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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)

Показать все
  • · 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)

Formal solutions to the KP hierarchy

2016 · ARTICLE · en

We find all formal solutions to the -dependent KP hierarchy. They are characterized by certain Cauchy-like data. The solutions are found in the form of formal series for the tau-function of the hierarchy and for its logarithm (the F-function). An explicit combinatorial description of the coefficients of the series is provided.

DOI ↗ PDF ↗

Trigonometric version of quantum–classical duality in integrable systems

2016 · ARTICLE · en

We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars-Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero-Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.

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Theta vocabulary II. Multidimensional case

2016 · ARTICLE · en

It is shown that the Jacobi and Riemann identities of degree four for the multidimensional theta functions as well as the Weierstrass identities emerge as algebraic consequences of the fundamental multidimensional binary identities connecting the theta functions with Riemann matrices tau and 2tau .

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Dispersionless Pfaff-Toda hierarchy and elliptic L¨owner equation

2016 · ARTICLE · en

We show that one-variable reductions of the Pfaff-Toda integrable hierarchy in the dispersionless limit are described by a system of coupled elliptic Löwner (Komatu-Goluzin) equations.

DOI ↗

Trigonometric version of quantum–classical duality in integrable systems

2016 · ARTICLE · en

We extend the quantum–classical duality to the trigonometric(hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars–Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars–Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero–Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.

DOI ↗

Symmetric solutions to dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics

2015 · ARTICLE · en

We explicitly construct the series expansion for a certain class of solutions to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric solutions. We express the Taylor coefficients through some universal combinatorial constants and find recurrence relations for them. These results are used to obtain new formulas for the genus 0 double Hurwitz numbers. They can also serve as a starting point for a constructive approach to the Riemann mapping problem and the inverse potential problem in 2D.

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Classical-Quantum Correspondence and Functional Relations for Painlevé Equations

2015 · ARTICLE · en

In light of the quantum Painlevé–Calogero correspondence, we investigate the inverse problem. We imply that this type of the correspondence (classical-quantum correspondence) holds true, and we find out what kind of potentials arise from the compatibility conditions of the related linear problems. The latter conditions are written as functional equations for the potentials depending on a choice of a single function—the left-upper element of the Lax connection. The conditions of the correspondence impose restrictions on this function. In particular, it satisfies the heat equation. It is shown that all natural choices of this function (rational, hyperbolic, and elliptic) reproduce exactly the Painlevé list of equations. In this sense, the classical-quantum correspondence can be regarded as an alternative definition of the Painlevé equations. © 2015, Springer Science+Business Media New York.

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Supersymmetric quantum spin chains and classical integrable systems

2015 · ARTICLE · en

For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians. © 2015, The Author(s).

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Theta vocabulary I

2015 · ARTICLE · en

This paper is an annotated list of transformation properties and identities satisfied by the four theta functions of one complex variable, presented in a ready-to-use form. An attempt is made to reveal a pattern behind various identities for the theta-functions. It is shown that all possible 3, 4 and 5-term identities of degree four emerge as algebraic consequences of the six fundamental bilinear 3-term identities connecting the theta-functions with different modular parameters 2τ

DOI ↗ PDF ↗

Эллиптическая параметризация пфаффовых интегрируемых иерархий в пределе нулевой дисперсии

2015 · ARTICLE · en

Показано, что бездисперсионные пределы иерархии Пфафф-КП (также известной как Пфаффовая Решетка и DKP) и иерархии Пфафф-Тода допускают переформулировку в терминах эллиптических функций. В эллиптической форме они выглядят соответственно как эллиптические деформации бездисперсионных иерархий КП и двумеризованной цепочки Тоды.

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Курсы (6)