p-Adic Mathematical Physics: The First 30 Years
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov

This publication is cited in the following articles:

1. Tom Hutchcroft, “Critical cluster volumes in hierarchical percolation”, Proceedings of London Math Soc, 130:1 (2025)  
2. Krzysztof Ciepliński, “On Ulam Stability of Functional Equations in Non-Archimedean Spaces”, Symmetry, 17:1 (2025), 112  
3. Igor V. Volovich, “On the Equivalence Between the Schrödinger Equation in Quantum Mechanics and the Euler-Bernoulli Equation in Elasticity Theory”, P-Adic Num Ultrametr Anal Appl, 17:1 (2025), 78  
4. Roman Urban, “A Dyson-type series solution to some time-dependent Schrödinger equations on finite adeles”, J. Pseudo-Differ. Oper. Appl., 16:1 (2025)  
5. J. P. Velasquez-Rodriguez, “Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d\le 5$”, Bol. Soc. Mat. Mex., 31:2 (2025)  
6. Ivan Dimitrijević, Branko Dragovich, Zoran Rakić, Jelena Stanković, Springer Proceedings in Mathematics & Statistics, 473, Lie Theory and Its Applications in Physics, 2025, 169  
7. Oded Shor, Felix Benninger, Andrei Khrennikov, “Relational information framework, causality, unification of quantum interpretations and return to realism through non-ergodicity”, Sci Rep, 15:1 (2025)  
8. Sangtae Jeong, Yongjae Kwon, “Minimality criteria for rational functions over Z”, Journal of Mathematical Analysis and Applications, 2025, 129624  
9. Luis Crespo, Álvaro Pelayo, “The p-Adic Jaynes–Cummings Model in Symplectic Geometry”, J Nonlinear Sci, 35:4 (2025)  
10. I. Dimitrijevic, B. Dragovich, Z. Rakic, J. Stankovic, “Nonlocal de Sitter $\sqrt{dS}$ Gravity Model and Its Applications”, Russ. J. Math. Phys., 32:1 (2025), 11  
11. Maxwell C. Siegel, “The Collatz Conjecture & Non-Archimedean Spectral Theory - Part II - $\left(p,q\right)$-Adic Fourier Analysis and Wiener's Tauberian Theorem”, P-Adic Num Ultrametr Anal Appl, 17:2 (2025), 187  
12. M. M. Rahmatullaev, O. U. Akhmedov, A. M. Tukhtabaev, “$p$-Adic Quasi Gibbs Measures for the SOS Model on the Cayley Tree of Order Two”, P-Adic Num Ultrametr Anal Appl, 17:2 (2025), 173  
13. PATRICK ERIK BRADLEY, ÁNGEL MORÁN LEDEZMA, “A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS”, Reports on Mathematical Physics, 95:2 (2025), 155  
14. A. P. Zubarev, “On the Analog of the Kolmogorov-Arnold Superposition Representation for Continuous Functions of Several $p$-Adic Variables”, P-Adic Num Ultrametr Anal Appl, 17:3 (2025), 326  
15. Tran Thi Nang, Kieu Huu Dung, Pham Thi Kim Thuy, “Variable Morrey–Herz spaces estimate for p-adic Hausdorff operators”, J Anal, 2025  
16. Humberto Llinás, Ismael Gutiérrez, Anselmo Torresblanca, Javier De La Hoz, Brian Llinás, “A Bibliometric and Topic Modeling Analysis of the p-Adic Theory Literature Using Latent Dirichlet Allocation”, Mathematics, 13:18 (2025), 2932  
17. Ángel Morán Ledezma, “Time-varying energy landscapes and temperature paths: dynamic transition rates in locally ultrametric complex systems”, J. Stat. Mech., 2025:11 (2025), 113501  
18. J G Polli, E P Raposo, G M Viswanathan, M G E da Luz, “Stochastic-like characteristics of arithmetic dynamical systems: the Collatz hailstone sequences”, J. Phys. Complex., 5:1 (2024), 015011  
19. Philip Easo, Tom Hutchcroft, Jana Kurrek, “Double-exponential susceptibility growth in Dyson's hierarchical model with |x - y|-2 interaction”, Journal of Mathematical Physics, 65:2 (2024)  
