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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)

Elliptic solutions to integrable nonlinear equations and many-body systems

2019 · ARTICLE · en

We review elliptic solutions to integrable nonlinear partial differential and difference equations (KP, mKP, BKP, Toda) and derive equations of motion for poles of the solutions. The pole dynamics is given by an integrable many-body system (Calogero-Moser, Ruijsenaars-Schneider). The basic tool is the auxiliary linear problems for the wave function which yield equations of motion together with their Lax representation. We also discuss integrals of motion and properties of the spectral curves.

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Toda lattice hierarchy and trigonometric Ruijsenaars-Schneider hierarchy

2019 · ARTICLE · en

We consider solutions of the 2D Toda lattice hierarchy which are trigonometric functions of the ``zeroth'' time $t_0=x$. It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this correspondence to the level of hierarchies: the dynamics of poles with respect to the $m$-th hierarchical time $t_m$ (respectively, $\bar t_m$) of the 2D Toda lattice hierarchy is shown to be governed by the Hamiltonian which is proportional to the $m$-th Hamiltonian $\mbox{tr}\, L^m$ (respectively, $\mbox{tr}\, L^{-m}$) of the Ruijsenaars-Schneider model, where $L$ is the Lax matrix.

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Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian

2018 · ARTICLE · en

We discuss a self-dual form or the Backlund transformations for the continuous (in time variable) glN Ruijsenaars-Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars-Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero-Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars-Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian be means of the simple pole ansatz likewise the Calogero-Moser models arise from ordinary intermediate long wave and Benjamin-Ono equations.

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Spin generalization of the Calogero-Moser hierarchy and the matrix KP hierarchy

2018 · ARTICLE · en

We establish a correspondence between rational solutions to the matrix KP hierarchy and the spin generalization of the Calogero-Moser system on the level of hierarchies. Namely, it is shown that the rational solutions to the matrix KP hierarchy appear to be isomorphic to the spin Calogero-Moser system in a sense that the dynamics of poles of solutions to the matrix KP hierarchy in the higher times is governed by the higher Hamiltonians of the spin Calogero-Moser integrable hierarchy with rational potential.

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KZ-Calogero correspondence revisited

2017 · ARTICLE · en

We discuss the correspondence between the Knizhnik–Zamolodchikov equations associated with GL(N) and the n-particle quantum Calogero model in the case when n is not necessarily equal to N. This can be viewed as a natural 'quantization' of the quantum-classical correspondence between quantum Gaudin and classical Calogero models.

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Multi-variable reductions of the dispersionless DKP hierarchy

2017 · PREPRINT · en

We consider multi-variable reductions of the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) in the elliptic parametrization. The reduction is given by a system of elliptic Loewner equations supplemented by a system of partial differential equations of hydrodynamic type. The compatibility conditions for the elliptic Loewner equations are derived. They are elliptic analogues of the Gibbons-Tsarev equations. We prove solvability of the hydrodynamic type system by means of the generalized hodograph method. The associated diagonal metric is proved to be of the Egorov type.

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QKZ-Ruijsenaars correspondence revisited

2017 · ARTICLE · en

We discuss the Matsuo-Cherednik type correspondence between the quantum Knizhnik-Zamolodchikov equations associated with GL(N) and the n-particle quantum Ruijsenaars model, with n being not necessarily equal to N. The quasiclassical limit of this construction yields the quantum-classical correspondence between the quantum spin chains and the classical Ruijsenaars models

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Асимметричная шестивершинная модель и классическая система частиц Рейсенарса–Шнайдера

2017 · ARTICLE · ru

Обсуждается соответствие между моделями, решаемыми анзацем Бете, и классическими интегрируемыми системами типа Калоджеро. Это соответствие проиллюстрировано на простейшем примере неоднородной асимметричной 6-вершинной модели параметризованной тригонометрическими (гиперболическими) функциями

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Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles

2017 · ARTICLE · en

We discuss the correspondence between models solved by the Bethe ansatz and classical integrable systems of the Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric six-vertex model parameterized by trigonometric(hyperbolic) functions.

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Multi-variable reductions of the dispersionless DKP hierarchy

2017 · ARTICLE · en

We consider multi-variable reductions of the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) in the elliptic parametrization. The reduction is given by a system of elliptic Löwner equations supplemented by a system of partial differential equations of hydrodynamic type. The compatibility conditions for the elliptic Löwner equations are derived. They are elliptic analogues of the Gibbons–Tsarev equations. We prove solvability of the hydrodynamic type system by means of the generalized hodograph method. The associated diagonal metric is proved to be of the Egorov type.

DOI ↗ PDF ↗

Курсы (6)