Steklov Mathematical Institute

Home page

Russian page

Dissertation Councils

Staff

Events

Charter

Address

8 Gubkina Str. Moscow,
119333, Russia
Tel.: +7(495) 984 81 41
Web site: www.mi-ras.ru
E-mail: steklov@mi-ras.ru

View Map

Directions

Zotov Andrei Vladimirovich
(recent publications)

by years

scientific publications

by types




2026
1.	D. A. Domanevsky, A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Integrable deformations of principal chiral model from solutions of associative Yang–Baxter equation”, Izv. Math., 90:1 (2026), 109–143, arXiv: 2501.08777
2.	A. M. Mostovskii, A. V. Zotov, “Classical elliptic ${\rm BC}_1$ Ruijsenaars–van Diejen model: relation to Zhukovsky–Volterra gyrostat and 1-site classical $XYZ$ model with boundaries”, Theoret. and Math. Phys., 226:2 (2026), 189–216, arXiv: 2601.06826
3.	M. Matushko, A. Mostovskii, A. Zotov, “$R$-matrix valued Lax pair for elliptic Calogero–Inozemtsev system and associative Yang–Baxter equations of $\mathrm{BC}_n$ type”, Lett. Math. Phys., 116 (2026), 11, 35 pp., arXiv: 2503.22659	1 ^[x]
4.	D. Murinov, A. Zotov, “Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain”, Journal of Geometry and Physics, 226 (2026), 105848, 23 pp., arXiv: 2602.08143	1 ^[x]
5.	Andrei Zotov, “Integrable open elliptic Toda chain with boundaries”, Journal of Mathematical Physics, 67 (2026), 072704, 11 pp., arXiv: 2602.13903

2025
6.	Andrei Zotov, “On the Field Analogue of the Elliptic Spin Calogero–Moser Model: Lax Pair and Equations of Motion”, Functional Analysis and Its Applications, 59:2 (2025), 142–158, arXiv: 2407.13854
7.	R. A. Potapov, A. V. Zotov, “Interrelations between dualities in classical integrable systems and a classical–classical version of the quantum–classical duality”, Theoret. and Math. Phys., 222:2 (2025), 252–275, arXiv: 2410.19035
8.	D. Domanevsky, A. Zotov, “Classical Integrable Spin Chains of Landau–Lifshitz type from R-matrix Identities”, JETP Letters, 121:12 (2025), 921–926, arXiv: 2505.09918
9.	A. V. Zotov, “2D Classical Integrable Field Theories from Hitchin Systems on $\mathrm {SL}(NM,\mathbb C)$-Bundles with Non-trivial Characteristic Classes”, Proc. Steklov Inst. Math., 330 (2025), 479–510
10.	K. Atalikov, A. Zotov, “Field generalization of elliptic Calogero–Moser system in the form of higher rank Landau–Lifshitz model”, Journal of Experimental and Theoretical Physics, 168:4 (2025), 476–484, arXiv: 2506.00938
11.	R. Potapov, A. Zotov, “Large $N$ limit of spectral duality in classical integrable systems”, Eur. Phys. J. C, Part. Fields, 85 (2025), 1331, 12 pp., arXiv: 2508.16470
12.	Dmitrii Murinov, Andrei Zotov, “Classical $r$-matrix structure for elliptic Ruijsenaars chain and $1+1$ field analogue of Ruijsenaars–Schneider model”, J. Phys. A, 58:50 (2025), 505205, 27 pp., arXiv: 2508.12656	2 ^[x]

2024
13.	M. Matushko, A. Zotov, “Supersymmetric generalization of $q$-deformed long-range spin chains of Haldane–Shastry type and trigonometric $\mathrm{GL}(N\|M)$ solution of associative Yang–Baxter equation”, Nuclear Phys. B, 1001 (2024), 116499, 14 pp., arXiv: 2312.04525	4 ^[x]
14.	K. R. Atalikov, A. V. Zotov, “Gauge equivalence of $1+1$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model”, Theoret. and Math. Phys., 219:3 (2024), 1004–1017, arXiv: 2403.00428
15.	Andrei Zotov, “Non-ultralocal classical $r$-matrix structure for $1+1$ field analogue of elliptic Calogero–Moser model”, J. Phys. A, 57 (2024), 315201, 28 pp., arXiv: 2404.01898	5 ^[x]

2023
16.	M. Matushko, A. Zotov, “Elliptic generalisation of integrable $q$-deformed anisotropic Haldane–Shastry long-range spin chain”, Nonlinearity, 36:1 (2023), 319, 36 pp., arXiv: 2202.01177	11 ^[x]
17.	JETP Letters, 117:8 (2023), 630–634
18.	K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation”, Theoret. and Math. Phys., 216:2 (2023), 1083–1103, arXiv: 2303.02391
19.	M. Matushko, Andrei Zotov, “Anisotropic spin generalization of elliptic Macdonald–Ruijsenaars operators and $R$-matrix identities”, Ann. Henri Poincaré, 24 (2023), 3373–3419, arXiv: 2201.05944	10 ^[x]

