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In summary, the dispersion relation in a plasmon system becomes linear for small values of q due to the influence of the vector potential.f

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Here is a reference: http://rmf.smf.mx/pdf/rmf/39/4/39_4_640.pdf

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Ok, I suppose he means the nabla in reduced density. Using the ansatz for the charge distribution given above, I find for the electric potential ##E=(\kappa/(iq) e_x+\mathrm{sgn}(z)e_z)\rho/2 \exp(-\kappa |z|) \exp(iqx-i\omega t)##, where ##\kappa=\sqrt(|\omega^2-q^2|)##.

Hence the driving force in equation 5 does not depend linearly on q but on kappa. For large values of q, kappa goes like q but for small values like omega. Hence for small values of q there should the dispersion relation changes.

Hence the driving force in equation 5 does not depend linearly on q but on kappa. For large values of q, kappa goes like q but for small values like omega. Hence for small values of q there should the dispersion relation changes.

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Thank you very much for your insightful advice !

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there might be some small errors, but the expression for E is a correct solution of the wave equation for z not equal zero while forming the divergence yields the correct charge density. Forming the 2d-divergence in eq. 5 ammounts to multiplication of the x component with iq which yields kappa.

Maybe you could post your solution?

Maybe you could post your solution?

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So what is the z-component of the electric field you found?

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Current density is completely determined by continuity.

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I'm much grateful for your comments which have led me to a good understanding of my problem. As this understanding is significant in improving one of my recent manuscripts, which I'll submit for publication, I'm thinking formally acknowledging you or adding you as a coauthor. So, if possible, I hope to discuss more by private emails, instead here. I definitely have to know you real profile before I can do this.

Thanks.

hiyok

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