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

Entropy Content During Nanometric Stick-Slip Motion

To explore the existence of self-organization during friction, this paper considers the motion of all atoms in a systems consisting of an Atomic Force Microscope metal tip sliding on a metal slab. The tip and the slab are set in relative motion with constant velocity. The vibrations of individual atoms with respect to that relative motion are obtained explicitly using Molecular Dynamics with Embedded Atom Method potentials. First, we obtain signatures of Self Organized Criticality in that the stick-slip jump force probability densities are power laws with exponents in the range (0.5, 1.5) for aluminum and copper. Second, we characterize the dynamical attractor by the entropy content of the overall atomic jittering. We find that in all cases, friction minimizes the entropy and thus makes a strong case for self-organization

Micro-thermography for imaging ice crystal growth and nucleation inside non-transparent materials

Ice crystal growth and nucleation rate measurements are usually done using visible light micros-copy in liquid and transparent samples. Yet, the understanding of important practical problems depends on monitoring ice growth inside solid materials. For example, how rapid ice growth leads to structural damage of food, or how the final structure of cementitious materials is affect-ed by ice during curing. Imaging crystal growth inside solid materials cannot be done with visi-ble light and is intrinsically more challenging than visible light imaging. Thermography is a technique that uses thermal (Infra-red) cameras to monitor temperature changes in a material, and it has been used to provide qualitative description of ice propagation and nucleation with a low spatial resolution. Here, we describe a method that uses a novel micro-thermography system to image ice nucleation, growth and melting inside non-transparent samples. This method relies on two major components: a cold stage with accurate temperature control (±0.001 ºC) and a thermal camera with high spatial and temperature resolution. Our experiments include imaging of ice formation and growth in pure water first, and inside plant leaves used as a model for a non-transparent material. Ice growth rate of 2.2 mm/s was measured inside a plant leaf at -12 ºC and ice nucleation in single plant cells was observed as a hot spot having a diameter of 160 µm. The results presented here provide experimental proof that high-quality imaging of ice growth is achievable, thus paving the way to quantitative measurements of ice growth kinetics and ice nu-cleation in solid materials