Localization of massless Dirac particles via spatial modulations of the Fermi velocity

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.Comment: 9 pages, 6 figure

Time domain phase measuring apparatus

The phase and/or period stability of a device is determined by connecting the device in one orthogonal arm of a phase detector having a mixer. In the other arm is an adjustable, variable phase shift device. The output of the mixer is fed through an active low pass filter to derive a DC voltage indicative of the phase shift. The variable phase device is adjusted so that the DC voltage will nullify the phase shift of the tested device under normal conditions. The DC voltage level is converted into a time interval indicative of the phase change of the tested device by determining when the level equals the amplitude of a low frequency ramp voltage. The interval between adjacent equality points can be measured or the period between a reference point on the ramp voltage and the quality be measured

Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas

We study the fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas using the field theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially suppressed beyond the thermal length. We obtain analytical expressions for the induced interaction at zero and finite temperature that are valid at arbitrary distances. We discuss experimental realizations as well as possible formation of bound states of two impurities, known as bipolarons.Comment: 14 pages, 1 figure; accepted to Physical Review

Fragmentation with a Steady Source

We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior is robust as it is independent of the details of the input as well as the spatial dimension. The full time dependent behavior is obtained analytically for arbitrary inputs, and is found to exhibit a universal scaling behavior.Comment: 4 page