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A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wavefunction in the molecular limit, we determine the critical value for the polaron to molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et. al. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron to molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance., Comment: 10 pages, 4 figures, RevTex4, minor changes, references added

We discuss the suppression of Coulomb effects in the low temperature conductanceg(T) of small tunnel junctions with increasing dissipation or bare conductanceg. The conductance is expressed in terms of the spin correlation fuction of a classical one dimensionalXY-model with ferromagnetic nearest neighbor plus inverse square interaction. It is shown that at low temperatures the conductance vanishes asymptotically likeT2 instead of exponentially. A Coulomb gap in the sense of a thermally activated contribution tog(T) is present only for bare conductances smaller thangc∼1. A simple model for the spin correlation functions is compared with experiments.

We study the diffusion of a quantum Brownian particle in a one-dimensional periodic potential with substitutional disorder. The particle is coupled to a dissipative environment, which induces a frictional force proportional to the velocity. The dynamics for arbitrary temperature is studied by using Feynman's influence-functional theory. We calculate the mobility to lowest order in the disorder and strength of the periodic potential. It is shown that for weak dissipation the linear mobility, which vanishes atT=0 due to localization effects, may exhibit a maximum and a subsequent minimum with increasing temperature. The relation to the diffusion of heavy particles in metals or doped semiconductors is briefly discussed.

Based on the recent free electron model for cohesion in narrow metallic constrictions by Stafford et al., we calculate the quantum fluctuations in the cohesive force versus elongation. The fluctuations are dominated by states near the Fermi energy, thus explaining their apparently universal magnitude of order epsilon_F/lambda_F. We present numerical results for the force fluctuations in a simple geometry and show that they are well described by the contributions of a few classical periodic orbits in the Balian-Bloch trace formula for the density of states of transverse motion., Comment: 4 pages, 2 figures, RevTeX, minor changes, to appear in Phys. Rev. B Rapid. Comm

We discuss the phase diagram of regular networks of quantum mechanical Josephson junctions in one and two dimensions for different choices of the Coulomb interaction between pairs. In a particular case this is equivalent to a quantum interface with lateral tunneling along the boundary. Using a functional integral approach the partition function is transformed into that of classical roughening or Coulomb gas problems. It is shown, in particular, that the structure of the phase diagram depends crucially on the form of the Coulomb interaction and that with dissipative interactions both globally and locally superconducting phases are possible. The relation of our results to recent experiments on granular superconducting films and ideal Josephson junction arrays is discussed briefly.

Recent experiments on granular films have shown an apparently universal maximum normal state sheet resistance of around 6.5 kΩ above which superconductivity cannot be established. A possible explanation for this phenomenon is presented which is based on the competition between quantum fluctuations in the phase of the superconducting order parameter and dissipative effects. The films are modelled by locally superconducting grains coupled through Josephson junctions. Quantum fluctuations in the phases of individual grains may lead to a state in which the Cooper pair number rather than its conjugate phase is a good quantum number and superconductivity is destroyed. Dissipative effects tend to suppress these fluctuations and lead to the appearance of a new type of superconducting state possessing only short range phase coherence. This occurs for normal state resistances smaller than the quantum unit h/4e 2=6.5 kΩ, in agreement with the experimentally observed threshold.

A quantum theory of cooling of a mechanical oscillator by radiation pressure-induced dynamical back-action is developed, which is analogous to sideband cooling of trapped ions. We find that final occupancies well below unity can be attained when the mechanical oscillation frequency is larger than the cavity linewidth. It is shown that the final average occupancy can be retrieved directly from the optical output spectrum., Comment: 5 pages, 2 figures

We show that strong pairing correlations in Fermi gases lead to the appearance of a gap-like structure in the RF-spectrum, both in the balanced superfluid and in the normal phase above the Clogston-Chandrasekhar limit. The average RF-shift of a unitary gas is proportional to the ratio of the Fermi velocity and the scattering length with the final state. In the strongly imbalanced case, the RF-spectrum measures the binding energy of a minority atom to the Fermi sea of majority atoms. Our results provide a qualitative understanding of recent experiments by Schunck et.al., Comment: revised version, 4 pages, 3 figures, RevTex4

