Registration Number
0223U004915,
(0120U104781)
, R & D reports
Title
Equilibrium and non-equilibrium processes in quantum integrable models in condensed matter physics
popup.stage_title
Повна статистика переносу заряду в одновимірних системах. Повна статистика переносу заряду для конформного дефекту. Кореляційні функцій в XXZ спіновому ланцюжку та в моделі Ліба-Лінігера. Рівняння Пенлеве та детермінанти Фредгольма
Head
Iorgov Mykola Z., Доктор фізико-математичних наук
Registration Date
08-12-2023
Organization
М.М.Bogolyubov Institute of Theoretical Physics of the National Academy of Sciences of Ukraine
popup.description1
The objectives of this Project address equilibrium and non-equilibrium processes in low-dimensional quantum systems. The main peculiarity of these systems is that the standard methods usually cannot be applied there. For instance, the Landau Fermi-liquid theory that describes fermions in 3D is not applicable for one-dimensional quantum systems. Instead, one has to introduce Tomonaga-Luttinger theory, along with new mathematical methods such as bosonization and soft-modes summation. The applicability of the Tomonaga-Luttinger theory and its various generalizations to the description of the specific physical one-dimensional systems is of interest to many groups in the world and presents the main direction of our Project. We will focus mainly on quantum integrable systems. Integrability allows us to advance in the exact
computations and address nonperturbative regimes. Even when it is impossible to perform analytic calculations to the very end, the intermediate results significantly facilitate numerical calculations and asymptotic analysis. The exact computations require application of the modern
algebraic and analytical mathematical methods: two-dimensional conformal field theory, the non-linear steepest descent method in the matrix Riemann-Hilbert problem, combinatorial methods of the form-factor summations, the theory of isomonodromic deformations and Painleve equations. The necessity to apply these mathematical methods to specific physical problems naturally brings yet another goal of this Project — the improvement and expansion of the methods themselves.The obtained results are expected to be important both for physical applications and
pure mathematics.
popup.description2
The Project is devoted to the investigation of correlation functions in quantum integrable systems for equilibrium finite-entropy initial states, or in the out-of-equilibrium setup. The behavior of such correlation functions is distinct from the vacuum case due to the very different nature of excitations. Integrability allows us to present correlation functions in form-factor series and, in some cases, even get closed analytical expressions in terms of Fredholm determinants. The aim of the Project is twofold: at first, we will develop resummation techniques of the form-factor series in order to describe the asymptotic behavior of the correlation functions, and, secondly, we apply these and similar techniques to describe physical problems such as correlation functions in spin chains, transport problems, kinetics of the mobile impurities in ultracold atomic gases, and to analyze purely mathematical problems related to the isomonodromic deformations and Painleve equations.
Product Description
popup.authors
Gamayun Oleksandr V.
Zhuravlev Yuri S.
popup.nrat_date
2023-12-08
