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Забродин Антон Владимирович

Факультет математики

Профиль на hse.ru ↗ тел.: 12728
Публикаций
78
Языков
1
Наград
4
Конференций
8
Профиль Публикации (78) Курсы (6)

Профессиональные интересы

Интегрируемые системы классической и квантовой физикиТеория случайных матриц и ее приложенияконформная теория поляМатематические модели процессов роста и формирования структур

Должности

  • профессор — Факультет математики
  • Старший научный сотрудник — Факультет математики

Био

  • · Начал работать в НИУ ВШЭ в 2011 году.
  • · Научно-педагогический стаж: 42 года.

Образование

  • 1999 · Доктор физико-математических наук
  • 1989 · Кандидат физико-математических наук
  • 1984 · Специалитет: Московский государственный университет им. М.В. Ломоносова, специальность «Физика», квалификация «Физик»

Опыт работы

  • · 2011: Работает в НИУ ВШЭ с года

Награды и поощрения

  • · Надбавка за публикацию в журнале из Списка А (и приравненном к нему научном издании) (2025–2026, 2024–2025, 2023–2024)
  • · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2021–2022, 2019–2021, 2017–2019)
  • · Надбавка за статью в зарубежном рецензируемом журнале (2015–2017, 2013–2015)
  • · Лучший преподаватель — 2012

Гранты и проекты

  • — · 2014 Грант РФФИ 14-01-90405 "Теория представлений, гомологическая алгебра и интегрируемые системы, российско-украинский грант (участник проека)

Конференции (8)

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  • · 2025: V Конференция математических центров России (Красноярск). Доклад: Интегрируемая деформация системы Руйсенарса-Шнайдера
  • · 2021: Международная конференция «Интегрируемость», посвященная 75-летию А. К. Погребкова (Москва). Доклад: Field analog of the Ruijsenaars-Schneider model from elliptic families of solutions to the 2D Toda lattice
  • · 2018: Классические и квантовые интегрируемые системы (Протвино). Доклад: Спиновое обобщение иерархии Калоджеро-Мозера и матричная иерархия КП
  • · 2016: Classical and quantum integrable systems and supersymmetry (Тянцзинь). Доклад: Supersymmetric quantum spin chains and classical integrable models
  • · 2015: LPT ENS (Париж). Доклад: «Квантовые спиновые цепочки и интегрируемые системы классической механики»
  • · 2015: семинар Кобе по интегрируемым системам (Кобе). Доклад: «Спектры квантовых магнетиков и интегрируемые системы многих частиц классической механики»
  • · 2014: Международная конференция "Физика и математика нелинейных явлений" (Галлиполи). Доклад: "Бездисперсионная иерархия DKP и эллиптическое уравнение Левнера"
  • · 2013: Synthesis of integrabilities in the context of duality between the string theory and gauge theories (Москва). Доклад: Quantum transfer matrices and classical tau-functions

Идентификаторы исследователя

Публикации (78)

Quantum-classical duality for Gaudin magnets with boundary

2020 · ARTICLE · en

We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HjG with particles velocities q˙j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.

DOI ↗ PDF ↗

Dynamics of poles of elliptic solutions to the BKP equation

2020 · ARTICLE · en

We derive equations of motion for poles of elliptic solutions to the B-version of the Kadomtsev–Petviashvili equation (BKP). The basic tool is the auxiliary linear problem for the Baker–Akhiezer function. We also discuss integrals of motion for the pole dynamics which follow from the equation of the spectral curve.

DOI ↗

Scalar products of Bethe vectors in the 8-vertex model

2020 · ARTICLE · en

We obtain a determinant representation of normalized scalar products of onshell and off-shell Bethe vectors in the inhomogeneous 8-vertex model. We consider the case of rational anisotropy parameter and use the generalized algebraic Bethe ansatz approach. Our method is to obtain a system of linear equations for the scalar products, prove its solvability and solve it in terms of determinants of explicitly known matrices.

DOI ↗ PDF ↗

Loewner equations and reductions of dispersionless hierarchies

2020 в печати · PREPRINT · en

The equations of Loewner type can be derived in two very different contexts: one of them is complex analysis and the theory of parametric onformal maps and the other one is the theor of integrable systems.In this paper we compare the both approaches. After recalling the derivation of Loewner equations based on complex analysis we review one- and multi-variable reductions of dispersionless integrable hierarchies (dKP, dBKP, dToda and dDKP). The one-variable reductions are described by solutions of different versions of Loewner equation: chordal (rational) for dKP, quadrant for dBKP, radial (trigonometric) for dToda and elliptic for DKP.We also discuss multi-variable reductions which are given by a system of Loewner equations supplemented by a system of patial differential equations of hydrodynamic type. The solvability of the hydrodynamic type system can be proved by means of the generalized hodograph method.

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Dynamics of poles of elliptic solutions to the BKP equation

2020 · ARTICLE · en

We derive equations of motion for poles of elliptic solutions to the B-version of the Kadomtsev-Petviashvili equation (BKP). The basic tool is the auxiliary linear problem for the Baker-Akhiezer function. We also discuss integrals of motion for the pole dynamics which follow from the equation of the spectral curve.

DOI ↗ PDF ↗

Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary

2020 · ARTICLE · en

We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras B-N, C-N, D-N to the case of supersymmetric gl(m|n) Gaudin models with m + n = 2. Namely, we show that the spectra of quantum Hamiltonians for all such magnets being identified with the classical particles velocities provide the zero level of the classical action variables.

DOI ↗

Quantum-classical duality for Gaudin magnets with boundary

2020 в печати · ARTICLE · en

We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HGj with particles velocities q˙j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.

DOI ↗ PDF ↗

Supersymmetric extension of qKZ-Ruijsenaars correspondence

2019 · ARTICLE · en

We describe the correspondence of the Matsuo-Cherednik type between the quantum nn -body Ruijsenaars-Schneider model and the quantum Knizhnik-Zamolodchikov equations related to supergroup GL(N|M)GL(N|M) . The spectrum of the Ruijsenaars-Schneider Hamiltonians is shown to be independent of the {\mathbb Z}_2 -grading for a fixed value of N+M , so that N+M+1 different qKZ systems of equations lead to the same n -body quantum problem. The obtained results can be viewed as a quantization of the previously described quantum-classical correspondence between the classical n -body Ruijsenaars-Schneider model and the supersymmetric GL(N|M) quantum spin chains on n sites.

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Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy

2019 · ARTICLE · en

We introduce the discrete time version of the spin Calogero-Moser system. The equations of motion follow from the dynamics of poles ofrational solutions to the matrix Kadomtsev-Petviashvili hierarchy with discrete time. The dynamics of poles is derived using the auxiliarylinear problem for the discrete flow

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Matrix modified Kadomtsev-Petviashvili hierarchy

2019 · ARTICLE · en

Using the bilinear formalism, we consider multicomponent and matrix Kadomtsev-Petviashvili hierarchies. The main tool is the bilinear identity for the tau function realized as a vacuum expectation value of a Clifford group element composed of multicomponent fermionic operators. We also construct the Baker– Akhiezer functions and obtain auxiliary linear equations that they satisfy.

DOI ↗ PDF ↗

Курсы (6)