Interplay of electronic and mechanical properties of nanoelectromechanical systems (NEMS) has been in the focal point of research interest in recent years. In this talk, after brief overview of experimental realizations of such systems, I will present our analysis of two NEMS structures, a mechanical oscillator coupled to an electrical tunnel junction and a quantum shuttle. The explicit expressions for the oscillator (shuttle) damping/decoherence rate, fluctuations of the oscillator (shuttle) position, and for nonlinear conductance of these NEMS have been obtained on the microscopic basis and their voltage and temperature dependencies have been determined. I will also discuss the applications of these models to description of the tunneling in long molecules and electron transport in manganites. Finally, I will describe the directions of our future projects in this field.

First order phase transitions such as the ferroelectric phase transition play a central role in the functional properties of materials; detailed microscopic characterization of the first-order solid-solid transformation has been difficult, however, because bulk measurements often obscure the crucial importance of the surface and defects. We characterize the size-dependent evolution of ferroelectricity in individual, single-crystalline perovskite nanowires using variable-temperature scanning probe microscopy in ultrahigh vacuum, and without the difficulties of ensemble averaging. The measurements show that the ferroelectric phase transition temperature is depressed as the nanowire diameter decreases, reaching room temperature for 3 nm diameter nanowires. Using a combination of density functional theory calculations, phenomenological Landau theory, and thermodynamic analysis, we propose and discuss a new mechanism for surface charge screening in which ferroelectricity is stabilized and even enhanced in smaller domains.

In recent years, whispering-gallery modes (WGMs) of micrometer-sized dielectric spheres (microresonators) have been used in a number of applications, including cavity quantum electrodynamics, trace-gas and chemical detection, biosensing, and nonlinear optics. A convenient method for exciting these modes is photon tunneling from an adjacent tapered optical fiber carrying the incident laser light. The most useful WGMs propagate in circular paths near the sphere's equator and their evanescent part allows interaction with the surrounding environment. By bringing an additional sphere nearly in contact with an excited microresonator, evanescent mode coupling between the two spheres is realized. Experiments performed with coupled fused-silica microresonators show that interference between co-resonant modes of the two spheres gives rise to spectral features that are analogous to those observed in an atomic ensemble that is driven under coherent quantum interference conditions.

We study the decay of an atomic BEC population N(τ) from the leaking boundaries of an Optical Lattice (OL). For a rescaled interatomic interaction strength λ>λ_b, self-trapped Discrete Breathers (DB's) are created, preventing the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DB's, result in avalanches (jumps) in N(τ) which for λ_b<λ<λ_* follow a scale free distribution P(J=δN)≅1/J^α. A theoretical analysis of the mixed phase-space of the system, indicate that 1<α<3 in agreement with our numerical findings. We point out that although our focus is given to atomic BECs, our results are also relevant in a large variety of contexts, most prominently being the light emittance from coupled non-linear optics waveguides

Photonic crystals, in this case periodic structures of dielectrics, can be used to control light propagation through geometry and dielectric contrast.  An especially attractive application for photonic crystals is to construct localized electromagnetic modes by introducing defects in the periodic structure.  These confined modes could be used as optical resonators, laser cavities being the most obvious application. In this seminar, I will discuss a theoretical approach for calculating the photonic structure of defects in 2D photonic crystals. The central feature of this approach is the construction of a basis set of local vector Wannier functions from the perfect crystal eigenstates. It has been proposed [1] that this basis be used to expand photonic crystal defect states analogous to the famous expansion in linear combinations of atomic orbitals of the electronic structure of the ideal silicon vacancy [2]. These approaches rely on a small number of basis states local to the defect region. In this work, we replace the fourier expansion of the perfect crystal by a real-space description in vector finite-elements. This method allows the computation of the Wannier basis on the same grid used to compute the perfect structure and results in a straightforward defect eigenvalue problem. I will present results that verify the eigenmodes of the crystal and examine the physics of selected defect modes.
[1] K.M. Leung, J. Opt. Soc. Am. B 10, 303 (1993).
[2] G.A. Baraff and M. Schluter, PRL 41, 892 (1978); J. Bernholc, N.O. Lipari, and S.T. Pantelides, PRL 41, 895 (1978).

A general introduction to elements of semiconductor physics is presented, including discussions of E-k diagrams as well as the four fundamental electron-phonon interactions. The quantum-generalized Boltzmann equation is reviewed and applied to high-field transport in a semiconductor. From this analysis a new kinetic equation for the electron distribution function is derived which includes terms corresponding to the four electron-phonon interactions. In the quasi-classical limit, it is found that the acoustic strain interaction dominates, which gives rise to a reduced kinetic equation. In the steady-state limit this equation yields a second-order nonlinear differential equation for the perturbation distribution. The exact solution of the related nonlinear equation represents a significant new result. The distribution function is a generalized Fermi-Dirac distribution which contains the electric field explicitly and is found to reduce to correct forms in various limits.** The analysis is then extended to Silicon, where `equivalent' intervalley scattering comes into play. Drift velocity obtained from the approximate solution of resulting equations is found to agree with observed values for electric fields up to 105 V/cm. A criterion is described discerning between linear and nonlinear electric field effects. * This research includes results from four publications:
1. Phys. Rev. B34, 7063 (1986)
2. J. Appl. Phys. 62, 177 (1987)
3. J. Appl. Phys. 63, 5363 (1988)
4. Phys. Rev. B40, 5624 (1989)
** This `SL Distibution,' appears in the 4th edition of B. Ridley's book, Quantum processs; in semiconductor.