Geometric view on noneikonal waves

Dodin, I. Y.

doi:10.1016/j.physleta.2014.04.004

Cited by 34 publications

(74 citation statements)

References 95 publications

(148 reference statements)

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“…The recent work [41] is the brilliant confirmation of the given conclusion. The given work is in fact a new original version of quantum mechanics.…”

Section: Analysis Of the Second Main Postulate And The Ways Of Qusupporting

confidence: 68%

“…Its quantization is nevertheless very natural within the new formalism and can be performed exactly like to the first quantization in the traditional quantum mechanics. A number of advantages has the quantum mechanics version proposed in [41] in comparison with the traditional quantum mechanics. Especially significant, that both the spaces Ψ and X, even more generally, space-time, and commutation relations need to be postulated, in distinction from the traditional quantum mechanics.…”

Section: Analysis Of the Second Main Postulate And The Ways Of Qumentioning

confidence: 99%

See 1 more Smart Citation

To Principles of Quantum Mechanics Development

Yerchuck¹,

Dovlatova²,

Borovik³

et al. 2014

IJP

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New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed.The conclusion on the status of the second main postulate is given. Its formulation in all textbooks has to be represented in the form of statement, since the hypothesis of Schrödinger on the existance of the field scalar function, being to be observable quantity, just charge density, is strictly proved for the case of EM-field, the role of which is argued to be decisive for the dynamics of the atomic systems. It is shown, that the field scalar function, being to be the function the only of coordinates and time, actually describes the state of the system. The second main postulate in Schrödinger formulation is mathematically strictly grounded, but in the popular probabilistic form used in modern textbooks on quantum theory it cannot be proved. The probabilistic theatise, proposed by Born is true in a number of special cases, quite correctly indicated by Dirac.The possible ways of the development of quantum theory, based on clear understanding of the origin of corpuscular-wave dualism are analysed.

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“…The recent work [41] is the brilliant confirmation of the given conclusion. The given work is in fact a new original version of quantum mechanics.…”

Section: Analysis Of the Second Main Postulate And The Ways Of Qusupporting

confidence: 68%

Section: Analysis Of the Second Main Postulate And The Ways Of Qumentioning

confidence: 99%

To Principles of Quantum Mechanics Development

Yerchuck¹,

Dovlatova²,

Borovik³

et al. 2014

IJP

View full text Add to dashboard Cite

show abstract

“…At m < ∼ 7, Landau damping is negligible at our parameters, so the wave total action I is conserved [29]. Since the Langmuir wave temporal spectrum is localized in the vicinity of ω pe , one can adopt the standard linear relation between the action and the wave energy E, namely, I ≈ E/ω pe [37].…”

Section: Resultsmentioning

confidence: 99%

Kinetic simulations of ladder climbing by electron plasma waves

et al. 2017

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The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on whether the wave spectrum is discrete (bounded plasma) or continuous (boundless plasma), this phenomenon is called ladder climbing (LC) or autoresonant acceleration of plasmons. It was first proposed by Barth et al. [Phys. Rev. Lett. 115, 075001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.075001] based on a linear fluid model. In this paper, LC of electron plasma waves is investigated using fully nonlinear Vlasov-Poisson simulations of collisionless bounded plasma. It is shown that, in agreement with the basic theory, plasmons survive substantial transformations of the spectrum and are destroyed only when their wave numbers become large enough to trigger Landau damping. Since nonlinear effects decrease the damping rate, LC is even more efficient when practiced on structures like quasiperiodic Bernstein-Greene-Kruskal (BGK) waves rather than on Langmuir waves per se.

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“…Let us write the fluctuating fields as elements of an abstract Hilbert space L 2 (R 3 ) of wave states with inner product (Dodin 2014;Littlejohn & Winston 1993)…”

Section: Abstract Vector Representationmentioning

confidence: 99%

Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation

2019

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The formation of zonal flows from inhomogeneous drift-wave (DW) turbulence is often described using statistical theories derived within the quasilinear approximation. However, this approximation neglects wave-wave collisions. Hence, some important effects such as the Batchelor-Kraichnan inverse-energy cascade are not captured within this approach. Here we derive a wave kinetic equation that includes a DW collision operator in the presence of zonal flows. Our derivation makes use of the Weyl calculus, the quasinormal statistical closure, and the geometrical-optics approximation. The obtained model conserves both the total enstrophy and energy of the system. The derived DW collision operator breaks down at the Rayleigh-Kuo threshold. This threshold is missed by homogeneous-turbulence theory but expected from a full-wave quasilinear analysis. In the future, this theory might help better understand the interactions between drift waves and zonal flows, including the validity domain of the quasilinear approximation that is commonly used in literature. Singh et al. 2014). The WKE has the intuitive form of the Liouville equation for the DW action density J in the ray phase space (Parker 2016;Ruiz et al. 2016;Zhu et al. 2018c;Parker 2018; Zhu et al. 2018a,b):where Ω is the local DW frequency, Γ is a dissipation rate due to interactions with ZFs, and {·, ·} is the canonical Poisson bracket. (For the sake of clarity, terms related to external forcing and dissipation are omitted here.) However, as with all QL models, Eq. (1.1) neglects nonlinear wave-wave scattering, and in consequence, is not able to capture the Batchelor-Kraichnan inverse-energy cascade (Srinivasan & Young 2012) or produce the Kolmogorov-Zakharov spectra for DWs (Connaughton et al. 2015). Hence, a question remains as to whether the existing WKE for inhomogeneous turbulence can be complemented with a wave-wave collision operator C[J, J]. The goal of this work is to calculate C[J, J] explicitly. Starting from the generalized Hasegawa-Mima equations (gHME) (Krommes & Kim 2000; Smolyakov & Diamond 1999), we derive a WKE with a DW collision operator C[J, J] for inhomogeneous DW turbulence. Our derivation is based on the Weyl calculus (Weyl 1931), which makes our approach similar to that in Ruiz et al. (2016) where the QL approximation was used. However, in contrast to Ruiz et al. (2016), we do not rely on the QL approximation here but instead account for DW collisions perturbatively using the quasinormal approximation. The main result of this work are Eqs. (4.12) and (4.22). In this final result, DWs are modeled in a similar manner as in Eq. (1.1). The difference is that Eq. (4.12) includes nonlinear DW scattering, which is described by a wave-wave collision operator C[J, J] that is bilinear in the DW wave-action density J. The resulting model conserves the two nonlinear invariants of the gHME, which are the total enstrophy and the total energy. The present formulation is fundamentally different from the previously reported homogeneous weak-wave-turbulence mode...

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Geometric view on noneikonal waves

Cited by 34 publications

References 95 publications

To Principles of Quantum Mechanics Development

To Principles of Quantum Mechanics Development

Kinetic simulations of ladder climbing by electron plasma waves

Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation

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