Ultrametric and p-adic analysis and applications in physics and biology, quantum probability and applications in physics, stochastic limit of quantum theory.
Biography
Graduated from Physical Faculty of Moscow State University (department of Quantum Statistics and Field Theory). Ph.D. obtained in 1991 at Steklov Mathematical Institute. D.Sci. degree obtained in 2007 at Steklov Mathematical Institute. Published more than 50 papers.
Main publications:
S.V. Kozyrev, Methods and applications of ultrametric and $p$-adic analysis: from wavelet theory to biophysics, Sovrem. Probl. Mat., 12, Steklov Math. Inst., RAS, Moscow, 2008
S.V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376, arXiv: math-ph/0012019
V.A. Avetisov, A.H. Bikulov, S.V. Kozyrev, “Application of p-adic analysis to models of spontaneous breaking of replica symmetry”, J. Phys. A: Math. Gen., 32:50 (1999), 8785–8791, arXiv: cond-mat/9904360
S.V. Kozyrev, I.V. Volovich, “The Arrhenius formula in kinetic theory and Witten's spectral asymptotics”, J. Phys. A: Math. Theor., 44 (2011), 215202, 10 pp., arXiv: 1008.4487
L. Accardi, S.V. Kozyrev, I.V. Volovich, “Dynamics of dissipative two-level system in the stochastic approximation”, Phys. Rev. A, 56:4 (1997), 2557–2562, arXiv: quant-ph/9706021
S. V. Kozyrev, “How to explain grokking”, Comput. Math. Math. Phys., 66:5 (2026), 953–957
2025
2.
S. V. Kozyrev, I. A. Lopatin, A. N. Pechen, “Generalization in learning: Eyring formula and predator-prey model”, Lobachevskii J. Math., 46:6 (2025), 2591–2600
3.
I. A. Lopatin, S. V. Kozyrev, A. N. Pechen, Predator–Prey Model: Driven Hunt for Accelerated Grokking, 2025, 15 pp., arXiv: 2509.10562
4.
Sergei V. Kozyrev, “Action in Physics, Biology and AI”, P-Adic Numbers Ultrametric Anal. Appl., 17:4 (2025), 379–384
2024
5.
S. V. Kozyrev, “Lotka–Volterra model with mutations and generative adversarial networks”, Theoret. and Math. Phys., 218:2 (2024), 276–284
6.
Sergei V. Kozyrev, Ilya A. Lopatin, Alexander N. Pechen, “Control of overfitting with physics”, Entropy, 26:12 (2024), 1090, 16 pp., arXiv: 2412.10716
Sergei V. Kozyrev, Alexander N. Pechen, “Amplification of quantum transfer and quantum ratchet”, Phys. Scr., 98:12 (2023), 125122, 12 pp.
12.
B. Dragovich, A. Yu. Khrennikov, I. V. Volovich, S. V. Kozyrev, “On the Occasion of the Centenary of the Birth of V. S. Vladimirov (1923–2012)”, p-Adic Numbers, Ultrametric Analysis and Applications, 15:3 (2023), 243–244
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “Giorgio Parisi: The Nobel Prize in Physics 2021”, P-Adic Numbers Ultrametric Anal. Appl., 14:1 (2022), 81–83
Sergei V. Kozyrev, Alexander N. Pechen, “Quantum feedback control in quantum photosynthesis”, Phys. Rev. A, 106 (2022), 32218, 10 pp., arXiv: 2105.12128
L. Accardi, B. Dragovich, S. V. Kozyrev, A. S. Trushechkin, “Preface”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2202002, 1 pp.
17.
S. V. Kozyrev, “Landau–Zener formula and non-secular transitions”, Int. J. Mod. Phys. A, 37:20-21 (2022), 2243015, 9 pp., arXiv: 2201.07223
2021
18.
Branko Dragovich, Andrei Yu. Khrennikov, Sergei V. Kozyrev, Nataša. Ž. Mišić, “$p$-Adic Mathematics and Theoretical Biology”, Biosystems, 199 (2021), 104288, 10 pp.
Alexei N. Nekrasov, Yuri P. Kozmin, Sergey V. Kozyrev, Rustam H. Ziganshin, Alexandre G. de Brevern, Anastasia A. Anashkina, “Hierarchical structure of protein sequence”, Int. J. Mol. Sci., 22:15 (2021), 8339, 12 pp.
