CC BY
22Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2019
KRAMERS-KRONIG RELATIONS FOR THE DIELECTRIC PERMITTIVITY OF THE COULOMB SYSTEM WITH A SINGLE-PARTICLE BOSE-
EINSTEIN CONDENSATE
V. B. Bobrov, S. A. Trigger
Joint Institute for High Temperatures, RAS, Moscow, Russia
Using the linear response theory and the concept of non-diagonal long-range order, the Kramers-Kronig relations for the dielectric permittivity of an unordered Coulomb system in the presence of a single-particle Bose-Einstein condensate for nuclei are obtained.
The presence of a single-particle Bose-Einstein condensate for nuclei in a disordered Coulomb system fundamentally changes the behavior of the dielectric permittivity e(a>) in the extremely low frequency region rn ^ 0 due to the appearance of a second-order singularity, which is completely determined by the number density of nuclei in a single-particle Bose-Einstein condensate. This circumstance not only leads to a significant change in the Kramers-Kronig relations for the dielectric permittivity, but can also be used for the experimental determination of the quantity of the number density of nuclei in a single-particle Bose-Einstein condensate , which is the most important task to date. Note, that due to the use of linear response theory for description of the dielectric permittivity and the concept of non-diagonal long-range order for the description of single-particle Bose-Einstein condensate, the results are valid outside the framework of perturbation theory for the Coulomb interaction between charged particles.
This work has been supported by the Russian Foundation for Basic Research (grant no. 17-0200573).
References
[1] V. B. Bobrov, S. A. Trigger, G.J.F. van Heijst, and P.P.J.M. Schram, EPL 90, 10003 (2010).
[2] V. B. Bobrov, S. A. Trigger, and A. G. Zagorodny, Phys. Lett. A 375, 84 (2010).
[3] V. B. Bobrov and S. A. Trigger, J. Phys. A: Math.Theor. 43, 365002 (2010). [4] V. B. Bobrov, Phys. Rev. E 86, 026401 (2012).
[5] V. B. Bobrov, S. A. Trigger, and A. G. Zagorodny, EPL 101, 16002 (2013).
[6] V. B. Bobrov and S. A. Trigger, Theor. Math. Phys. 193, 404 (2018).
