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Information × Registration Number 0120U104781, ( 0220U104463  0222U003796  0222U003798  0223U004915  ) R & D request Title Equilibrium and non-equilibrium processes in quantum integrable models in condensed matter physics Head Iorgov Mykola Z., Доктор фізико-математичних наук Registration Date 11-11-2020 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.nrat_date 2024-12-10 Close