We study the interaction of two localized impurities in a repulsive one-dimensional Fermi liquid via bosonization. In a previous paper [Phys. Rev. A 72, 023616 (2005)], it was shown that at distances much larger than the interparticle spacing the impurities interact through a Casimir-type force mediated by the zero sound phonons of the underlying quantum liquid. Here we extend these results and show that the strength and sign of this Casimir interaction depend sensitively on the impurities separation. These oscillations in the Casimir interaction have the same period as Friedel oscillations. Their maxima correspond to tunneling resonances tuned by the impurities separation., This paper is a continuation of Phys. Rev. A 72, 023616 (2005). v2: two appendix added

We calculate the damping of the Bogoliubov-Anderson mode in a one-dimensional two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-Ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther-Emery liquid of weakly bound pairs to a Lieb-Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks-Girardeau gas with a universal constant $\alpha_{\zeta}=0.38$ in the viscosity $\zeta=\alpha_{\zeta}\hbar n$ for T=0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases., Comment: 9 pages, 3 figures, published version (minor changes)

We discuss the effective interactions between two localized perturbations in one-dimensional (1D) quantum liquids. For non-interacting fermions, the interactions exhibit Friedel oscillations, giving rise to a RKKY-type interaction familiar from impurity spins in metals. In the interacting case, at low energies, a Luttinger liquid description applies. In the case of repulsive fermions, the Friedel oscillations of the interacting system are replaced, at long distances, by a universal Casimir-type interaction which depends only on the sound velocity and decays inversely with the separation. The Casimir-type interaction between localized perturbations embedded in a fermionic environment gives rise to a long range coupling between quantum dots in ultracold Fermi gases, opening a novel alternative to couple qubits with neutral atoms. We also briefly discuss the case of bosonic quantum liquids in which the interaction between weak impurities turns out to be short ranged, decaying exponentially on the scale of the healing length., Comment: 14 pages, 1 figure, to appear in Phys. Rev. A

Cold atoms in optical lattices provide a novel class of many body systems with widely tunable interactions. They allow quantum state engineering of complex many body states and a study of their associated quantum phase transitions, including dynamics. Basic phenomena in strong correlation physics like the Mott-Hubbard-transition, the BCS-BEC-crossover, Luttinger-liquids or quantum impurity problems can be realized. As two simple examples, we discuss the superfluid to Mott-insulator transition of Bosons and Luttinger-liquid physics in 1D atomic wires.

We investigate a quasi-one-dimensional system of trapped cold bosonic atoms in an optical lattice by using the density-matrix renormalization group to study the Bose-Hubbard model at T= 0 for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local-density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half-width of the interference peak.

We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed., corrected typos, minor modifications, submitted version

We study the dynamic structure factor for density and spin within the crossover from BCS superfluidity of atomic fermions to the Bose-Einstein condensation of molecules. Both structure factors are experimentally accessible via Bragg spectroscopy, and allow for the identification of the pairing mechanism: the spin structure factor allows for the determination of the two particle gap, while the collective sound mode in the density structure reveals the superfluid state., Comment: 4 pages, 3 figures

We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength, and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time-of-flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii- or Bogoliubov-type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behavior.

It is shown that the Goldstone modes associated with a broken continuous symmetry lead to anomalously large fluctuations of the zero field order parameter at any temperature below T_c. In dimensions 2, Comment: final version, minor changes

An important characteristic of a superfluid is the critical temperature Tc , below which it forms from an ordinary fluid, but a more detailed understanding comes from measuring other thermodynamic and quantum-mechanical parameters. For systems in which the superfluid is created by pairing fermions (for example, the electron superfluid in superconductors), Tc is often very low compared to another characteristic temperature of mobile fermions, their Fermi temperature T F. Thus, superconductivity has not been observed at room temperature. On page 563 of this issue, Ku et al. ( 1 ) present precise measurements of thermodynamic quantities of an ultracold gas of lithium-6 atoms—fermions—with strong attractive interactions that explicitly show the superfluid transition through changes in the compressibility and the heat capacity. The absolute temperatures here are on the order of only 100 nK, but this Fermi gas provides an example of a high-temperature superfluid: No other system has ever been observed with a transition temperature as high as ∼16% of T F. Scaled to the density of electrons in metals, T c would occur far above room temperature.

