Fractional Angular Momentum Research Articles

Induced fractional zero-point angular momentum for charged particles of the Bohm–Aharonov system by means of a “spectator” magnetic field

An induced fractional zero-point angular momentum of charged particles by the Bohm–Aharonov (BA) vector potential is realized via a modified combined trap. It explores a “spectator” mechanism in this type of quantum effects: In the limit of the kinetic energy approaching one of its eigenvalues the BA vector potential alone cannot induce a fractional zero-point angular momentum at quantum mechanical level in the BA magnetic field-free region; But when there is a “spectator” magnetic field the BA vector potential induces a fractional zero-point angular momentum. The “spectator” does not contribute to such a fractional angular momentum, but plays essential role in guaranteeing non-trivial dynamics at quantum mechanical level in the required limit. This “spectator” mechanism is significant in investigating the BA effects and related topics in both aspects of theory and experiment.

Fractional and integer angular momentum wavefunctions localized on classical orbits: the case of E = 0

In two-dimensional space, where the intermediate statistics between bosons and fermions are possible, we study a localization of some stationary coherent states on classical orbits in the potentials V(r) = −γν/rν, γν > 0 for the total energy E = 0. It is shown that excellent quantum-classical correspondence can be reached for two large classes of classical orbits with ν < −2 (open curves) and with ν > 2 (closed curves). To that purpose, it was necessary to introduce fractional angular momenta for some values of ν. They are a consequence of imposing special boundary conditions on the used wavefunctions.

Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation

We consider a class of self-trapped spatiotemporal solitons: spatiotemporal necklace-ring solitons, whose intensities are azimuthally periodically modulated. We reveal numerically that the spatiotemporal necklace-ring solitons carrying zero, integer, and even fractional angular momentum can be self-trapped over a huge propagation distance in the three-dimensional cubic-quintic complex Ginzburg-Landau equation, even in the presence of random perturbations.

Necklace-ring vector solitons.

We introduce novel classes of optical vector solitons that consist of incoherently coupled self-trapped "necklace" beams carrying zero, integer, and even fractional angular momentum. Because of the stabilizing mutual attraction between the components, such stationary localized structures exhibit quasistable propagation for much larger distances than the corresponding scalar vortex solitons and expanding scalar necklace beams.

VORTEX IN CHIRAL SUPERCONDUCTING STATE

We have investigated the vortex in chiral superconductors, especially in p-wave case. In chiral superconductors the Cooper pair has orbital angular momentum hence U(1), parity (P) and time reversal symmetry (T) are broken simultaneously. We have found that the vortex has fractional charge and fractional angular momentum which comes from P- and T-violation. The fractionalization of the angular momentum suggests that the vortex could be an anyon which obeys the fractional statistics. We have also pointed out that the electric field is induced near the vortex core and non-trivial electromagnetic phenomena are expected to occur.

From Gauging Nonrelativistic Translations to N-Body Dynamics

We consider the gauging of space translations with time-dependent gauge functions. Using a fixed time gauge of relativistic theory, we consider the gauge-invariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d×(d+1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d=2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern–Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. We describe the effective interaction of the d=2 N-particle problem and discuss its classical solution for N=2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H=H(x, p;H) which implies, after quantization, a nonstandard form of the Schrödinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r≤r0) and the scattering states with continuum energy correspond to the classical motion for r>r0. We extend our considerations by introducing an external constant magnetic field and, for N=2, provide the classical and quantum solutions in the confined and unconfined regimes.

Integer and Fractional Angular Momentum Borne on Self-Trapped Necklace-Ring Beams

We present self-trapped necklace-ring beams that carry and conserve angular momentum. Such beams can have a fractional ratio of angular momentum to energy, and they exhibit a series of phenomena typically associated with rotation of rigid bodies and centrifugal force effects.

Translational Chern–Simons action and new planar particle dynamics

We consider a nonstandard D=2+1 gravity described by a translational Chern–Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H= H( x, p;H) what implies, after quantization, a nonstandard form of the Schrödinger equation with energy-dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r≤ r 0) and the scattering states with continuous energy correspond to classical motion for r> r 0.

