Method of canonical transformations in the theory of quantum gases interacting with radiation

M. S. Bulakhov; A. S. Peletminskii; P. P. Kostrobij; I. A. Ryzha; Yu. V. Slyusarenko

doi:10.5488/cmp.28.23302

Authors

M. S. Bulakhov Akhiezer Institute for Theoretical Physics, NSC Kharkiv Institute of Physics and Technology, 1 Akademichna St., 61108 Kharkiv, Ukraine https://orcid.org/0000-0002-8409-5558
A. S. Peletminskii Akhiezer Institute for Theoretical Physics, NSC Kharkiv Institute of Physics and Technology, 1 Akademichna St., 61108 Kharkiv, Ukraine https://orcid.org/0000-0001-6352-4838
P. P. Kostrobij Lviv Polytechnic National University, 12 S. Bandera Str., 79013 Lviv, Ukraine https://orcid.org/0000-0002-4428-1647
I. A. Ryzha Lviv Polytechnic National University, 12 S. Bandera St., 79013 Lviv, Ukraine https://orcid.org/0000-0001-6647-0521
Yu. V. Slyusarenko Akhiezer Institute for Theoretical Physics, NSC Kharkiv Institute of Physics and Technology, 1 Akademichna St., 61108 Kharkiv, Ukraine; Lviv Polytechnic National University, 12 S. Bandera St., 79013 Lviv, Ukraine; V. N. Karazin National University of Kharkiv, 4 Svobody Sq., 61022 Kharkiv, Ukraine https://orcid.org/0000-0001-5298-0731

DOI:

https://doi.org/10.5488/cmp.28.23302

Keywords:

quantum gases, photons, canonical transformations, dressed atoms, dispersion law, effective mass

Abstract

An approach to the theoretical study of effects and phenomena in quantum gases interacting with radiation is proposed. The approach is based on a modification of the canonical transformation method, which was once used to diagonalize Hamiltonians describing the interaction of electrons with phonons in a solid. The capabilities of the method are demonstrated by studying the influence of photons on the spectral characteristics of atoms of quantum gases interacting with radiation. Within the framework of the developed approach, the effect of “dressing” atoms of quantum gases by a cloud of virtual photons is investigated and expressions for the energy characteristics of such dressed atoms — quasiparticles are obtained. The problem of defining the concept of the effective mass of such quasiparticles is discussed.

References

Klaers J., Schmitt J., Vewinger F., Weitz M., Nature, 2010, 468, 545. DOI: https://doi.org/10.1038/nature09567

Klaers J., Schmitt J., Damm T., Dung D., Vewinger F., Weitz M., Proc. SPIE, 2013, 468, 8600. DOI: https://doi.org/10.1117/12.2001831

Slyusarenko Yu. V., Slyusarenko O. Yu., J. Math. Phys., 2017, 58, 1133021. DOI: https://doi.org/10.1063/1.5010334

Kruchkov A., Slyusarenko Yu., Phys. Rev. A, 2013, 88, 013615. DOI: https://doi.org/10.1103/PhysRevA.88.013615

Boichenko N., Slyusarenko Yu., Condens. Matter Phys., 2015, 18, 43002. DOI: https://doi.org/10.5488/CMP.18.43002

Peletmiskii A. S., Slyusarenko Yu. V., Sotnikov A. G., Theory of Exotic States in Quantum Fermi and Bose Systems, Naukova Dumka, Kyiv, 2023 (in Ukrainian).

Euler H., Kockel B., Naturwissenschaften, 1935, 23, 246. DOI: https://doi.org/10.1007/BF01493898

Akhieser A., Landau L., Pomeranchook I., Nature, 1936, 138, 206. DOI: https://doi.org/10.1038/138206a0

Bulakhov M. S., Peletminskii A. S., Slyusarenko Yu. V., Ukr. J. Phys., 2024, 69, No. 8, 600. DOI: https://doi.org/10.15407/ujpe69.8.600

Altschul B., Astropart. Phys., 2008, 29, 290. DOI: https://doi.org/10.1016/j.astropartphys.2008.02.006

Pérez Rojas H., Rodríguez Querts E., Eur. Phys. J. C, 2014, 74, 2899. DOI: https://doi.org/10.1140/epjc/s10052-014-2899-y

Saglam Z., Sahin G., J. Mod. Phys., 2015, 6, 937. DOI: https://doi.org/10.4236/jmp.2015.67098

Landau L. D., Lifshits E. M., Quantum Mechanics: Non-Relativistic Theory, Course of Theoretical Physics, Vol. 3, Pergamon Press, Oxford New York, third edn., 1977.

Peletminskii S. V., Slyusarenko Yu. V., J. Math. Phys., 2005, 46, 022301. DOI: https://doi.org/10.1063/1.1812359

Frölich H., Proc. Roy. Soc. A, 1952, 215, 291. DOI: https://doi.org/10.1098/rspa.1952.0212

Davydov A. S., Pestryakov G. M., Phys. Status Solidi B, 1972, 49, 505. DOI: https://doi.org/10.1002/pssb.2220490212

Kittel C., Introduction to Solid State Physics, Wiley, Hoboken, NJ, eighth edn., 2005.

Wikipedia, Effective mass (solid-state physics) — Wikipedia, the free encyclopedia, 2025, [Online; accessed 10-Feb-2025], URL https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics).

Peletminskii A. S., Peletminskii S. V., Slyusarenko Yu. V., J. Phys. B: At. Mol. Opt. Phys., 2017, 50, 145301. DOI: https://doi.org/10.1088/1361-6455/aa75d6

Zagorodny A. G., Slyusarenko Yu. V., Shulga S. N., Low Temp. Phys., 2018, 44, 1049. DOI: https://doi.org/10.1063/1.5055846

Akhiezer A. I., Peletminskii S. V., Methods of Statistical Physics, Pergamon, Oxford, 1981.