Related papers: Fractional currents and Young geometric integratio…
It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…
We show that fractional charges can be realized at the boundaries of a linear array of tunnel coupled quantum dots in the presence of a periodically modulated onsite potential. While the charge fractionalization mechanism is similar to the…
The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
The persistent Hall voltage and current in an isolated annulus in a strong perpendicular magnetic field, at odd inverse filling factor, and in the presence of a weak constriction is obtained as a function of temperature, and flux piercing…
We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
It is shown that a pointlike composite having charge and magnetic moment displays a confining potential for the static interaction while simultaneously obeying fractional statistics in a pure gauge theory in three dimensions, without a…
We consider an infinitely long 0-$\pi$ Josephson junction consisting of 0 and $\pi$ regions having different critical current densities $j_{c,0}$ and $j_{c,\pi}$. The ground state of such a junction corresponds to a spontaneosly formed…
Given a finite locally free resolution of a coherent analytic sheaf $\mathcal F$, equipped with Hermitian metrics and connections, we construct an explicit current, obtained as the limit of certain smooth Chern forms of $\mathcal F$, that…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
A new class of fractional-order stochastic evolution equations of the form $(\partial_t + A)^\gamma X(t) = \dot{W}^Q(t)$, $t\in[0,T]$, $\gamma \in (0,\infty)$, is introduced, where $-A$ generates a $C_0$-semigroup on a separable Hilbert…
We present new geometric formulations for the fractional spin particle models on the minimal phase spaces. New consistent couplings of the anyon to background fields are constructed. The relationship between our approach and previously…
A canonically defined mod 2 linear dependency current is associated to each collection of m sections of a real rank n vector bundle. This current is supported on the linear dependency set of the collection of sections. It is defined…
Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra.…
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose…
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…
The fractional Yamabe problem, proposed by Gonz\'{a}lez-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
A profound manifestation of topologically non-trivial states of matter is the occurrence of fractionally charged elementary excitations. The quantum spin Hall insulator state is a fundamentally novel quantum state of matter that exists at…