Registration Number
0225U001558,
(0122U001514)
, R & D reports
Title
The role of few-particle effects in shaping the properties of macroscopic systems in bounded geometries
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Роль кількачастинкових ефектів у формуванні властивостей макроскопічних систем в обмежених геометріях
Head
Rovenchak Andrii A., Доктор фізико-математичних наук
Registration Date
03-02-2025
Organization
Ivan Franko National University of Lviv
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Development of theoretical approaches to the calculation of thermodynamic functions and energy characteristics (parameters of spectra, densities of state) of few- and many-particle quantum systems with bounded geometries (i.e. in spaces with dimension D<3, including fractional ones that effectively model porous media, and in external potentials, which in particular model nanoscale objects). Study of thermodynamic properties of low-dimensional many-boson and many-fermion systems with different types of short-range interactions between particles. Identification of the conditions for the emergence of universality in 3- and 4-particle physics of systems with bounded geometry and in fractional dimensions, and elucidation of the role of few-particle quantum effects in shaping the properties of macroscopic systems. Development of new models of fractional statistics. Formulation of quantum-statistical bases of the description of interrelation between the observed phenomena in heterostructures and their parameters.
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For the first time, the existence of bound states consisting of four particles in low-dimensional quantum systems has been shown, thanks to a special effect observed in the interaction of three particles. This study helps to better understand how groups of particles behave in such systems, as well as how their characteristics can be predicted in the thermodynamic limit. The induced interaction of heavy particles in Bose media with a different number of dimensions, including two-dimensional ones, has been investigated, and the appearance of Bose–Einstein condensate in one-dimensional systems placed in external potentials of the exponential type is predicted. A new way of describing the two-dimensional Fermi gas and anyons—special quantum quasiparticles that effectively arise in two-dimensional structures—is proposed using modifications of Fermi–Dirac statistics, which will help to more accurately study the effects of particle interactions in quantum systems. These results will contribute to the development of technologies for the creation of quantum registers and nanoelectronics, as well as to the improvement of methods for calculating the energy, thermodynamic, and transport properties of complex quantum systems (for instance, nanoheterostructures). The acquired knowledge can be used in scientific institutes and educational institutions to study many-particle quantum systems with various types of interactions.
Product Description
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Ivashchyshyn Fedir O.
Hryhorchak Orest I.
Lapko Vladyslav D.
Nikolaieva Alona O.
Panochko Halyna I.
Pastukhov Volodymyr S.
Sobko Bohdana Yu.
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2025-02-03
