Related papers: Fractional quantum numbers deduced from experiment…
Using Caputo fractional derivative of order $\alpha $ we build the fractional jet bundle of order $\alpha $ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We have calculated the fractional charge of quasiparticles in a cluster of electrons. The 61 values have been calculated which are exactly the same as the measured values. In a previous eprint we have calculated 85 values which are the same…
Most of the fractions observed to date belong to the sequences $\nu=n/(2pn\pm 1)$ and $\nu=1-n/(2pn\pm 1)$, $n$ and $p$ integers, understood as the familiar {\em integral} quantum Hall effect of composite fermions. These sequences fail to…
Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating multiple…
A method for describing charged relativistic Fermi fields is proposed, in which particles of opposite charges are treated equally and states with negative energy are excluded. The concept of charge quantum number is introduced. Fields of…
In wide GaAs quantum wells where two electric subbands are occupied we apply a parallel magnetic field or increase the electron density to cause a crossing of the two $N=0$ Landau levels of these subbands and with opposite spins. Near the…
We develop a theory of quadratic quantum measurements by a mesoscopic detector. It is shown that quadratic measurements should have non-trivial quantum information properties, providing, for instance, a simple way of entangling two…
Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate…
The notion of fractional charges was up until now reserved for quasiparticle excitations emerging in strongly correlated quantum systems, such as Laughlin states in the fractional quantum Hall effect, Luttinger quasiparticles, or…
The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law and their…
We experimentally study electron transport between edge states in the fractional quantum Hall effect regime. We find an anomalous increase of the transport across the 2/3 incompressible fractional stripe in comparison with theoretical…
We study quantum-fluctuation-driven fractionalized phases in the vicinity of altermagnetic order. First, the long-range magnetic orders in the vicinity of collinear altermagnetism are identified; these feature a non-coplanar "orbital…
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau…
This letter extends previous findings on the modified Schr\"odinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a…
We report the observation of fractional shifts in the experimental stability diagrams of PbTe nanowire quantum dots. Although this behavior may appear to suggest fractional charge transport, akin to that reported in the fractional quantum…