Persons: Zotov Andrei Vladimirovich, List of publications

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Zotov Andrei Vladimirovich

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1.	D. Domanevsky, A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation”, Izv. RAN. Ser. Mat. (to appear) , arXiv: 2501.08777

2026
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”, TMF, 2026 (to appear)

2025
3.	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
4.	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
5.	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
6.	A. V. Zotov, “2d classical elliptic integrable field theories from Hitchin systems on ${\rm SL}(NM,\mathbb C)$-bundles with characteristic classes”, Contemporary Mathematics and Its Applications: Proceedings of Sino-Russian Mathematical Meetings, Collected papers, Trudy Mat. Inst. Steklova, 330, Steklov Math. Inst., Moscow, 2025 (to appear)
7.	K. Atalikov, A. Zotov, “Field generalization of elliptic Calogero–Moser system in the form of higher rank Landau–Lifshitz model”, ZhETF, 168:4 (2025), 476–484 , arXiv: 2506.00938
8.	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
9.	Dmitrii Murinov, Andrei Zotov, “Classical r-matrix structure for elliptic Ruijsenaars chain and 1+1 field analogue of Ruijsenaars-Schneider model”, Journal of Physics A: Mathematical and Theoretical, 2025 (Published online) , arXiv: 2508.12656

2024
10.	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	1 ^[x]
11.	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
12.	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	2 ^[x]

2023
13.	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	5 ^[x]
14.	JETP Letters, 117:8 (2023), 630–634
15.	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
16.	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	4 ^[x]

2022
17.	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]
18.	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	7 ^[x]
19.	A. Zabrodin, A. Zotov, “Field analogue of the Ruijsenaars–Schneider model”, JHEP, 2022:7 (2022), 23 , 51 pp., arXiv: 2107.01697	9 ^[x]
20.	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
21.	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	3 ^[x]
22.	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
23.	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	7 ^[x]
24.	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]
25.	I. A. Sechin, A. V. Zotov, Theoret. and Math. Phys., 208:2 (2021), 1156–1164 , arXiv: 2104.04963
26.	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
27.	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]
28.	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
29.	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]
30.	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]
31.	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	11 ^[x]
32.	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
33.	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
34.	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]
35.	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.

2019
36.	A. Grekov, A. Zabrodin, A. Zotov, “Supersymmetric extension of qKZ-Ruijsenaars correspondence”, Nuclear Phys. B, 939 (2019), 174–190 , arXiv: 1810.12658	7 ^[x]
37.	Yu. Chernyakov, S. Kharchev, A. Levin, M. Olshanetsky, A. Zotov, “Generalized Calogero and Toda models”, JETP Letters, 109:2 (2019), 136–143
38.	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
39.	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	16 ^[x]
40.	A. V. Zotov, “Relativistic interacting integrable elliptic tops”, Theoret. and Math. Phys., 201:2 (2019), 1563–1578 , arXiv: 1910.08246
41.	A. Grekov, I. Sechin, A. Zotov, “Generalized model of interacting integrable tops”, JHEP, 2019:10 (2019), 81 , 33 pp., arXiv: 1905.07820	11 ^[x]
42.	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	10 ^[x]

2018
43.	I. Sechin, A. Zotov, “R-matrix-valued Lax pairs and long-range spin chains”, Phys. Lett. B, 781 (2018), 1–7 , arXiv: 1801.08908	15 ^[x]
44.	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	6 ^[x]
45.	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]
46.	A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770
47.	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	12 ^[x]

2017
48.	A. Zabrodin, A. Zotov, “KZ-Calogero correspondence revisited”, J. Phys. A, 50 (2017), 205202 , 12 pp., arXiv: 1701.06074	10 ^[x]
49.	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
50.	A. Zabrodin, A. Zotov, “QKZ–Ruijsenaars correspondence revisited”, Nuclear Phys. B, 922 (2017), 113–125 , arXiv: 1704.04527	8 ^[x]
51.	JETP Letters, 106:3 (2017), 179–183
52.	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
53.	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	7 ^[x]
54.	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]
55.	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	5 ^[x]
56.	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
57.	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	13 ^[x]
58.	A. V. Zotov, “Higher-order analogues of the unitarity condition for quantum $R$-matrices”, Theoret. and Math. Phys., 189:2 (2016), 1554–1562

2015
59.	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]
60.	G. Aminov, A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and Knizhnik–Zamolodchikov–Bernard equations”, JETP Letters, 101:9 (2015), 648–655
61.	A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423 , arXiv: 1212.5813	5 ^[x]
62.	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	16 ^[x]
63.	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
64.	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	27 ^[x]
65.	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
66.	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]
67.	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	32 ^[x]
68.	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	21 ^[x]
69.	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	23 ^[x]