20. Roman Urban, “The Vladimirov operator with variable coefficients on finite adeles and the Feynman formulas for the Schrödinger equation”, Journal of Mathematical Physics, 65:4 (2024)  
21. Ekaterina Yurova Axelsson, Andrei Khrennikov, “Generation of genetic codes with 2-adic codon algebra and adaptive dynamics”, BioSystems, 240 (2024), 105230  
22. Paolo Aniello, Sonia L'Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter, “Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups”, Lett Math Phys, 114:3 (2024)  
23. Maxwell C. Siegel, “The Collatz Conjecture & Non-Archimedean Spectral Theory - Part I - Arithmetic Dynamical Systems and Non-Archimedean Value Distribution Theory”, P-Adic Num Ultrametr Anal Appl, 16:2 (2024), 143  
24. E. A. Kurianovich, A. I. Mikhailov, I. V. Volovich, “On the theory of relativistic Brownian motion”, P-Adic Numbers Ultrametric Anal. Appl., 16:2 (2024), 113–127      
25. M. M. Rahmatullaev, Z. T. Abdukaxorova, “$\boldsymbol{H}_{\boldsymbol{A}}$-Weakly Periodic $\boldsymbol{p}$-Adic Generalized Gibbs Measures for Ising Model on a Cayley Tree”, Lobachevskii J Math, 45:1 (2024), 504  
26. Branko Dragovich, “A closed universe with hybrid nonlocality”, Int. J. Geom. Methods Mod. Phys., 21:10 (2024)  
27. Roman Urban, “Feynman formulas for qp- and pq-quantization of some Vladimirov type time-dependent Hamiltonians on finite adeles”, Anal.Math.Phys., 14:5 (2024)  
28. Paolo Aniello, Stefano Mancini, Vincenzo Parisi, “Quantum mechanics on a p-adic Hilbert space: Foundations and prospects”, Int. J. Geom. Methods Mod. Phys., 21:10 (2024)  
29. Branko Dragovich, Nataša Ž. Mišić, “The genetic code and its p-adic ultrametric modeling”, BioSystems, 246 (2024), 105322  
30. Alexey S. Koshelev, Handbook of Quantum Gravity, 2024, 1  
31. K. H. Dung, P. T. K. Thuy, “Rough Hardy-Littlewood Operators on $p$-Adic Function Spaces with Variable Exponents”, P-Adic Num Ultrametr Anal Appl, 16:3 (2024), 219  
32. V. A. Aguilar-Arteaga, S. M. Delfín-Prieto, S. Estala-Arias, “Finite Adelic Wavelet Bases and a Pseudodifferential Equation”, P-Adic Num Ultrametr Anal Appl, 16:3 (2024), 275  
33. Tyler Pierce, Rahul Rajkumar, Andrea Stine, David Weisbart, Adam M. Yassine, “Brownian motion in a vector space over a local field is a scaling limit”, Expositiones Mathematicae, 2024, 125607  
34. Otabek Khakimov, Farrukh Mukhamedov, “On set of p-adic Gibbs measures for the countable state 1D SOS model”, J. Phys. A: Math. Theor., 57:43 (2024), 435202  
35. Ekaterina Yurova Axelsson, Andrei Khrennikov, “Universal dynamical function behind all genetic codes: P-adic attractor dynamical model”, BioSystems, 2024, 105353  
36. A. Kh. Bikulov, A. P. Zubarev, “Power Laws and Logarithmic Oscillations in Diffusion Processes on Discrete Ultrametric Spaces”, P-Adic Num Ultrametr Anal Appl, 16:4 (2024), 327  
37. P. T. K. Thuy, “Multilinear Fractional Hardy Operators on $p$-Adic Functional Spaces with Variable Exponents”, P-Adic Num Ultrametr Anal Appl, 16:4 (2024), 375  
38. Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev, Nurkhon Samijonova, “Weakly periodic p-adic quasi-Gibbs measures for the Potts model on a Cayley tree”, Lett Math Phys, 114:6 (2024)  
39. Alexey S. Koshelev, Handbook of Quantum Gravity, 2024, 1397  
40. Alexey S. Koshelev, “Infinite derivative theories and equations”, Eur. Phys. J. Plus, 139:12 (2024)  
41. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On the Occasion of the Centenary of the Birth of V. S. Vladimirov (1923–2012)”, P-Adic Num Ultrametr Anal Appl, 15:3 (2023), 243  
42. Paolo Aniello, “States, observables and symmetries in p-adic quantum mechanics”, J. Phys.: Conf. Ser., 2667:1 (2023), 012055  
43. Rahul Rajkumar, David Weisbart, “Components and Exit Times of Brownian Motion in Two or More p-Adic Dimensions”, J Fourier Anal Appl, 29:6 (2023)  
44. Evgeny Zelenov, “Coherent states of the $p$-adic Heisenberg group and entropic uncertainty relations”, P-Adic Numbers Ultrametric Anal. Appl., 15:3 (2023), 195–203      
45. Kieu Huu Dung, Pham Thi Kim Thuy, “Commutators of Hardy-Littlewood operators on p-adic function spaces with variable exponents”, Open Mathematics, 21:1 (2023)  
46. Evgeny Zelenov, “On geometry of $p$-adic coherent states and mutually unbiased bases”, Entropy, 25:6 (2023), 902–8    
47. F. M. Mukhamedov, M. M. Rahmatullaev, A. M. Tukhtabaev, R. Mamadjonov, “The $p$-adic Ising model in an external field on a Cayley tree: periodic Gibbs measures”, Theoret. and Math. Phys., 216:2 (2023), 1238–1253          
48. A. Kh. Bikulov, A. P. Zubarev, “Oscillations in $p$-Adic Diffusion Processes and Simulation of the Conformational Dynamics of Protein”, P-Adic Num Ultrametr Anal Appl, 15:3 (2023), 169  
49. Oded Shor, Amit Yaniv-Rosenfeld, Avi Valevski, Abraham Weizman, Andrei Khrennikov, Felix Benninger, “EEG-based spatio-temporal relation signatures for the diagnosis of depression and schizophrenia”, Sci Rep, 13:1 (2023)  
50. M. C. Siegel, “Infinite Series Whose Topology of Convergence Varies From Point to Point”, P-Adic Num Ultrametr Anal Appl, 15:2 (2023), 133  
51. Ivan Dimitrijevic, Branko Dragovich, Zoran Rakic, Jelena Stankovic, “On the Schwarzschild-de Sitter metric of nonlocal de sitter gravity”, Filomat, 37:25 (2023), 8641  
52. 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        
53. Nacima Memić, “Mahler Coefficients of Some 3-adic Ergodic Functions”, Acta Math Vietnam, 47:3 (2022), 597  
54. Matt Visser, “Which Number System Is “Best” for Describing Empirical Reality?”, Mathematics, 10:18 (2022), 3340  
55. Steven Duplij, “Polyadic Rings of p-Adic Integers”, Symmetry, 14:12 (2022), 2591  
56. Branko Dragovich, “A p-Adic Matter in a Closed Universe”, Symmetry, 14:1 (2022), 73  
57. Farrukh Mukhamedov, Otabek Khakimov, Abdessatar Souissi, “A Few Remarks on Supercyclicity of Non-Archimedean Linear Operators on $c_0(\mathbb N)$”, P-Adic Num Ultrametr Anal Appl, 14:1 (2022), 64  
58. Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev, “On periodic p-adic generalized Gibbs measures for Ising model on a Cayley tree”, Lett Math Phys, 112:6 (2022)  
59. E. I. Zelenov, “On geometry of $p$-adic polynomials”, Int. J. Mod. Phys. A, 37:20 (2022), 2243026–5    
60. A. Kh. Bikulov, A. P. Zubarev, “The Sojourn Time Problem for a $p$-Adic Random Walk and its Applications”, P-Adic Num Ultrametr Anal Appl, 14:4 (2022), 265  
61. Christopher Sinclair, Contemporary Mathematics, 778, 𝑝-Adic Analysis, Arithmetic and Singularities, 2022, 279  
62. A.R. Fuquen-Tibatá, H. García-Compeán, W.A. Zúñiga-Galindo, “Euclidean quantum field formulation of p-adic open string amplitudes”, Nuclear Physics B, 975 (2022), 115684  
63. Roman Urban, “On a diffusion on finite adeles and the Feynman-Kac integral”, Journal of Mathematical Physics, 63:12 (2022)  
