Exact localized solutions of two-dimensional field theories of massive fermions with Fermi interactions

Lee, S. Y.; Kuo, T. K.; Gavrielides, A.

doi:10.1103/physrevd.12.2249

Cited by 83 publications

(65 citation statements)

References 12 publications

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“…In the low-momentum limit, the spinor BEC may be described by a particular type of two-component NLDE. We show that for the case of attractive interactions, the condensate may become self-trapped, resembling chiral confinement, previously discussed in the context of the massive Thirring and Gross-Neveu models [33,34]. Contrary to two-component vector solitons, discussed in nonlinear optics and cold gases [35,36], the two components are not only coupled by the interatomic interactions, but by the spin-orbit coupling as well.…”

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confidence: 57%

Chiral Confinement in Quasirelativistic Bose-Einstein Condensates

et al. 2010

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In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coupling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multidimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.PACS numbers: 42.50. Gy, 37.10.De, 42.25.Bs Although cold gases are typically neutral, artificial electromagnetism may be induced by several means, including rotation [1], manipulation of atoms in optical lattices [2,3,4], and the use of laser arrangements [5]. Interestingly, seminal experiments on optically created gauge fields have been recently reported [6]. Artificial electromagnetism has attracted a growing attention in recent years, partially due to the possibility of achieving nonAbelian gauge fields [4,5], which establish fascinating links between cold gases and high-energy physics [4,7,8]. A striking example is given by the possibility of inducing quasi-relativistic physics in cold atoms despite the extremely low velocities involved [9]. In particular, under proper conditions cold atoms may experience an effective spin-orbit coupling, which leads to a Dirac cone in the dispersion [10], resembling the case of yet another paradigm of modern physics, namely graphene [11,12]. Similar phenomena are expected in cold atoms and graphene including Veselago lensing [9,13,14].Interparticle interactions lead to inherent nonlinearities in Bose-Einstein condensates (BECs). At sufficiently low temperatures the BEC physics is described by a nonlinear Schödinger equation similar to that found in nonlinear optics [1]. Resemblances between both fields have been successfully explored in recent years, most remarkably in what concerns the physics of solitons [15,16,17,18,19], for which nonlinearity and dispersion compensate leading to a non-dispersing solution. Nonlinearity plays also an important role in high-energy physics. Indeed, non-linear Dirac equations (NLDEs), and more generally non-linear spinor fields, have been studied extensively, starting with the pioneering works of Ivanenko [20], Weyl [21], and Heisenberg [22]. These equations may present also localized solutions [23,24].In this Letter we explore the nonlinear physics of a multicomponent BEC (also called spinor BEC [25]) in the presence of an optically-induced spin-orbit coupling. In the low-momentum limit, the spinor BEC may be described by a particular type of two-component NLDE. We show that for the case of attractive interactions, the condensate may become self-trapped, rese...

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confidence: 57%

Chiral Confinement in Quasirelativistic Bose-Einstein Condensates

et al. 2010

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“…Later, Strauss and Vasquez [13] were able to study the stability of this model under dilatation and found the domain of stability for the Soler solutions. Solitary waves in the 1+1 dimensional nonlinear Dirac equation have been studied [14,15] in the past in case the nonlinearity parameter k = 1, i.e. the massive Gross-Neveu [16] (with N = 1, i.e.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytic solutions to coupled nonlinear Dirac equations

2017

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We consider the coupled nonlinear Dirac equations (NLDE's) in 1+1 dimensions with scalarscalar self interactions g 2 1 2 (ψψ) 2 + g 2 2 2 (φφ) 2 + g 2 3 (ψψ)(φφ) as well as vector-vector interactions of the form g 2 1 2 (ψγµψ)(ψγ µ ψ) + g 2 2 2 (φγµφ)(φγ µ φ) + g 2 3 (ψγµψ)(φγ µ φ). Writing the two components of the assumed solitary wave solution of these equation in the form ψ = e −iω 1 t {R1 cos θ, R1 sin θ}, φ = e −iω 2 t {R2 cos η, R2 sin η}, and assuming that θ(x), η(x) have the same functional form they had when g3=0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 2 3 /g 2 2 and g 2 3 /g 2 1 . In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.

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“…Some analytical solitary wave solutions have been obtained in a series of research works [8][9][10]. With regard to more general initial conditions, however, it is difficult to derive the exact solutions of the NLD equation.…”

Section: Introductionmentioning

confidence: 99%

Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation

Zhang

Shao

2017

Discrete Dynamics in Nature and Society

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A high-order accuracy numerical method is proposed to solve the (1 + 1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. Numerical results are given to validate the accuracy of these schemes and to study the interaction dynamics of the nonlinear Dirac solitary waves.

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Exact localized solutions of two-dimensional field theories of massive fermions with Fermi interactions

Cited by 83 publications

References 12 publications

Chiral Confinement in Quasirelativistic Bose-Einstein Condensates

Chiral Confinement in Quasirelativistic Bose-Einstein Condensates

Approximate analytic solutions to coupled nonlinear Dirac equations

Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation

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