Discrete Mass, Elementary Length, and a Topological Invariant as a Consequence of a Relativistic Invariant Variational Principle

Enz, U.

doi:10.1103/physrev.131.1392

Cited by 64 publications

(15 citation statements)

References 4 publications

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“…However, here a neutron is not thought to be a point particle, but rather a more or less extended object ("ship+bow wave"; here the possibility of a description of an individual object by means of a soliton solution of a nonlinear evolution equation should be mentioned, e.g. Enz [441]). Indeed, the 'individual contextual state' can be seen as a description of an object that for the largest part chooses one path, but for a small, although for later interference essential part, also follows the other path.…”

Section: Contextual States In Neutron Interference Experimentsmentioning

confidence: 99%

Foundations of Quantum Mechanics, an Empiricist Approach

Muynck¹

2002

146

291

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Section: Contextual States In Neutron Interference Experimentsmentioning

confidence: 99%

Foundations of Quantum Mechanics, an Empiricist Approach

Muynck¹

2002

146

291

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“…In the nonrelativistic limit (q) 2 1, γ ≈ 1 and we obtain for the force law where the modulus parameter l (usually denoted by m) is l = 4C 2C+kc 1 . For the above initial conditions we find and sn(x,l) is a Jacobi elliptic function.…”

Section: Spatially Periodic Potentialsmentioning

confidence: 91%

Nonlinear Dirac equation solitary waves in external fields

et al. 2012

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We consider nonlinear Dirac equations (NLDE's) in the 1 + 1 dimension with scalar-scalar self-interaction g 2 κ+1 (¯ ) κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP (t)/dq(t) < 0. Here P (t) is the momentum of the solitary wave, andq is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP (t)/dq(t) > 0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort in shape.

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“…Among those, stochastic perturbations are very much of interest in view of their highly non trivial effects on nonlinear systems [8], and a great deal of work has been devoted to them [2,4,5]. In particular, of the very many nonlinear models applied to physical problems, the sine-Gordon (sG) equation has been considered in much detail in this context, as it applies to, e.g., propagation of ultra-short optical pulses in resonant laser media [9], a unitary theory of elementary particles [10][11][12][13], propagation of magnetic flux in Josephson junctions [14], transmission of ferromagnetic waves [15], epitaxial growth of thin films [16][17][18], motion of dislocations in crystals [19,20], flux-line unlocking in type II superconductors [21], or DNA dynamics [22][23][24], situations in which noise (of different origins) can play, and often does, a crucial role. As an example, let us mention the recent work on long Josephson junctions reported in [25], where the authors calculated the escape rate from the zero-voltage a e-mail: anxo@math.uc3m.es state induced by thermal fluctuations, obtaining very satisfactory results compared with the experimental ones.…”

Section: Introductionmentioning

confidence: 99%

Thermal diffusion of sine-Gordon solitons

2000

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We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temperature. We find that the kink behavior is very similar to that obtained in the overdamped limit: There is a quadratic dependence on temperature in the diffusion coefficient that comes from the interaction among the kink and phonons, and the average value of the wave function increases with $\sqrt{t}$ due to the variance of the centers of individual realizations and not due to kink distortions. These analytical results are fully confirmed by numerical simulations.Comment: 8 pages, 4 figures, accepted for publication in European Physical Journal

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Discrete Mass, Elementary Length, and a Topological Invariant as a Consequence of a Relativistic Invariant Variational Principle

Cited by 64 publications

References 4 publications

Foundations of Quantum Mechanics, an Empiricist Approach

Foundations of Quantum Mechanics, an Empiricist Approach

Nonlinear Dirac equation solitary waves in external fields

Thermal diffusion of sine-Gordon solitons

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