Sergei V. Kozyrev, “Learning problem for functional programming and model of biological evolution”, P-Adic Numbers Ultrametric Anal. Appl., 12:2 (2020), 112–122
A. N. Nekrasov, Y. P. Kozmin, S. V. Kozyrev, N. G. Esipova, R. H. Ziganshin, A. A. Anashkina, “Levels of hierarchical organization of protein sequences. Entropy Characteristics Analysis”, Biophysics, 65:6 (2020), 1965–1071
2019
25.
S. V. Kozyrev, “Model of Vibrons in Quantum Photosynthesis as an Analog of a Model of Laser”, Proc. Steklov Inst. Math., 306 (2019), 145–156
26.
Sergei V. Kozyrev, “Code Biology and Kolmogorov Complexity”, Advances in Artificial Systems for Medicine and Education II. AIMEE2018 2018., International Conference of Artificial Intelligence, Medical Engineering, Education (6-8 October, Moscow, Russia), Adv. Intell. Syst. Comput., 902, eds. Hu Z., Petoukhov S., He M., Springer, 2019, 93–101
2018
27.
S. V. Kozyrev, “Quantum Transport in Degenerate Systems”, Proc. Steklov Inst. Math., 301 (2018), 134–143
28.
A.Yu. Khrennikov, S.V. Kozyrev, W.A. Zuniga-Galindo, Ultrametric Pseudodifferential Equations and Applications, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 2018, 250 pp.
29.
S.V. Kozyrev, I.V. Volovich, “Dark states in quantum photosynthesis”, Trends in Biomathematics: Modeling, Optimization and Computational Problems, Proceedings of BIOMAT 2017 Conference (Institut vychislitelnoi matematiki RAN, Moskva, 30 oktyabrya –3 noyabrya 2017 g), eds. R.P. Mondaini, Springer, Berlin, 2018, 13-26, arXiv: 1603.07182
V. S. Anashin, B. Dragovich, A. N. Kochubei, S. V. Kozyrev, and I. V. Volovich, “Andrei Yurievich Khrennikov and his Research”, P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 344–347
2017
32.
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov, “p-Adic Mathematical Physics: The First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121, arXiv: 1705.04758
I. Ya. Aref'eva, G. S. Djordjevic, A. Yu. Khrennikov, S. V. Kozyrev, Z. Rakic, I. V. Volovich, “p-Adic mathematical physics and B. Dragovich research”, P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017), 82–85
S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, I. V. Volovich, “Flows in nonequilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021, 19 pp., arXiv: 1612.00213
A. N. Nekrasov, A. A. Zinchenko, D. M. Karlinskii, S. V. Kozyrev, “Metod issledovaniya ierarkhicheskikh elementov v prirodnykh aminokislotnykh posledovatelnostyakh”, Uspekhi sovremen. estestvozn., 2016, no. 11, 242–248
2015
38.
I. Ya. Aref'eva, I. V. Volovich, S. V. Kozyrev, “Stochastic limit method and interference in quantum many-particle systems”, Theoret. and Math. Phys., 183:3 (2015), 782–799
39.
A. Khrennikov, S. Kozyrev, A. Månsson, “Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 18:2 (2015), 1550013, 16 pp., arXiv: 1312.7528
S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196
43.
S. V. Kozyrev, “Cluster networks and Bruhat–Tits buildings”, Theoret. and Math. Phys., 180:2 (2014), 958–966
2013
44.
A. Yu. Khrennikov, S. V. Kozyrev, K. Oleschko, A. G. Jaramillo, M. de Jesus Correa Lopez, “Application of p-adic analysis to time series”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 16:4 (2013), 1350030, 15 pp., arXiv: 1312.3878
S. Albeverio, S. V. Kozyrev, “Clustering by hypergraphs and dimensionality of cluster systems”, p-Adic Numbers, Ultrametric Analysis and Applications, 4:3 (2012), 167–178, arXiv: 1204.5952
S. Albeverio, S. V. Kozyrev, Lattice model of protein conformations, 2012, arXiv: 1207.7317
47.
S. V. Kozyrev, Classification by ensembles of neural networks, 2012, arXiv: 1202.4170
2011
48.
A. Yu. Khrennikov, S. V. Kozyrev, “$p$-Adic integral operators in wavelet bases”, Dokl. Math., 83:2 (2011), 209–212
49.