Vortex with fractional quantum numbers in a chiralp-wave superconductor

We show that a vortex in a chiral p-wave superconductor, which has the ${p}_{x}{+ip}_{y}$-wave pairing state and breaks $U(1),$ parity and time reversal symmetry simultaneously, has fractional charge $\ensuremath{-}ne/4$ and fractional angular momentum $\ensuremath{-}{n}^{2}/16$ (n; vorticity). This suggests that the vortex could be anyon and could obey fractional statistics. Electromagnetic property of the vortex is also discussed and we find that an electric field is induced near the vortex core.

Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect

Applying a bi-local mean field approximation to the fractional quantum Hall state of $\nu=1/3$, we obtain charged and neutral vortex mean field solutions numerically. We calculate the mean field energy and the fluctuation corrections. The charged vortex has a fractional charge and a fractional angular momentum. The neutral vortex is a bound state of two charged vortices and has a zero charge and a zero angular momentum. The creation energy of the neutral vortex is about a half of the pair creation energy of two charged vortices. The magnetic field dependence of the gap energy agrees with the Laughlin's quasiparticle gap energy.

A Mean Field Theory for the Quantum Hall Liquid. II: The Vortex Solution

In the Fractional Quantum Hall state, we introduce a bi-local mean field and get vortex mean field solutions. Rotational invariance is imposed and the solution is constructed by means of numerical self-consistent method. It is shown that vortex has a fractional charge, a fractional angular momentum and a magnetic field dependent energy. In $\nu=1/3$ state, we get finite energy gap at $B=10,15,20[T]$. We find that the gap vanishes at $B=5.5[T]$ and becomes negative below it. The uniform mean field becomes unstable toward vortex pair production below $B=5.5[T]$.

Magnetic moment and third virial of non-relativistic anyons

We compute the spontaneous magnetic moment associated with the orbital fractional angular momentum of non-relativistic anyons and the contribution of regular states to the third virial coefficient. The latter is independent of statistics.

Nontopological Chern-Simons vortices in a scale-invariant tricritical Abelian Higgs model

It is shown that the scale-invariant tricritical lambda 21( phi * phi )3-Abelian Higgs model with the Chern-Simons term has nontopological charged vortex solutions of finite energy, fractional angular momentum and anomalous scale dimension. For a specific choice of the coupling lambda 1, first-order Bogomolny-type equations are obtained and it is shown that unlike the second-order equations, these first-order equations do not admit charge vortex solutions of finite energy.

Stringlike excitations with fractional spin in 3+1 dimensions.

It is shown that composites formed from charged one-dimensional objects and vortices in a multiply connected three-dimensional space which is invariant under O(2) rotations can have fractional angular momentum.

New model of fractional spin.

A line-charge--neutron composite is proposed as a new model for fractional spin. Considering time-varying line-charge configurations, the kinetic angular momentum is a constant of motion while the canonical angular momentum is not. This result is contrary to the case with magnetic flux tubes. The fractional angular momentum (spin) is, therefore, determined without ambiguity.

Comment on "Fractional angular momentum and magnetic-flux quantization"

Comment on "Fractional angular momentum and magnetic-flux quantization"

Liang and Ding reply.

A reply to the comment on fractional angular momentum and magnetic-flux quantization in superconductors is given. The existence of a field-free region between the applied magnetic flux and the surrounding supercomductor is a crucial condition for the rest of the fractional quantum of magnetic flux and anyons. (AIP)

Are cyons really anyons?

An unresolved issue in (2 + 1)-dimensional quantum mechanics is whether a composite object formed from a charged particle bound to a magentic flux tube carries fractional angular momentum. We argue that this is indeed so, that the result confirms Wilczek's generalized connection of spin and statistics, and that further confirmation is provided by the recently discovered induced charged and spin of flux tubes in (2 + 1)-dimensional QED, a theory in which different spin and statistics are defined at short- and at long-distance scales.

Fractional angular momentum and magnetic-flux quantization.

It is shown that the fractional angular momentum of charged particles orbiting around a magnetic flux tube would result in fractional magnetic-flux quantization. A crucial experiment to test for the fractional quantum of magnetic-flux as well as anyons is proposed and analyzed.

ANGULAR MOMENTUM OF SUPERELECTRONS AND THE MAGNETIC FLUX QUANTIZATION

It is shown that the magnetic flux quanmzation should be consistent with the angular momentum quantization of superelectrons. The fractional angular momentum would lead to the fractional quantization of magnetic flux which does not contradict the theory of superconductivity and the result of previous experiments. We propose and analyse a crucial experiment to test the fractional quantum of magnetic flux as well as any"-on"s.