2013
70.	JETP Letters, 97:1 (2013), 45–51
71.	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	61 ^[x]
72.	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	17 ^[x]
73.	A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338
74.	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]
75.	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	40 ^[x]

2012
76.	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	18 ^[x]
77.	A. Zabrodin, A. Zotov, “Quantum Painlevé-Calogero correspondence for Painlevé VI”, J. Math. Phys., 53:7 (2012), 073508 , 19 pp., arXiv: 1107.5672	20 ^[x]
78.	A. Zabrodin, A. Zotov, “Quantum Painlevé-Calogero correspondence”, J. Math. Phys., 53:7 (2012), 073507 , 19 pp., arXiv: 1107.5672	28 ^[x]
79.	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	18 ^[x]
80.	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	11 ^[x]

2011
81.	Andrei V. Zotov, “1+1 Gaudin Model”, SIGMA, 7 (2011), 067 , 26 pp., arXiv: 1012.1072	15 ^[x]

2009
82.	Andrey M. Levin, Mikhail A. Olshanetsky, Andrei V. Zotov, “Monopoles and Modifications of Bundles over Elliptic Curves”, SIGMA, 5 (2009), 065 , 22 pp., arXiv: 0811.3056	9 ^[x]

2008
83.	A. V. Zotov, A. M. Levin, M. A. Olshanetsky, Yu. B. Chernyakov, “Quadratic algebras related to elliptic curves”, Theoret. and Math. Phys., 156:2 (2008), 1103–1122 , arXiv: 0710.1072

2007
84.	A. Levin, A. Zotov, “On rational and elliptic forms of Painlevé VI equation”, Moscow Seminar on Mathematical Physics. II, Amer. Math. Soc. Transl. Ser. 2, 221, Amer. Math. Soc., Providence, RI, 2007, 173–183	6 ^[x]

2006
85.	A. V. Zotov, A. M. Levin, “Integrable Model of Interacting Elliptic Tops”, Theoret. and Math. Phys., 146:1 (2006), 45–52
86.	Yu. Chernyakov, A. M. Levin, M. Olshanetsky, A. Zotov, “Elliptic Schlesinger system and Painlevé VI”, J. Phys. A: Math. Gen., 39:39 (2006), 12083–12101 , arXiv: nlin/0602043	18 ^[x]
87.	A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Painlevé VI, rigid tops and reflection equation”, Comm. Math. Phys., 268:1 (2006), 67–103 , arXiv: math/0508058	29 ^[x]
88.	A. V. Zotov, “Classical integrable systems and their field-theoretical generalizations”, Physics of Particles and Nuclei, 37:3 (2006), 400-443

2005
89.	M. A. Olshanetsky, A. V. Zotov, “Isomonodromic problems on elliptic curve, rigid tops and reflection equations”, Elliptic Integrable Systems, Rokko Lectures in Mathematics, 18, eds. M. Noumi, K. Takasaki, Kobe University, Japan, 2005, 149-172 http://www.math.kobe-u.ac.jp/publications/rlm18/10.pdf

2004
90.	A. Zotov, “Elliptic linear problem for the Calogero-Inozemtsev model and Painlevé VI equation”, Lett. Math. Phys., 67:2 (2004), 153–165 , arXiv: hep-th/0310260	21 ^[x]

2003
91.	A. Zotov, “Elliptic linear problem for Painlevé VI equation with spectral parameter”, Quantum groups and integrable systems, Czechoslovak J. Phys., 53:11 (2003), 1147–1152	1 ^[x]
92.	H. W. Braden, V. A. Dolgushev, M. A. Olshanetsky, A. V. Zotov, “Classical $r$-matrices and the Feigin-Odesskii algebra via Hamiltonian and Poisson reductions”, J. Phys. A, 36:25 (2003), 6979–7000 , arXiv: hep-th/0301121	19 ^[x]
93.	A. M. Levin, M. A. Olshanetsky, A. Zotov, “Hitchin systems—symplectic Hecke correspondence and two-dimensional version”, Comm. Math. Phys., 236:1 (2003), 93–133 , arXiv: nlin/0110045	72 ^[x]

2001
94.	A. V. Zotov, Yu. B. Chernyakov, “Integrable Many-Body Systems via the Inosemtsev Limit”, Theoret. and Math. Phys., 129:2 (2001), 1526–1542
95.	A. Zotov, “On relation between Weyl and Kontsevich quantum products. Direct evaluation up to the $\hslash^3$-order”, Modern Phys. Lett. A, 16:10 (2001), 615–625	10 ^[x]