S. V. Kozyrev, A. Yu. Khrennikov, “Multidimensional $p$-adic metric and genetic code”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 113–117
50.
S. V. Kozyrev, I. V. Volovich, “The Arrhenius formula in kinetic theory and Witten's spectral asymptotics”, J. Phys. A, 44:21 (2011), 215202, 10 pp., arXiv: 1008.4487
A. Yu. Khrennikov, S. V. Kozyrev, “Genetic code and deformation of the 2-dimensional 2-adic metric”, P-Adic Numbers Ultrametric Anal. Appl., 3:2 (2011), 165–168
A. Yu. Khrennikov, S. V. Kozyrev, “Replica procedure for probabilistic algorithms as a model of gene duplication”, Dokl. Math., 84:2 (2011), 726–729, arXiv: 1105.2893
2010
53.
A. Yu. Khrennikov, S. V. Kozyrev, “2-Adic degeneration of the genetic code and energy of binding of codons”, Quantum bio-informatics III, QP–PQ: Quantum Probab. White Noise Anal., 26, World Sci. Publ., Hackensack, NJ, 2010, 193–204
S. Albeverio, S. V. Kozyrev, “Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function”, P-Adic Numbers Ultrametric Anal. Appl., 2:1 (2010), 21–34, arXiv: 1105.1506
S. Albeverio, S. V. Kozyrev, “Multidimensional $p$-adic wavelets for the deformed metric”, P-Adic Numbers Ultrametric Anal. Appl., 2:4 (2010), 265–277, arXiv: 1105.1524
S. Albeverio, S. V. Kozyrev, “Frames of $p$-adic wavelets and orbits of the affine group”, P-Adic Numbers, Ultrametric Analysis, and Applications, 1:1 (2009), 18–33, arXiv: 0801.4713
60.
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On $p$-adic mathematical physics”, P-Adic Numbers, Ultrametric Analysis, and Applications, 1:1 (2009), 1–17, arXiv: 0904.4205
I. V. Volovich, S. V. Kozyrev, $p$-Adicheskaya matematicheskaya fizika: osnovnye konstruktsii, primeneniya k slozhnym i nanoskopicheskim sistemam, Matematicheskaya fizika i eë prilozheniya. Vvodnye kursy. Vypusk 1, Samarskii gos. un-t, Samara, 2009 http://www.mi.ras.ru/noc/irreversibility/p-adicMF1.pdf
62.
S. Albeverio, S. V. Kozyrev, “Multidimensional ultrametric pseudodifferential equations”, Proc. Steklov Inst. Math., 265 (2009), 13–29, arXiv: 0708.2074
63.
S. Albeverio, S. V. Kozyrev, “Multidimensional basis of $p$-adic wavelets and representation theory”, P-Adic Numbers, Ultrametric Analysis, and Applications, 1:3 (2009), 181–189, arXiv: 0903.0461
S. V. Kozyrev, “Methods and applications of ultrametric and $p$-adic analysis: From wavelet theory to biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), 1–84
2008
66.
S. V. Kozyrev, “Toward an ultrametric theory of turbulence”, Theoret. and Math. Phys., 157:3 (2008), 1713–1722, arXiv: 0803.2719
S. V. Kozyrev, “Wavelets and spectral analysis of ultrametric pseudodifferential operators”, Sb. Math., 198:1 (2007), 97–116
69.
A.Yu.Khrennikov, S.V.Kozyrev, “Replica symmetry breaking related to a general ultrametric space III: The case of general measure”, Physica A: Statistical Mechanics and its Applications, 378:2 (2007), 283-298, arXiv: cond-mat/0603694
L. Accardi, S. V. Kozyrev, “Coherent population trapping and partial decoherence in the stochastic limit”, Internat. J. Theoret. Phys., 45:4 (2006), 677–694, arXiv: quant-ph/0303185
A.Yu.Khrennikov, S.V.Kozyrev, “Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals”, Physica A: Statistical Mechanics and its Applications, 359 (2006), 222-240, arXiv: cond-mat/0603685
A.Yu.Khrennikov, S.V.Kozyrev, “Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the $n\to0$ limit”, Physica A: Statistical Mechanics and its Applications, 359 (2006), 241-266, arXiv: cond-mat/0603687
L. Accardi, S.V.Kozyrev, A.N.Pechen, “Coherent Quantum Control of $\Lambda$–Atoms through the Stochastic Limit”, Quantum Information and Computing, QP-PQ: Quantum Probability and White Noise Analysis, 19, eds. L.Accardi, M.Ohya, N.Watanabe, World Scientific, Singapore, 2006, 1-17
79.