We calculate the vertex corrections within a model for fermion quasiparticles coupled with charge and spin fluctuations, which provide the relevant scattering mechanism near the stripe instability in high- ${T}_{c}$ cuprates. The logarithmic divergence of the vertex, which characterizes the spin-fermion model near the antiferromagnetic instability, is ruled out, due to the incommensuration of the charge and spin modulation within the stripe phase, as revealed by neutron scattering. This simplifies the skeleton structure of the problem. The vertex is negative in the relevant kinematical regime, effectively reducing the interaction strength. Our results apply to generic incommensurate instabilities of electronic origin.

We observe transport of electrons through a metallic island on the tip of a nanomechanical pendulum. The resulting tunneling current shows distinct features corresponding to the discrete mechanical eigenfrequencies of the pendulum. We report on measurements covering the temperature range from 300 K down to 4.2 K. We explain the I-V curve, which differs from previous theoretical predictions, with model calculations based on a Master equation approach., 5 pages, 4 jpeg-figures

By considering the stability of potential flow of a superfluid around large obstacles of size R, we derive an analytical result for the critical velocity that is of order ${v}_{c}\ensuremath{\sim}\ensuremath{\Elzxh}/mR,$ scaling inversely with obstacle size, in contrast to what is obtained from a Landau criterion. Our results are compared with numerical solutions of the Gross-Pitaevskii equation and with recent measurements of the critical velocity in Bose-Einstein condensates of dilute atomic gases.

We show that the condensate occupation of a superfluid Bose liquid quite generally exhibits anomalously large fluctuations at finite temperatures. In three dimensions, the variance scales like T^2 V^{4/3} at low T, generalizing the result obtained by Giorgini, Pitaevskii, and Stringari for a weakly interacting Bose gas. In two dimensions there is only a quasicondensate, and the fluctuations are of the same order as the mean value., 3 pages, Revtex, no figures. submitted to PRA

Motivated by recent experiments, we calculate both the average current and the current fluctuations for a metallic island which oscillates between two symmetric electrodes. Electrons can only tunnel on or off the island when it is close to one of the electrodes. Using a Master equation we investigate the accuracy of such an electron shuttle both analytically and numerically. It is shown that optimum operation is reached when the contact time is much larger than the RC-time., RevTeX, 8 pages, 5 figures

Based on a tunneling Hamiltonian description, we calculate the Josephson, normal and interference currents between two Bose-Einstein condensates described by the Bogoliubov theory. The dominant Josephson term is of first order in the tunneling with a critical current density proportional to the ground state pressure. In contrast to superconductors, the normal current remains finite at zero temperature. We discuss the dynamics of the relative phase in a semiclassical approximation derived from an exact functional integral approach, which includes the interaction effects at fixed total particle number. It is shown that the normal current leads to a damping of the Josephson oscillations and, at long times, eliminates the macroscopic quantum self trapping predicted by Smerzi et.al. Finally we give estimates for an experimental realization of Josephson tunneling in cold atomic gases, which indicate that coherent transfer of atoms might be realized with a $^{23}$Na condensate., Comment: 13 pages, 5 figures, RevTeX, largely extended version of earlier manuscript

We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a reentrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder., Comment: 4 pages, 2 eps figures, uses RevTeX

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like $T^{-a} \exp(b/T)$ with $a=(N-2)/(N-1)$ and $b=2\pi^2/(N-1)$. From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains., Comment: 6 pages, 3 eps figures, to appear in Eur. Phys. J. B (1998)

Recent measurements have shown oscillations in the upper critical field of simply connected mesoscopic superconductors. A quantitative theory of these effects is given here on the basis of a Ginzburg-Landau description. For small fields, the $H-T$ phase boundary exhibits a cusp where the screening currents change sign for the first time thus defining a lower critical field $H_{c1}$. In the limit where many flux quanta are threading the sample, nucleation occurs at the boundary and the upper critical field becomes identical with the surface critical field $H_{c3}$., Comment: 5 pages (Revtex and 2 PostScript figures), to apppear in Z. Phys. B

We use Feynman's influence-functional theory to study the quantum dynamics of a heavy particle moving in a free Fermi gas with arbitrary average velocity. A semiclassical expansion yields a nonlinear Langevin equation with the exact friction coefficient as derived in an earlier publication. The fluctuations around a steady state far from equilibrium are due to a nonclassical state-dependent noise term and can be described by a diffusion constant. In the limit of zero average velocity, the Einstein relation is fulfilled for arbitrary temperatures