2022
20.	A. Gorsky, M. Vasilyev, A. Zotov, “Dualities in quantum integrable many-body systems and integrable probabilities. Part I”, JHEP, 2022:4 (2022), 159, 86 pp., arXiv: 2109.05562	9 ^[x]
21.	A. Levin, M. Olshanetsky, A. Zotov, “2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles”, Eur. Phys. J. C, Part. Fields, 82 (2022), 635, 14 pp., arXiv: 2202.10106	10 ^[x]
22.	A. Zabrodin, A. Zotov, “Field analogue of the Ruijsenaars–Schneider model”, JHEP, 2022:7 (2022), 23, 51 pp., arXiv: 2107.01697	14 ^[x]
23.	K. Atalikov, A. Zotov, “Higher Rank 1 + 1 Integrable Landau–Lifshitz Field Theories from the Associative Yang–Baxter Equation”, JETP Letters, 115 (2022), 757-762, arXiv: 2204.12576
24.	E. Trunina, A. Zotov, “Lax equations for relativistic $\mathrm{G}\mathrm{L}(NM,\mathbb{C})$ Gaudin models on elliptic curve”, J. Phys. A, 55:39 (2022), 395202, 31 pp., arXiv: 2204.06137	6 ^[x]
25.	M. G. Matushko, A. V. Zotov, “On the $R$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators”, Theoret. and Math. Phys., 213:2 (2022), 1543–1559, arXiv: 2211.08529

2021
26.	K. Atalikov, A. Zotov, “Field theory generalizations of two-body Calogero–Moser models in the form of Landau–Lifshitz equations”, J. Geom. Phys., 164 (2021), 104161, 14 pp., arXiv: 2010.14297	13 ^[x]
27.	A. Grekov, A. Zotov, “Characteristic determinant and Manakov triple for the double elliptic integrable system”, SciPost Phys., 10:3 (2021), 055, 34 pp., arXiv: 2010.08077	7 ^[x]
28.	I. A. Sechin, A. V. Zotov, Theoret. and Math. Phys., 208:2 (2021), 1156–1164, arXiv: 2104.04963
29.	E. S. Trunina, A. V. Zotov, “Multi-pole extension of the elliptic models of interacting integrable tops”, Theoret. and Math. Phys., 209:1 (2021), 1331–1356, arXiv: 2104.08982
30.	A. Levin, M. Olshanetsky, A. Zotov, “Generalizations of parabolic Higgs bundles, real structures, and integrability”, J. Math. Phys., 62:10 (2021), 103502, 28 pp., arXiv: 2012.15529	1 ^[x]
31.	A. Grekov, A. Zotov, “On Cherednik and Nazarov–Sklyanin large $N$ limit construction for integrable many-body systems with elliptic dependence on momenta”, JHEP, 2021:12 (2021), 062, 43 pp., arXiv: 2102.06853	1 ^[x]

2020
32.	Sovremennye problemy matematicheskoi i teoreticheskoi fiziki, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Andreya Alekseevicha Slavnova, Trudy MIAN, 309, ed. A. K. Pogrebkov, N. A. Slavnov, A. A. Belavin, A. V. Zotov, I. V. Tyutin, MIAN, M., 2020, 346 pp.
33.	M. Vasilyev, A. Zabrodin, A. Zotov, “Quantum-classical duality for Gaudin magnets with boundary”, Nuclear Phys. B, 952 (2020), 114931, 20 pp., arXiv: 1911.11792	4 ^[x]
34.	A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetrization of elliptic $R$-matrices”, J. Phys. A, 53:18 (2020), 185202, 16 pp., arXiv: 1910.05712	1 ^[x]
35.	N. Slavnov, A. Zabrodin, A. Zotov, “Scalar products of Bethe vectors in the 8-vertex model”, JHEP, 2020:6 (2020), 123, 53 pp., arXiv: 2005.11224	12 ^[x]
36.	I. A. Sechin, A. V. Zotov, “Integrable system of generalized relativistic interacting tops”, Theoret. and Math. Phys., 205:1 (2020), 1292–1303, arXiv: 2011.09599
37.	A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations”, J. Math. Phys., 61 (2020), 103504, 9 pp., arXiv: 1910.01814
38.	M. Vasilyev, A. Zabrodin, A. Zotov, “Quantum-classical correspondence for gl(1\|1) supersymmetric Gaudin magnet with boundary”, J. Phys. A, 53:49 (2020), 494002, 20 pp., arXiv: 2006.06717	2 ^[x]

