**Authors:**

**Peletmynskiy Oleksandr Sergiyovych**, senior staff scientist of Department of statistical physics and quantum field theory, O.I. Akhiezer Institute for Theoretical Physics, National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, senior staff scientist, candidate (PhD) of mathematical and physical sciences; National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, Kharkiv, Ukraine; V.N. Karazin Kharkiv National University, Kharkiv, Ukraine.

https://orcid.org/0000-0001-6352-4838

**Slyusarenko Yuriy Viktorovych**, head of Department of statistical physics and quantum field theory, O.I. Akhiezer Institute for Theoretical Physics, National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, professor, academician of NAS of Ukraine, doctor of mathematical and physical sciences; National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, Kharkiv, Ukraine; V.N. Karazin Kharkiv National University, Kharkiv, Ukraine.

https://orcid.org/0000-0001-5298-0731

**Sotnikov Andrii Gennadijovych**, leading staff scientist of Department of statistical physics and quantum field theory, O.I. Akhiezer Institute for Theoretical Physics, National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, senior researcher, doctor of mathematical and physical sciences; National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, Kharkiv, Ukraine; V.N. Karazin Kharkiv National University, Kharkiv, Ukraine.

https://orcid.org/0000-0002-3632-4790

**Reviewers:**

**Azaryenkov Mykola Oleksijovych**, professor at the Education and Research Institute “School of Physics and Technology”, V.N. Karazin National University, professor, academician of NAS of Ukraine, doctor of mathematical and physical sciences; V.N. Karazin Kharkiv National University, Kharkiv, Ukraine.

https://orcid.org/0000-0002-4019-4933

**Bakai Oleksandr Stepanovych**, head of department of theory of condensed matter and nuclear matter, O.I. Akhiezer Institute for Theoretical Physics, National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, professor, academician of NAS of Ukraine, doctor of mathematical and physical sciences; Bakai O.S.: National Science Center “Kharkiv Institute of Physics and Technology”, NAS of Ukrarine, Kharkiv, Ukraine.

https://www.scopus.com/authid/detail.uri?authorId=7004702496

**Affiliation:**

**Project: **Scientific book

**Year: **2023

**Publisher: **PH "Naukova Dumka"

**Pages: **480

**DOI: **

https://doi.org/10.15407/978-966-00-1851-8

**ISBN: **978-966-00-1851-8

**Language: ** Ukrainian

**How to Cite:**

Peletmynskiy, O., Slyusarenko, Y., Sotnikov, A. (2023) Theory of exotic states in quantum Fermi and Bose systems. Kyiv, Naukova Dumka. 480 p. [in Ukrainian].

**Abstract:**

The monograph is devoted to the main aspects of theoretical description of quantum many-body systems with Bose-Einstein or Fermi-Dirac statistics. We provide a review of modern methods of theoretical research, both analytical and numerical, as well as experimental realizations of unique effects and phenomena in quantum systems. The main attention is given to the theoretical study of exotic states in degenerate gases of atoms and quasiparticles.

We develop a methology to accurately determine chemical potentials and other thermodynamic characteristics of ideal Bose and Fermi gases. These allow us to describe the ultraslow-light phenomenon in ultracold atomic gases in the framework of the microscopic approach that accounts for the internal degrees of freedom of bound states. The formalism relies on the linear response theory applied for the case of weak perturbation by the external elecromagnetic field. We also study Bose-Einstein condensation of photons in ideal atomic gases in different regimes of degeneracy of atomic and photonic components.

A special attention is given to the Bogoliubov method of quasiaverages and related theory of a weakly interacting Bose gas with condensate. We extend the Bogoliubov theory to examine the spinor condensate and its magnetic states, as well as the condensate of heteronuclear Fermi-Fermi molecules. We also study a spatially periodic state of Bose-Einstein condensate, which can serve as a model for supersolid state of matter and develop the hydrodynamic theory of the latter.

We outline the main statements of the Fermi liquid theory including the Pomeranchuk stability conditions of the normal state. It is shown that the violation of stability conditions results in certain phase transitions associated with the breaking of translational symmetry and rotational symmetry in the momentum space. We review a progress in the theoretical description of ultracold Fermi gases consisting of neutral atoms in the presence of the optical lattice spatial modulation. In case of multicomponent systems, a number of unique magnetically-ordered states are theoretically studied and predicted. We also develop a theory of highly dispersive spinful excitons in cobaltite compounds that explains certain unusual magnetic properties and effects in the resonant inelastic X-ray scattering on these materials.

**Keywords:**

Quantum statistics, Bose gases, Fermi gases, ultracold atomic gases, quantum degeneracy, second quantization, linear response theory, Green’s functions, ultraslow light, Bose-Einstein condensation, condensate of photons, condensate of molecules, spinor condensate, quasiparticles, quasiaverages, Fermi liquid, stability conditions, phase transitions, superfluid quantum crystal, supersolid, order parameter, macroscopic equations of motion, hydrodynamics, Galilean invariance, relativistic invariance, spin-wave theory, Shrieffer-Wolff transformations, dynamical mean-field theory, optical lattices, Hubbard model, Heisenberg model, magnetic ordering, antiferromagnet, exitonic insulator, spinful excitons.

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