64. Oded Shor, Felix Benninger, Andrei Khrennikov, “Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe”, Entropy, 24:2 (2022), 181  
65. Ulrich K. Beckering Vinckers, Álvaro de la Cruz-Dombriz, Ivan Kolář, Francisco J. Maldonado Torralba, Anupam Mazumdar, “Ghost-free infinite-derivative dilaton gravity in two dimensions”, Phys. Rev. D, 106:6 (2022)  
66. A.Kh. Bikulov, A.P. Zubarev, “Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin”, Physica A: Statistical Mechanics and its Applications, 583 (2021), 126280  
67. Miriam Bocardo-Gaspar, Hugo García-Compeán, Edgar Y. López, Wilson A. Zúñiga-Galindo, “Local Zeta Functions and Koba–Nielsen String Amplitudes”, Symmetry, 13:6 (2021), 967  
68. Bourama Toni, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, The Mathematics of Patterns, Symmetries, and Beauties in Nature, 2021, 117  
69. Hao Hua, Ludger Hovestadt, “p-adic numbers encode complex networks”, Sci Rep, 11:1 (2021)  
70. Farrukh Mukhamedov, Otabek Khakimov, Abdessatar Souissi, “Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean c0(N) Space”, Mathematics, 9:22 (2021), 2986  
71. Ivan Dimitrijevic, Branko Dragovich, Zoran Rakic, Jelena Stankovic, “New Cosmological Solutions of a Nonlocal Gravity Model”, Symmetry, 14:1 (2021), 3  
72. Bourama Toni, W. A. Zúñiga-Galindo, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, Advances in Non-Archimedean Analysis and Applications, 2021, 1  
73. Samih Lazaiz, “A look at nonexpansive mappings in non-Archimedean vector spaces”, Moroccan Journal of Pure and Applied Analysis, 7:1 (2021), 173  
74. Farrukh Mukhamedov, Otabek Khakimov, “Translation‐invariant generalized P‐adic Gibbs measures for the Ising model on Cayley trees”, Math Methods in App Sciences, 44:16 (2021), 12302  
75. Oded Shor, Felix Benninger, Andrei Khrennikov, “Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity”, Entropy, 23:8 (2021), 971  
76. Oded Shor, Felix Benninger, Andrei Khrennikov, “Representation of the Universe as a Dendrogramic Hologram Endowed with Relational Interpretation”, Entropy, 23:5 (2021), 584  
77. Farrukh Mukhamedov, Otabek Khakimov, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, Advances in Non-Archimedean Analysis and Applications, 2021, 115  
78. Branko Dragovich, Andrei Yu. Khrennikov, Sergei V. Kozyrev, Nataša. Ž. Mišić, “$p$-Adic Mathematics and Theoretical Biology”, Biosystems, 199 (2021), 104288–10        
79. F. M. Mukhamedov, O. N. Khakimov, “$p$-adic monomial equations and their perturbations”, Izv. Math., 84:2 (2020), 348–360            
80. Denys I. Bondar, Alexander N. Pechen, “Uncomputability and complexity of quantum control”, Sci. Rep., 10:1 (2020), 1195–10        
81. H. García-Compeán, Edgar Y. López, W. A. Zúñiga-Galindo, “p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field”, Nuclear Physics B, 951 (2020), 114904  
82. Felix M. Lev, “Symmetries in Foundation of Quantum Theory and Mathematics”, Symmetry, 12:3 (2020), 409  
83. Samuel Estala-Arias, “Pseudodifferential operators and Markov processes on certain totally disconnected groups”, Statistics & Probability Letters, 164 (2020), 108811  
84. Branko Dragovich, Mukadas D. Missarov, “Random Triangles in a Metric Space of Sequences”, P-Adic Num Ultrametr Anal Appl, 12:2 (2020), 171  
85. Dmitry S. Ageev, Andrey A. Bagrov, Askar A. Iliasov, “Coleman–Weinberg potential in $p$-adic field theory”, Eur. Phys. J. C, Part. Fields, 80 (2020), 859–10        