2019
39.	A. Grekov, A. Zabrodin, A. Zotov, “Supersymmetric extension of qKZ-Ruijsenaars correspondence”, Nuclear Phys. B, 939 (2019), 174–190, arXiv: 1810.12658	7 ^[x]
40.	Yu. Chernyakov, S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Generalized Calogero and Toda models”, JETP Letters, 109:2 (2019), 136–143
41.	I. A. Sechin, A. V. Zotov, “${\rm GL}_{NM}$ quantum dynamical $R$-matrix based on solution of the associative Yang–Baxter equation”, Russian Math. Surveys, 74:4 (2019), 767–769, arXiv: 1905.08724
42.	T. Krasnov, A. Zotov, “Trigonometric Integrable Tops from Solutions of Associative Yang–Baxter Equation”, Ann. Henri Poincaré, 20:8 (2019), 2671–2697, arXiv: 1812.04209	21 ^[x]
43.	A. V. Zotov, “Relativistic interacting integrable elliptic tops”, Theoret. and Math. Phys., 201:2 (2019), 1563–1578, arXiv: 1910.08246
44.	A. Grekov, I. Sechin, A. Zotov, “Generalized model of interacting integrable tops”, JHEP, 2019:10 (2019), 81, 33 pp., arXiv: 1905.07820	16 ^[x]
45.	M. Vasilyev, A. Zotov, “On factorized Lax pairs for classical many-body integrable systems”, Rev. Math. Phys., 31:6 (2019), 1930002, 45 pp., arXiv: 1804.02777	12 ^[x]

2018
46.	I. Sechin, A. Zotov, “R-matrix-valued Lax pairs and long-range spin chains”, Phys. Lett. B, 781 (2018), 1–7, arXiv: 1801.08908	21 ^[x]
47.	A. Grekov, A. Zotov, “On $R$-matrix valued Lax pairs for Calogero–Moser models”, J. Phys. A, 51 (2018), 315202, 26 pp., arXiv: 1801.00245	12 ^[x]
48.	A. V. Zabrodin, A. V. Zotov, “Self–dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian”, Nuclear Phys. B, 927 (2018), 550–565, arXiv: 1711.01036	8 ^[x]
49.	A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770
50.	S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Quasi-compact Higgs bundles and Calogero–Sutherland systems with two types of spins”, J. Math. Phys., 59:10 (2018), 103509, 36 pp., arXiv: 1712.08851	13 ^[x]

2017
51.	A. Zabrodin, A. Zotov, “KZ-Calogero correspondence revisited”, J. Phys. A, 50 (2017), 205202, 12 pp., arXiv: 1701.06074	10 ^[x]
52.	A. V. Zabrodin, A. V. Zotov, A. N. Liashyk, D. S. Rudneva, “Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles”, Theoret. and Math. Phys., 192:2 (2017), 1141–1153, arXiv: 1611.02497
53.	A. Zabrodin, A. Zotov, “QKZ–Ruijsenaars correspondence revisited”, Nuclear Phys. B, 922 (2017), 113–125, arXiv: 1704.04527	8 ^[x]
54.	JETP Letters, 106:3 (2017), 179–183
55.	A. Zotov, “Relativistic elliptic matrix tops and finite Fourier transformations”, Modern Phys. Lett. A, 32:32 (2017), 1750169, 22 pp., arXiv: 1706.05601	7 ^[x]

2016
56.	A. Levin, M. Olshanetsky, A. Zotov, “Yang–Baxter equations with two Planck constants”, J. Phys. A: Math. Theor., 49:1 (2016), 14003, 19 pp., Exactly Solved Models and Beyond: a special issue in honour of R. J. Baxter's 75th birthday, arXiv: 1507.02617	9 ^[x]
57.	M. Beketov, A. Liashyk, A. Zabrodin, A. Zotov, “Trigonometric version of quantum–classical duality in integrable systems”, Nuclear Phys. B, 903 (2016), 150–163, arXiv: 1510.07509	20 ^[x]
58.	Ivan Sechin, Andrei Zotov, “Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices”, J. Math. Phys., 57:5 (2016), 53505, 14 pp., arXiv: 1511.08761	6 ^[x]
59.	A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations”, Theoret. and Math. Phys., 188:2 (2016), 1121–1154, arXiv: 1507.04265
60.	Andrey Levin, Mikhail Olshanetsky, Andrei Zotov, “Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation”, J. Phys. A, 49:39 (2016), 395202, 26 pp., arXiv: 1603.06101	18 ^[x]
61.	A. V. Zotov, “Higher-order analogues of the unitarity condition for quantum $R$-matrices”, Theoret. and Math. Phys., 189:2 (2016), 1554–1562