A.Yu.Khrennikov, S.V.Kozyrev, “Wavelets and the Cauchy problem for the Schrodinger equation on analytic ultrametric space”, Proceedings of the 2-nd Conference on Mathematical Modelling of Wave Phenomena 2005 (14–19 August 2005, Växjö, Sweden), AIP Conference Proceedings, 834, eds. B.Nilsson, L.Fishman, American Institute of Physics, Melville, New York, 2006, 344–350
2005
80.
A. Khrennikov, S. Kozyrev, “Contextual quantization and the principle of complementarity of probabilities”, Open Syst. Inf. Dyn., 12:3 (2005), 303–318, arXiv: quant-ph/0310114
S. V. Kozyrev, V. Al. Osipov, V. A. Avetisov, “Nondegenerate ultrametric diffusion”, J. Math. Phys., 46:6 (2005), 063302, 15 pp., arXiv: cond-mat/0403440
S. V. Kozyrev, A. Yu. Khrennikov, “Pseudodifferential operators on ultrametric spaces and ultrametric wavelets”, Izv. Math., 69:5 (2005), 989–1003
84.
A. Yu. Khrennikov, S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices”, Theoret. and Math. Phys., 144:2 (2005), 1166–1170
2004
85.
A. Khrennikov, S. Kozyrev, “The contextual quantization and the principle of complementarity of probabilities”, Quantum theory: reconsideration of foundations—2, Math. Model. Phys. Eng. Cogn. Sci., 10, Växjö Univ. Press, Växjö, 2004, 723–745
86.
L. Accardi, S. V. Kozyrev, “Superfluidity in the stochastic limit”, Discrete Dyn. Nat. Soc., 2004, no. 1, Special issue in memory of Ilya Prigogine, 3–17
87.
S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators: Methods and Applications”, Proc. Steklov Inst. Math., 245 (2004), 143–153
88.
S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and $p$-Adic Wavelets”, Theoret. and Math. Phys., 138:3 (2004), 322–332
2003
89.
L. Accardi, S. Kozyrev, “Quantum Boltzmann statistics in interacting systems”, Stochastic analysis and mathematical physics II, Trends Math., Birkhäuser, Basel, 2003, 1–7
90.
L. Accardi, S. Kozyrev, “Quantum Boltzmann statistics in interacting systems”, Quantum probability and infinite dimensional analysis (Burg, 2001), QP–PQ: Quantum Probab. White Noise Anal., 15, World Sci. Publ., River Edge, NJ, 2003, 21–28
91.
A. Khrennikov, S. V. Kozyrev, “Noncommutative probability in classical disordered systems”, Phys. A, 326:3-4 (2003), 456–463, arXiv: quant-ph/0211033
S. V. Kozyrev, “Rigged Hilbert Space of Free Coherent States and $p$-Adic Numbers”, Theoret. and Math. Phys., 135:2 (2003), 642–650
93.
S. V. Kozyrev, “The noncommutative replica procedure”, Foundations of probability and physics, 2 (Växjö, 2002), Math. Model. Phys. Eng. Cogn. Sci., 5, Växjö Univ. Press, Växjö, 2003, 359–373
94.
S. Kozyrev, A. Khrennikov, “Noncommutative probability in classical systems”, Foundations of probability and physics, 2 (Växjö, 2002), Math. Model. Phys. Eng. Cogn. Sci., 5, Växjö Univ. Press, Växjö, 2003, 375–383
95.
L. Accardi, K. Imafuku, S.V. Kozyrev, “Interaction of 3-level atom with radiation”, OPTICS AND SPECTROSCOPY, 94:6 (2003), 904-910
V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, V. A. Osipov, “$p$-adic models of ultrametric diffusion constrained by hierarchical energy landscapes”, J. Phys. A, 35:2 (2002), 177–189, arXiv: cond-mat/0106506
L. Accardi, S. Kozyrev, “Lectures on quantum interacting particle systems”, Quantum interacting particle systems (Trento, 2000), QP–PQ: Quantum Probab. White Noise Anal., 14, World Sci. Publ., River Edge, NJ, 2002, 1–195
S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376
2001
99.