86. Ngoc Mai Tran, “Tropical Gaussians: a brief survey”, Alg. Stat., 11:2 (2020), 155  
87. E. I. Zelenov, “Entropy Gain in $p$-Adic Quantum Channels”, Phys. Part. Nucl., 51:4 (2020), 485–488          
88. J. P. Velasquez-Rodriguez, “Hörmander Classes of Pseudo-Differential Operators over the Compact Group of p-Adic Integers”, P-Adic Num Ultrametr Anal Appl, 12:2 (2020), 134  
89. Victor A. Aguilar-Arteaga, Manuel Cruz-López, Samuel Estala-Arias, “Non-Archimedean analysis and a wave-type pseudodifferential equation on finite adèles”, J. Pseudo-Differ. Oper. Appl., 11:3 (2020), 1139  
90. Giuseppe Iurato, Andrei Yu. Khrennikov, “A Reader's Comment on: “Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees””, P-Adic Num Ultrametr Anal Appl, 12:1 (2020), 68  
91. Ismael Gutiérrez García, Anselmo Torresblanca-Badillo, “Some classes of non-archimedean pseudo-differential operators related to Bessel potentials”, J. Pseudo-Differ. Oper. Appl., 11:3 (2020), 1111  
92. Ivan Dimitrijevic, Branko Dragovich, Alexey S. Koshelev, Zoran Rakic, Jelena Stankovic, “Some Cosmological Solutions of a New Nonlocal Gravity Model”, Symmetry, 12:6 (2020), 917  
93. Alexey S. Koshelev, Anna Tokareva, “Nonlocal self-healing of Higgs inflation”, Phys. Rev. D, 102:12 (2020)  
94. Igor V. Volovich, “Complete integrability of quantum and classical dynamical systems”, P-Adic Numbers Ultrametric Anal. Appl., 11:4 (2019), 328–334        
95. Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson, “p-adic CFT is a holographic tensor network”, J. High Energ. Phys., 2019:4 (2019)  
96. I. Dimitrijevic, B. Dragovich, Z. Rakic, J. Stankovic, “Cosmological Solutions of Some Nonlocal Gravity Models”, Proc. Steklov Inst. Math., 306 (2019), 66–73            
97. I. Dimitrijevic, B. Dragovich, A.S. Koshelev, Z. Rakic, J. Stankovic, “Cosmological solutions of a nonlocal square root gravity”, Physics Letters B, 797 (2019), 134848  
98. Branko Dragovich, Nataša Ž. Mišić, “p-Adic hierarchical properties of the genetic code”, Biosystems, 185 (2019), 104017  
99. Tim Palmer, “Experimental Non-Violation of the Bell Inequality”, Entropy, 20:5 (2018), 356  
100. Ingmar Saberi, “Holography and Local Fields”, P-Adic Num Ultrametr Anal Appl, 10:3 (2018), 151  
101. Anselmo Torresblanca-Badillo, W. A. Zúñiga-Galindo, “Non-Archimedean Pseudodifferential Operators and Feller Semigroups”, P-Adic Num Ultrametr Anal Appl, 10:1 (2018), 57  
102. A G Buchovets, P V Moskalev, “Ultrametric properties of the attractor spaces for random iterated linear function systems”, J. Phys.: Conf. Ser., 973 (2018), 012028  
103. M. Bocardo-Gaspar, H. García-Compeán, W. A. Zúñiga-Galindo, “On p-adic string amplitudes in the limit p approaches to one”, J. High Energ. Phys., 2018:8 (2018)  
104. Abdelmalek Abdesselam, “Towards Three-Dimensional Conformal Probability”, P-Adic Num Ultrametr Anal Appl, 10:4 (2018), 233  
105. Alexandra V. Antoniouk, Klaudia Oleschko, Anatoly N. Kochubei, Andrei Yu. Khrennikov, “A stochastic p-adic model of the capillary flow in porous random medium”, Physica A: Statistical Mechanics and its Applications, 505 (2018), 763  
106. Farrukh Mukhamedov, Hasan Ak{\i}n, Mutlay Dogan, “On chaotic behaviour of the p-adic generalized Ising mapping and its application”, Journal of Difference Equations and Applications, 2017, 1