Anyons and Chiral Solitons on a Line

Aglietti, U.; Griguolo, Luca; Jackiw, R.; Pi, So‐Young; Seminara, Domenico

doi:10.1103/physrevlett.77.4406

Cited by 126 publications

(183 citation statements)

References 10 publications

Supporting

Mentioning

177

Contrasting

Order By: Relevance

“…which is the Madelung fluid representation of (11 If interaction between material particles is the delta function pair form then potential V(q) = gq 2 /2 and Eq. (11) becomes…”

Section: Dimensional Reduction Of Chern-simons Theorymentioning

confidence: 99%

See 1 more Smart Citation

Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

Lee

Pashaev

2012

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

a b s t r a c tNew Broer-Kaup type systems of hydrodynamic equations are derived from the derivative reaction-diffusion systems arising in SL(2, R) Kaup-Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of chiral solitons in quantum potential as a dimensional reduction of 2 + 1 dimensional Chern-Simons theory for anyons is shown. By the Hirota bilinear method, soliton solutions are constructed and the resonant character of soliton interaction is found.

show abstract

“…which is the Madelung fluid representation of (11 If interaction between material particles is the delta function pair form then potential V(q) = gq 2 /2 and Eq. (11) becomes…”

Section: Dimensional Reduction Of Chern-simons Theorymentioning

confidence: 99%

“…To do the gauge field component B in Section 2 to be dynamical, following [11] we introduce the corresponding kinetic term so that…”

Section: Dynamical Bf Theorymentioning

confidence: 99%

Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

Lee

Pashaev

2012

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

show abstract

“…In some special cases, solitary waves do not support arbitrary speeds and can propagate only with definite velocities determined from the parameters of the nonlinear equation. These so-called chiral solitons have received much attention lately due to their recent associations with the nonlinear Schrödinger equation and the fractional quantum Hall effect [6,7,8]. Moreover, we have also recently pointed [9] to the presence of chiral kink soliton solutions in generalized KdV-Burgers-Huxley (gKdVBH) equations in the form…”

Section: Introductionmentioning

confidence: 99%

Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity

Raposo

Bazeia

1999

Physics Letters A

View full text Add to dashboard Cite

We describe exact kink soliton solutions to nonlinear partial differential equations in the generic form u t + P (u)u x + νu xx + δu xxx = A(u), with polynomial functions P (u) and A(u) of u = u(x, t), whose generality allows the identification with a number of relevant equations in physics. We emphasize the study of chirality of the solutions, and its relation with diffusion, dispersion, and nonlinear effects, as well as its dependence on the parity of the polynomials P (u) and A(u) with respect to the discrete symmetry u → −u. We analyze two types of kink soliton solutions, which are also solutions to 1 + 1 dimensional φ 4 and φ 6 field theories.

show abstract

“…We will consider an atomic Bose-Einstein condensate subject to a laser field configuration which gives rise to a synthetic vector potential, whose zeroth-order contribution with respect to the ratio between the atom-atom and atom-field interaction, emulates a constant magnetic field. However, in a mean field picture, detunings from the atomic resonance can be induced by collisions, which results in an unconventional current nonlinearity [24,26,27], and corresponds to the semiclassical, or mean-field limit of an interacting gauge theory [28].…”

Section: Introductionmentioning

confidence: 99%

Quantized vortices in interacting gauge theories

Butera¹,

Valiente²,

Öhberg³

2015

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are twolevel atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle zeroth-order vector potential corresponds to a constant synthetic magnetic field. We find a new exotic type of current non-linearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate the rotational properties of this system in the Thomas-Fermi limit, focusing in particular on the physical conditions that make the existence of a quantized vortex in the system energetically favourable with respect to the non-rotating solution. We point out that two different physical interpretations can be given to this new non linearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. Looking at the problem from both of these viewpoints, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating states depends on the density of the cloud.

show abstract

Anyons and Chiral Solitons on a Line

Cited by 126 publications

References 10 publications

Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity

Quantized vortices in interacting gauge theories

Contact Info

Product

Resources

About