L. Accardi, S. V. Kozyrev, “Superfluidity in the stochastic limit”, Infinite dimensional analysis and quantum probability theory (Kyoto, 2000), Sūrikaisekikenkyūsho Kōkyūroku, no. 1227, 2001, 1–13
100.
L. Accardi, S. V. Kozyrev, “On the structure of Markov flows”, Irreversibility, probability and complexity (Les Treilles/Clausthal, 1999), Chaos Solitons Fractals, 12, no. 14-15, 2001, 2639–2655, arXiv: quant-ph/9911078
L. Accardi, S.V. Kozyrev, “The stochastic limit of quantum spin system”, Statistical Physics. Proceedings of the 3rd Tohwa International Meeting on Statistical Physics. (Tohwa University, Fukuoka, Japan, November 8-11, 1999.), AIP Proceedings, 519, eds. M. Tokuyama, H.E. Stanley, American Institute of Physics, 2000, 599–610
V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, “Application of $p$-adic analysis to models of breaking of replica symmetry”, J. Phys. A, 32:50 (1999), 8785–8791
V. A. Avetisov, A. Kh. Bikulov, S. V. Kozyrev, “Description of logarithmic relaxation by a model of a hierarchical random walk”, Dokl. RAN, 368:2 (1999), 164–167
L. Accardi, S. V. Kozyrev, I. V. Volovich, “Dynamical $q$-deformation in quantum theory and the stochastic limit”, J. Phys. A, 32:19 (1999), 3485–3495, arXiv: math/9807137
L. Accardi, S. V. Kozyrev, I. V. Volovich, “The hot free algebra”, Recent trends in infinite-dimensional noncommutative analysis (Kyoto, 1997), Sūrikaisekikenkyūsho Kōkyūroku, no. 1035, 1998, 1–18
107.
S. V. Kozyrev, “Free coherent states and distributions on $p$-adic numbers”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 1:2 (1998), 349–355
L. Accardi, I. V. Volovich, S. V. Kozyrev, “A new algebra in the stochastic approximation for the model of a particle interacting with a quantum field”, Theoret. and Math. Phys., 116:3 (1998), 1050–1062
1997
109.
S. V. Kozyrev, “Ultrametric space of free coherent states”, Theoret. and Math. Phys., 110:2 (1997), 265–266
110.
L. Accardi, S. V. Kozyrev, I. V. Volovich, “Dynamics of dissipative two–level system in the stochastic approximation”, Phys.Rev.A., 56:4 (1997), 2557–2562, arXiv: quant-ph/9706021
S. V. Kozyrev, “Nonarchimedean space of states in the model of polymerization”, Theoret. and Math. Phys., 112:3 (1997), 1192–1198
1995
112.
S. V. Kozyrev, “Isomorphism of stable and regular representations of the algebra of functions on a quantum group”, Dokl. RAN, 343:4 (1995), 445–447
113.
L. Accardi, I. Ya. Aref'eva, S. V. Kozyrev, I. V. Volovich, “The master field for large-$N$ matrix models and quantum groups”, Modern Phys. Lett. A, 10:31 (1995), 2323–2333, arXiv: hep-th/9503041
S. V. Kozyrev, “Exact calculability, semigroup of representations, and the stability property for representations of the algebra of functions on the quantum group $SU_{q}(2)$”, Theoret. and Math. Phys., 101:2 (1994), 1269–1280
1992
115.
S. V. Kozyrev, “Free motion of $q$-deformed quantum particle”, Theoret. and Math. Phys., 93:1 (1992), 1138–1141
Presentations in Math-Net.Ru
1.
Hamiltonian for the VICReg Algorithm S. V. Kozyrev Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" April 8, 2026 18:00
Что есть жизнь? Математический аспект S. V. Kozyrev International scientific conference “Infinite-dimensional analysis and mathematical physics” (IDAMPh 2026) January 27, 2026 10:30
Физические подходы в машинном обучении S. V. Kozyrev, I. Lopatin, A. N. Pechen Annual Session of Steklov Mathematical Institute (Best results 2025) November 18, 2025 16:55
7.
What Is Life? S. V. Kozyrev Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" October 29, 2025 19:35
2026
