Phonon-mediated thermal conductance of mesoscopic wires with rough edges

We present an analysis of acoustic phonon propagation through long, free-standing, insulating wires with rough surfaces. Due to a crossover from ballistic propagation of the lowest-frequency phonon mode at $\omega <\omega _{1}=\pi c/W$ to a diffusive (or even localized) behavior upon the increase of phonon frequency, followed by re-entrance into the quasi-ballistic regime, the heat conductance of a wire acquires an intermediate tendency to saturate within the temperature range $T\sim \hbar \omega_{1}/k_{B}$.Comment: 4 pages, 3 figures included; minor changes and corrections, figures 1 and 2 replaced by better versions; to appear in PRB Brief Report

Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects

Using a quantum noise approach, we discuss the physics of both normal metal and superconducting single electron transistors (SET) coupled to mechanical resonators. Particular attention is paid to the regime where transport occurs via incoherent Cooper-pair tunneling (either via the Josephson quasiparticle (JQP) or double Josephson quasiparticle (DJQP) process). We show that, surprisingly, the back-action of tunneling Cooper pairs (or superconducting quasiparticles) can be used to significantly cool the oscillator. We also discuss the physical origin of negative damping effects in this system, and how they can lead to a regime of strong electro-mechanical feedback, where despite a weak SET - oscillator coupling, the motion of the oscillator strongly effects the tunneling of the Cooper pairs. We show that in this regime, the oscillator is characterized by an energy-dependent effective temperature. Finally, we discuss the strong analogy between back-action effects of incoherent Cooper-pair tunneling and ponderomotive effects in an optical cavity with a moveable mirror; in our case, tunneling Cooper pairs play the role of the cavity photons.Comment: 27 pages, 7 figures; submitted to the New Journal of Physics focus issue on Nano-electromechanical Systems; error in references correcte

Regularization of the Hamiltonian constraint and the closure of the constraint algebra

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.Comment: 23 pages, epsfig.st

Damping and decoherence of a nanomechanical resonator due to a few two level systems

We consider a quantum model of a nanomechanical flexing beam resonator interacting with a bath comprising a few damped tunneling two level systems (TLS's). In contrast with a resonator interacting bilinearly with an ohmic free oscillator bath (modeling clamping loss, for example), the mechanical resonator damping is amplitude dependent, while the decoherence of quantum superpositions of mechanical position states depends only weakly on their spatial separation

Low-temperature heat transfer in nanowires

The new regime of low-temperature heat transfer in suspended nanowires is predicted. It takes place when (i) only ``acoustic'' phonon modes of the wire are thermally populated and (ii) phonons are subject to the effective elastic scattering. Qualitatively, the main peculiarities of heat transfer originate due to appearance of the flexural modes with high density of states in the wire phonon spectrum. They give rise to the $T^{1/2}$ temperature dependence of the wire thermal conductance. The experimental situations where the new regime is likely to be detected are discussed.Comment: RevTex file, 1 PS figur