Related papers: Fractional quantum numbers deduced from experiment…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
Fractional quantum Hall quasiparticles are famous for having fractional electric charge. Recent experiments report that the quasiparticles' effective electric charge determined through tunneling current noise measurements can depend on the…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
We generalize the fractional Caputo derivative to the fractional derivative ${{^CD}^{\alpha,\beta}_{\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\alpha$ and the right Caputo fractional…
We compute electromagnetic fields created by a relativistic charged spin-half particle in empty space at distances comparable to the particle Compton wavelength. The particle is described as a wave packet evolving according to the Dirac…
Electronic spins can form long-range entangled phases of condensed matter named quantum spin liquids. Their existence is conceptualized in models of two- or three-dimensional frustrated magnets that evade symmetry-breaking order down to…
We have examined the experiments performed by Goldman and Su, de-Picciotto et al, Samanadayar et al and Conforti et al in which it is claimed that a fractional charge of e/3 is found. In all of the measurements, the quantity measured is the…
In the experiments, the quantity measurd is the product of the charge and the magnetic field from which fractional charge is deduced. There is no objection to measuring the fractional charge as long as it is remembered that the product of…
The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.
We scatter a meson off of a scalar kink in quantum field theory, at leading order in perturbation theory. We calculate the full quantum state, at leading order, at all times and also check that the reflection and transmission coefficients…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
Electromagnetic properties of quark-like particles are examined in a classical field model involving extended dual electromagnetic fields. These can have fractional charges and a confining potential that derives essentially completely from…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric…
Fractional superstrings are non-trivial generalizations of ordinary superstrings and heterotic strings, and have critical spacetime dimensions which are less than ten by virtue of a worldsheet fractional supersymmetry relating worldsheet…