Un calcul de la theorie exacte de la diffusion, pour la densite des electrons autour des impuretes localisees dans les metaux volumiques pour un courant de transport quelconque, est effectue dans le cadre de l'approximation du gaz de Fermi non interactif. Au premier ordre dans le courant de transport, on recouvre le dipole de la resistivite residuelle de Landauer, plus des oscillations de Friedel supplementaires. Les calculs numeriques de la densite pour des courants arbitraires sont effectues pour les cas uni-, bi-, et tri-dimensionnels

Granular superconductors are strongly inhomogeneous systems consisting of locally superconducting grains in an insulating matrix. In these lectures we will discuss the consequences of the Coulomb interaction on the mesoscopic scale of grains and of dissipative effects in these systems. Throughout we assume that the granular system may be modelled as a network of tunnel junctions which are normal junctions above and Josephson junctions below the transition to local superconductivity at T c l . The lectures are organized as follows: section 2 starts with a discussion of tunneling in non-superconducting granular systems and in particular the behavior of the conductance due to the effects of finite size and charging in small grains. In section 3 we discuss the appearance of local superconductivity within the grains and the Josephson coupling between them. It is shown that both thermal fluctuations and Coulomb effects may lead to a destruction of global superconductivity. The influence of dissipative effects associated with normal electron tunneling is treated in section 4 for single junctions. In section 5 we determine the phase diagram at zero temperature of one and two-dimensional (2 D) networks of quantum Josephson junctions including dissipation. Finally in section 6 we discuss corresponding experiments on artificially created Josephson junction arrays and very thin granular films.

It is shown that the dephasing which suppresses the weak localization correction to the conductivity has the same physical origin than pair-breaking in superconductors and thus-following de Gennes-may be expressed in terms of the correlation function of the operator for time reversal.

The random walk of a particle in two models of an ideal lattice with internal states has been studied. In the first model one vertical ladder of energy levels exists at each lattice site, in the second model different ladders of levels lead to neighboring sites. In thermal equilibrium, the mobility of the particle was found frequency-independent in the first model and frequency-dependent in the second. The continuous-time random walk (CTRW) description of both models has been investigated. The waiting-time distribution for the first case has been obtained analytically in the Laplace domain. An example for φ (t) has been calculated numerically by inverse Laplace transformation. In the second case an extension of the CTRW description to a backward jump model has been performed and the corresponding waiting-time distributions have been calculated.

This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For $sl1$ the system is localized at zero temperature, and at finite $T$ relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For $sg2$ it undergoes underdamped coherent oscillations for all relevant temperatures, while for $1lsl2$ there is a crossover from coherent oscillation to overdamped relaxation as $T$ increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case, $s=1$, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature $T$: over most of the ($\ensuremath{\alpha}$,$T$) plane (including the whole region $\ensuremath{\alpha}g1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low $T$ and $0l\ensuremath{\alpha}l\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.

The coupling between the phase and the electromagnetic field in the case of a tunnel junction is treated by Feynmans path integral method. It is shown that the elimination of the field leads to a frequency dependent mass for the motion of the phase ψ, which is simply related to the effective dielectric constant of the junction. Considering tunneling as a motion in imaginary time one obtains a polaron like mass enhancement connected to the dielectric function at positive imaginary frequencies, which essentially leads to the Caldeira-Leggett reduction of the elastic tunneling probability. In the weak damping limit it is shown that the emission of real excitations during tunneling is a higher order effect. At low temperatures the damping finally is determined by the linewidth of electromagnetic radiation at the Josephson plasma frequency.

We study a simple quantum-mechanical generalization of the resistively shunted junction model to describe the current-voltage characteristic of a single Josephson junction. An exact series representation is given for the nonlinear resistance, which is valid for arbitrary temperature and dissipation and includes both classical and quantum phase slips. For sufficiently high temperature, the quantum effects disappear and \ensuremath{\Elzxh} cancels from the corresponding series. The resulting expression is equivalent to classical Brownian motion in a periodic potential with friction coefficient \ensuremath{\gamma}. We derive a rigorous expression for the leading quantum corrections to the classical result which are of order ${\ensuremath{\Elzxh}}^{2}$. In the overdamped limit they are equivalent to a renormalization of the barrier, whereas for \ensuremath{\gamma}\ensuremath{\rightarrow}0 they are bounded below by the effect of an additional bias of order \ensuremath{\Elzxh}\ensuremath{\gamma}. An approximate continued fraction is derived for the resistance in the general case, which becomes exact in the classical high-damping limit. It is evaluated numerically and leads to reasonable qualitative results for small barriers, unless the temperature approaches zero. We discuss the possibility of seeing the quantum effects in junctions with small capacity, in particular the existence of a regime with negative differential resistance and the implications of our results to the quasireentrant behavior observed in thin superconducting granular films.