2015
62.	G. Aminov, H. W. Braden, A. Mironov, A. Morozov, A. Zotov, “Seiberg-Witten curves and double-elliptic integrable systems”, J. High Energy Phys., 2015, no. 1, 033, 15 pp., arXiv: 1410.0698	17 ^[x]
63.	G. Aminov, A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and Knizhnik–Zamolodchikov–Bernard equations”, JETP Letters, 101:9 (2015), 648–655
64.	A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423, arXiv: 1212.5813	6 ^[x]
65.	Zengo Tsuboi, Anton Zabrodin, Andrei Zotov, “Supersymmetric quantum spin chains and classical integrable systems”, J. High Energy Phys., 2015, no. 5, 086, 43 pp., arXiv: 1412.2586	18 ^[x]
66.	A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Quantum Baxter–Belavin $R$-matrices and multidimensional Lax pairs for Painlevé VI”, Theoret. and Math. Phys., 184:1 (2015), 924–939, arXiv: 1501.07351

2014
67.	A. Gorsky, A. Zabrodin, A. Zotov, “Spectrum of quantum transfer matrices via classical many-body systems”, J. High Energy Phys., 2014, no. 1, 070, 28 pp., arXiv: 1310.6958	30 ^[x]
68.	A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118, arXiv: 1311.4498
69.	G. Aminov, S. Arthamonov, A. Smirnov, A. Zotov, “Rational top and its classical $r$-matrix”, J. Phys. A: Math. Theor., 47:30 (2014), 305207, 19 pp., arXiv: 1402.3189	19 ^[x]
70.	A. Levin, M. Olshanetsky, A. Zotov, “Relativistic classical integrable tops and quantum $R$-matrices”, J. High Energy Phys., 2014, no. 7, 012, arXiv: 1405.7523	35 ^[x]
71.	A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and soliton equations related to eleven-vertex $R$-matrix”, Nuclear Physics B, 887 (2014), 400–422, arXiv: 1406.2995	24 ^[x]
72.	A. Levin, M. Olshanetsky, A. Zotov, “Planck constant as spectral parameter in integrable systems and KZB equations”, JHEP, 2014, no. 10, 109, 29 pp., arXiv: 1408.6246v2	27 ^[x]

2013
73.	JETP Letters, 97:1 (2013), 45–51
74.	A. Mironov, A. Morozov, B. Runov, Y. Zenkevich, A. Zotov, “Spectral duality between Heisenberg chain and Gaudin model”, Lett. Math. Phys., 103:3 (2013), 299–329, arXiv: 1206.6349	62 ^[x]
75.	A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes of $\mathrm{SL}(N,\mathbb C)$-bundles and quantum dynamical elliptic $R$-matrices”, J. Phys. A: Math. Theor., 46:3 (2013), 035201, 25 pp., arXiv: 1208.5750	18 ^[x]
76.	A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338
77.	G. Aminov, A. Mironov, A. Morozov, A. Zotov, “Three-particle integrable systems with elliptic dependence on momenta and theta function identities”, Phys. Lett. B, 726:4-5 (2013), 802–808, arXiv: 1307.1465	19 ^[x]
78.	A. Mironov, A. Morozov, B. Runov, Y. Zenkevich, A. Zotov, “Spectral dualities in XXZ spin chains and five dimensional gauge theories”, J. High Energy Phys., 2013, no. 12, 034, 11 pp., arXiv: 1307.1502	41 ^[x]

2012
79.	A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes and Hitchin systems. General construction”, Comm. Math. Phys., 316:1 (2012), 1–44, arXiv: 1006.0702	19 ^[x]
80.	A. Zabrodin, A. Zotov, “Quantum Painlevé-Calogero correspondence for Painlevé VI”, J. Math. Phys., 53:7 (2012), 073508, 19 pp., arXiv: 1107.5672	23 ^[x]
81.	A. Zabrodin, A. Zotov, “Quantum Painlevé-Calogero correspondence”, J. Math. Phys., 53:7 (2012), 073507, 19 pp., arXiv: 1107.5672	28 ^[x]
82.	A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Calogero-Moser systems for simple Lie groups and characteristic classes of bundles”, J. Geom. Phys., 62:8 (2012), 1810–1850, arXiv: 1007.4127	19 ^[x]
83.	Andrey M. Levin, Mikhail A. Olshanetsky, Andrey V. Smirnov, Andrei V. Zotov, “Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles”, SIGMA, 8 (2012), 095, 37 pp., arXiv: 1207.4386	12 ^[x]

2011
84.	Andrei V. Zotov, “1+1 Gaudin Model”, SIGMA, 7 (2011), 067, 26 pp., arXiv: 1012.1072	17 ^[x]

Full list of publications