Related papers: Some Basic Aspects of Fractional Quantum Numbers
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
Among the predicted properties of fractional quantum Hall states are fractionally charged quasiparticles and conducting edge-states described as chiral Luttinger liquids. In a system with a narrow constriction, tunneling of quasi-particles…
Strongly interacting electrons in a topologically non trivial band may form exotic phases of matter. An especially intriguing example of which is the fractional quantum anomalous Hall phase, recently discovered in twisted transition metal…
We propose an experiment to probe the unconventional quantum statistics of quasi-particles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts…
Fermion-number fractionalization without breaking of time-reversal symmetry was recently demonstrated for a field theory in $(2+1)$-dimensional space and time that describes the couplings between massive Dirac fermions, a complex-valued…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the nu=1/3 FQH state, a charge smoothly evolving…
Stationary solutions of the Chern-Simons effective field theory for the fractional quantum Hall systems with edges are presented for Hall bar, disk and annulus. In the infinitely long Hall bar geometry (non compact case), the charge density…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the…
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 employ the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms which are subjected to a geometric gauge field created by coupling two…
The fractional quantum hall effect (FQHE) is a milestone of modern day physics, its disovery paved the way for the study of fractional charges which do not obey abelian physics. However, all FQHE require an external magnetic field in order…
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…
The fractional quantum Hall states are non-Fermi liquids of electrons, in that their ground states and low energy excitations are described not in terms of electrons but in terms of composite fermions which are bound states of electrons and…
Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. Here…
We calculate the quantum statistical force acting on a partition wall that divides a one dimensional box into two halves. The two half boxes contain the same (fixed) number of noninteracting bosons, are kept at the same temperature, and…
The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice…
We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to…