Solitons in condensed matter: A paradigm

Bishop, A. R.; Krumhansl, J. A.; Trullinger, S. E.

doi:10.1016/0167-2789(80)90003-2

Cited by 287 publications

(158 citation statements)

References 88 publications

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“…where the last equality follows from the first integral of the equation of motion, i.e., dφ/dx = 2V (φ) [5,30]; again, without loss of generality, it is assumed that min φ V (φ) = 0, i.e., V (φ) ≥ 0 for all φ, which is always true when kink solutions exist.…”

Section: T = T I Cmentioning

confidence: 99%

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Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

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We obtain exact solutions for kinks in φ 8 , φ 10 and φ 12 field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lower-order φ 4 and φ 6 theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a φ 12 potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the φ 10 field theory, which is a quasi-exactly solvable (QES) model akin to φ 6 , we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

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Section: T = T I Cmentioning

confidence: 99%

“…This equation can be linearized about any of the equilibrium states φ e discussed above (e.g., φ e = 0, φ e = ±a, etc.) to obtain an equation for the perturbatioñ φ [30]:…”

Section: E Phononsmentioning

confidence: 99%

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Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

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“…The NLS equation plays an important role in plasma physics [DEGM82], statistical and condensed matter physics [BKT80], nonlinear optics [Ag01], hydrodynamics [ZK97], and magnetic systems [DHS01]. Recently, the NLS equation has been derived as the modulation equation for wave packets in spatially periodic media such as photonic band gap materials and Bose-Einstein condensates [dSS88,DGPS99].…”

Section: Introductionmentioning

confidence: 99%

Justification of the nonlinear Schrödinger equation in spatially periodic media

Busch

Schneider

Tkeshelashvili

et al. 2006

Z. angew. Math. Phys.

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“…As it is impossible to list but the most important publications in this field, we only give a few sample references. An introductory discussion of solitary excitations and a summarizing overview of typical problems can be found in [1]. In [2], an exhaustive review of solitons in magnetic systems is given.…”

Section: Introductionmentioning

confidence: 99%

Soliton diffusion on the classical, isotropic Heisenberg chain

2001

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Abstract. We investigate the diffusive motion of a solitary wave on a classical, isotropic, ferromagnetic Heisenberg spin chain with nearest-neighbour exchange interaction. The spins are coupled magnetically to Gaussian white noise and are subject to Gilbert damping. The noise induces a collective, stochastic time evolution of the solitary wave. Within a continuum version of the model we employ implicit collective variables to describe this stochastic behaviour. Thermally excited magnons are disregarded. We derive stochastic equations of motion for the collective variables and solve them numerically, in particular to obtain their variances as functions of time. These results are compared to data from spin dynamics simulations of a discrete chain. For some of the collective variables we find good agreement with respect to the long time behaviour, whereas for other variables the agreement is only qualitative; reasons for this are given. For shorter times we derive analytical expressions for the variances of the collective variables, which also agree well with spin dynamics.

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Solitons in condensed matter: A paradigm

Cited by 287 publications

References 88 publications

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Justification of the nonlinear Schrödinger equation in spatially periodic media

Soliton diffusion on the classical, isotropic Heisenberg chain

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