15 research outputs found
Green functions for generalized point interactions in 1D: A scattering approach
Recently, general point interactions in one dimension has been used to model
a large number of different phenomena in quantum mechanics. Such potentials,
however, requires some sort of regularization to lead to meaningful results.
The usual ways to do so rely on technicalities which may hide important
physical aspects of the problem. In this work we present a new method to
calculate the exact Green functions for general point interactions in 1D. Our
approach differs from previous ones because it is based only on physical
quantities, namely, the scattering coefficients, and , to construct .
Renormalization or particular mathematical prescriptions are not invoked. The
simple formulation of the method makes it easy to extend to more general
contexts, such as for lattices of general point interactions; on a line; on
a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR
Quantum mechanics of a free particle on a pointed plane revisited
The detailed study of a quantum free particle on a pointed plane is
performed. It is shown that there is no problem with a mysterious ``quantum
anticentrifugal force" acting on a free particle on a plane discussed in a very
recent paper: M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002), but we deal
with a purely topological efect related to distinguishing a point on a plane.
The new results are introduced concerning self-adjoint extensions of operators
describing the free particle on a pointed plane as well as the role played by
discrete symmetries in the analysis of such extensions.Comment: 4 figure
A Green's function approach to transmission of massless Dirac fermions in graphene through an array of random scatterers
We consider the transmission of massless Dirac fermions through an array of
short range scatterers which are modeled as randomly positioned -
function like potentials along the x-axis. We particularly discuss the
interplay between disorder-induced localization that is the hallmark of a
non-relativistic system and two important properties of such massless Dirac
fermions, namely, complete transmission at normal incidence and periodic
dependence of transmission coefficient on the strength of the barrier that
leads to a periodic resonant transmission. This leads to two different types of
conductance behavior as a function of the system size at the resonant and the
off-resonance strengths of the delta function potential. We explain this
behavior of the conductance in terms of the transmission through a pair of such
barriers using a Green's function based approach. The method helps to
understand such disordered transport in terms of well known optical phenomena
such as Fabry Perot resonances.Comment: 22 double spaced single column pages. 15 .eps figure
Quantum-mechanical Results For A Free Particle Inside A Box With General Boundary Conditions
The wave functions with the most general boundary conditions consistent with the conservation of probability for a free particle inside a box [Phys. Rev. D 42, 1194 (1990)] are calculated. The exact Green's functions and propagators for some special cases are obtained and a semiclassical approach for the propagators is considered. Finally, the influence of the boundary conditions over the path integral's formalism is briefly discussed. © 1995 The American Physical Society.5131811181
Propagator For The -function Potential Moving With Constant Velocity
We first evaluate the exact propagator for a -function potential moving with constant velocity by summing over the spectrum of eigenstates and by calculating the path integral directly. The one-time Greens functions are then derived from the Fourier transform of the propagator obtained. We finally investigate the propagator through an asymptotic approximation. © 1993 The American Physical Society.4764720472
Determining and characterizing families of electronic resonance states in open and closed coupled cavities
Here a straightforward procedure to characterize electronic resonances in arbitrary
coupled open or closed nano and micro structures â formed by cavities (or billiards)
connected by waveguides â is presented. Based on the boundary wall method, it identifies
families of states arising from continuous changes in the system geometric parameters
without the necessity to explicit calculate the eigenfunctions. Nevertheless, if desired
they also can be obtained with good numerical accuracy. As a case study, two rectangular
cavities coupled to waveguides is considered. It is exemplified how the bound states,
bound states in the continuum and truly transmission states respond to certain
modifications in the problem geometry. The analysis simplicity illustrates the potential
of the approach in ascertaining structures shapes with distinct resonance properties
Path Integral For The Quantum Baker's Map
We derive a formally exact sum of path integrals for the quantum propagator of the baker's transformation. The phases depend only on the classical actions as in usual phase space path integrals and the sums are over all the symbolic orbits. The deduction depends on multiple Poisson transformations, which lead to a further infinite sum of integrals, but our computations for the propagator and its trace for two iterations show that this is rapidly convergent. Explicit formulae for the quantum corrections to the semiclassical propagator are presented for this case.81436
LĂ©vy flights in random searches
We review the general search problem of how to find randomly located objects that can only be detected in the limited vicinity of a forager, and discuss its quantitative description using the theory of random walks. We illustrate LĂ©vy flight foraging by comparison to Brownian random walks and discuss experimental observations of LĂ©vy flights in biological foraging. We review recent findings suggesting that an inverse square probability density distribution P(â)âŒââ2 of step lengths â can lead to optimal searches. Finally, we survey the explanations put forth to account for these unexpected findings