Transitional random matrix theory nearest-neighbor spacing distributions

This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the transitional probability density functions, as well as suitable analytical approximations for cases not amenable to explicit representation

Permittivity from first principles

Dielectric properties of materials are generally introduced phenomenologically through empirical values of permittivity. While this approach is necessary for practical work, it must be recognized that it bypasses the question of whether it is possible to predict permittivity values from first principles and thus get a deeper grasp of the physics involved in bridging the microscopic system and its macroscopic properties. Theoretical frameworks to gain insight and to compute exactly permittivity values are desirable to understand the nuances that go into building this bridge. We introduce here such a theoretical model system to gain physical intuition on the microscopic origin of the permittivity. The system consists of electrons in a one-dimensional atomic chain in the presence of an external electric field, where each atom is a binding site. We first consider a single atom in an external field to study atomic polarization, justify the model, tune the parameters, and compare with perturbative approaches. We then consider the assembly of many such atoms in a periodic arrangement and study its band-structure, including explicitly the external electric field. Last, within this model we develop explicit formulas for the permittivity in terms of relevant physical parameters. Finally, we obtain a numerically value for the permittivity of the system for typical values of binding energy and electric field

Supersymmetric Displaced Number States

We introduce, generate and study a family of supersymmetric displaced number states (SDNS) that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis

Transport Through Disordered Silicon Oxide Quantum Structures

Silicon and oxygen semiconductor-atom structures (SAS) are built by alternating layers, creating structures similar to the traditional superlattices. These SAS have good electro-and photo-luminescence and may therefore form the basis of all-Si optoelectronic devices. Their I-V curves are only qualitatively understood. TEM images show that SAS have stacking faults and dislocations in substantial quantities as to affect response time and transmission. Experimental work has been done to understand why silicon may grow epitaxially after the oxygen barrier. This is never the case in Si/SiO2. If, during growth, the oxygen valve is left open, a large number of defects is generated in bulk silicon. By controlling the oxygen rate, it is possible to produce silicon on both sides of the oxygen interface with defect densities below 109/cm2. Nevertheless, the oxygen layer itself is typically broken up in islands. What is clear is that it is technically possible to produce SAS with negligible bulk defects but that still present strain and disorder at the oxygen interface. We have studied the effect of interface disorder and strain on SAS current-voltage curves. Their quality factor is extremely sensitive to the presence of imperfections. We will show the dependence of the spectrum on disorder. Work supported by Research Corporation

Disorder Characterization of Oxide/Silicon Interfaces from I-V Curves

In this paper, we present results on transmission-energy curves through quantum wells with disordered interfaces. We propose a rule to process experimental data to obtain information about the degree of disorder

Unexplored territory in the AFM force curve contains nanomechanics information

We demonstrate the existence of a previously unknown damped oscillating signal just after the point when an atomic force microscope tip hits a sample surface. This oscillating signal is below the noise in a single force-displacement measurement. Autocorrelating 20 measurements using the snap to contact feature as the reference mark allows the oscillation to be clearly visible above the noise. We show that the amplitude of the signal’s oscillation is largely insensitive to the speed with which the sample is brought toward the tip proving that the impulse that generates the signal comes primarily from the snap-to-contact event. This speed-independence sets a lower limit on how softly a sample may be interrogated when measuring mechanical properties in the surface region. Collection and analysis of this damped oscillating signal eliminates the need for standard low bandwidth lock-in based techniques to determine time dependent surface mechanical properties. This allows conventional atomic force microscopes to make a single pass of force collection over a surface and, after post-processing, yield the full time dependent mechanical behavior of the surface. To demonstrate a practical use of the oscillations, we produce images of a polystyrene/polyethylene sample where the contrast mechanisms are stiffness and viscosity