through a weak link

We consider mesoscopic thermal transport between two bulkdielectrics joined by a narrow wire or weak mechanical link. In the ‘‘tunneling’’ regime where the phonon transmission probability through the link is small and the thermal conductance is much less than pk 2T=6_; the thermal current is determined by a product of the local vibrational spectral densities of the two bodies. We derive an expression for the thermal current that is a thermal analog of the wellknown formula for the electrical current through a tunneling barrier. r 2002 Elsevier Science B.V. All rights reserved.

Trapped imbalanced fermionic superfluids in one dimension: A variational approach

We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Although we find no signature of the FFLO state in the densities of the two fermion species, we show that the oscillations of the order parameter appear in density-density correlations, both in-situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.

A fully controllable Kondo system: Coupling a flux qubit and an ultracold Fermi gas

We show that a composite spin-1/2 Kondo system can be formed by coupling a superconducting quantum interference device (SQUID) to the internal hyperfine states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit, acts as an effective magnetic impurity that induces spin-flip scattering near the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are at vastly different temperatures, the formation of a strongly correlated Kondo state between the two systems is found when the gas is cooled below the Kondo temperature; this temperature regime is within current experimental limits. Furthermore, the momentum distribution of the trapped fermions is calculated. We find that it clearly contains an experimental signature of this correlated state and the associated Kondo screening length. In addition to probing Kondo physics, the controllability of this system can be used to systematically explore the relaxation and equilibration of a strongly correlated system that has been initially prepared in a selected nonequilibrium state.

Infrared catastrophe and tunneling into strongly correlated electron systems : Exact x-ray edge limit for the one-dimensional electron gas and two-dimensional hall fluid

In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Greens function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the 1D electron gas and 2D Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozieres-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the 1D case but finding no changes in the DOS of the 2D Hall fluid with short-range interaction. We also provide, for the first time, an exact solution of the Nozieres-De Dominicis equation for the 2D electron gas in the lowest Landau level.