A phenomenological model is introduced for the dissipative quantum dynamics of the phase $\ensuremath{\varphi}$ across a current-biased Josephson junction. The model is invariant under $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\varphi}+2\ensuremath{\pi}$. This enables us to restrict $\ensuremath{\varphi}$ to the interval 0 to $2\ensuremath{\pi}$, equating $\ensuremath{\varphi}+2\ensuremath{\pi}$ with $\ensuremath{\varphi}$, and study the role played by the resulting nontrivial topology. Using Feynman's influence functional theory it is shown that the dissipation suppresses interference between paths with different winding numbers. For Ohmic dissipation this interference is completely destroyed, and $\ensuremath{\varphi}$ can effectively be treated as an extended coordinate. This justifies the use of the usual washboard potential description of a current-biased junction even in the quantum case, provided on Ohmic dissipation mechanism is present.

The influence of interactions between adsorbed particles on their diffusion constant is investigated by kinetic Ising models with independent nearest neighbour hops. This leads to expressions for the ratio of the diffusion constant at arbitrary coverage θ to its value at θ=0 as a function of the interaction energies relative to temperature. It is shown that under certain conditions this quantity obeys a particle-hole symmetry. Exact results in the whole range of densities are given in one dimension for nearest neighbour interaction. They already yield a qualitative agreement with experimental results and are also compared to corresponding numerical simulations. The introduction of a next nearest neighbour interaction is shown to produce drastic changes in the density dependence of the diffusion constant in some of the cases. A generalized quasichemical approximation and a virial expansion are made in two dimensions, leading to a better agreement with the measurements.

We study the statics and dynamics of a quantum Brownian particle moving in a periodic potential and coupled to a dissipative environment in a way which reduces to a Langevin equation with linear friction in the classical limit. At zero temperature there is a transition from an extended to a localized ground state as the dimensionless friction \ensuremath{\alpha} is raised through one. The scaling equations are derived by applying a perturbative renormalization group to the system's partition function. The dynamics is studied using Feynman's influence-functional theory. We compute directly the nonlinear mobility of the Brownian particle in the weak-corrugation limit, for arbitrary temperature. The linear mobility ${\ensuremath{\mu}}_{l}$ is always larger than the corresponding classical mobility which follows from the Langevin equation. In the localized regime \ensuremath{\alpha}g1, ${\ensuremath{\mu}}_{l}$ is an increasing function of temperature, consistent with transport via a thermally assisted hopping mechanism. For \ensuremath{\alpha}1, ${\ensuremath{\mu}}_{l}$(T) shows a nonmonotonic dependence on T with a minimum at a temperature ${T}^{\mathrm{*}}$. This is due to a crossover between quantum tunneling below ${T}^{\mathrm{*}}$ and thermally assisted hopping above ${T}^{\mathrm{*}}$. For low friction the crossover occurs when the particle's thermal de Broglie wavelength is roughly equal to the distance between minima in the periodic potential. We suggest that the regime \ensuremath{\alpha}1 describes the physics of the observed nonmonotonic temperature dependence of muon diffusion in metals.

We investigate the physical properties of quasi-1D quantum gases of fermion atoms confined in harmonic traps. Using the fact that for a homogeneous gas, the low energy properties are exactly described by a Luttinger model, we analyze the nature and manifestations of the spin-charge separation. Finally we discuss the necessary physical conditions and experimental limitations confronting possible experimental implementations., 4 pages, revtex4, 2 eps figures

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes a superfluid--Mott insulator transition. Confining a strongly interacting gas to one dimension generates an instability where an arbitrary weak potential is sufficient to pin the atoms into the Mott state; here, we derive the corresponding phase diagram. The commensurate pinned state may be detected via its finite excitation gap and the Bragg peaks in the static structure factor., 4 pages, 2 figures