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Ruelle,Statistical Mechanics, New York (1969).\nG. I. Kalmykov,Teor. Mat. Fiz.,84, 279 (1990).\nD. N. Zubarev,Dokl. Akad. Nauk SSSR,118, 903 (1958).\nG. E. Uhlenbeck and G. W. Ford,Lectures in Statistical Physics, AMS, Providence, R.I. (1963).\nF. M. Kuni,Statistical Physics and Thermodynamics [in Russian], Nauka, Moscow (1981).\nM. Toda, R. Kubo, and N. Saito,Statistical Physics. 1. Equilibrium Mechanics Springer-Verlag, Berlin (1983).\nL. E. Reichl,A Modern Course in Statistical Physics, Arnold, London (1980).\nA. I. Markushevich,Theory of Analytic Functions, Vols. 1 and 2 [in Russian], Nauka, Moscow (1967, 1968).\nA. I. Markushevich,Short Course in the Theory of Analytic Functions [in Russian] Nauka, Moscow (1966).\nF. Harary,Graph Theory, Addison-Wesley, Reading, Mass. (1969).",{"EN":252},"Functions that under certain assumptions are analytic continuations of Mayer expansions are found. It is shown that there exists a positive numberρ\n1 satisfying the following conditions: 1) for any interval of the form [0,ρ\n1(1−ε)], where 0\u003Cɛ\u003C1, there exists a region containing this interval in which there is defined a single-valued analytic single-sheeted function that is the inverse with respect to the analytic continuationf(z) of the Mayer expansion which represents the density as a function of the activity; 2) there does not exist a single-valued analytic function that would be the inverse with respect to the functionf(z) in a certain region containing the interval [0,ρ\n1]. It is shown to be possible to continue analytically the virial expansion along the path [0,ρ\n1(1−ε)], where 0\u003Cɛ\u003C1, and impossible to do this along the path [0,ρ\n1]. An equation that determines a positive numberz\n1 such thatρ\n1=f(z\n1) is found.",{"EN":254},"Analytic continuation of mayer and virial expansions",{"VOID":256},"10.1007\u002FBF01018709","PUBLICATION","Author affiliation is blank","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF01018709",[261],{"id":262,"sortIndex":19,"researcher":18,"roles":263,"affiliations":265,"properties":266},"b4ded67a-c5f3-4589-9ac2-7016adbf9df7",[264],"AUTHOR",[],{"title":267},{"VI":268},"G. I. Kalmykov","ARTICLE",{"url":259,"publisher":271,"properties":298},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":272,"slug":10,"properties":273,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":276,"manageAffiliations":277,"indexDatabases":278,"url":18,"thumbnailPath":18,"statistic":293,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":274,"title":275},{"VOID":13},{"EN":15},[],[],[279,286],{"id":80,"indexDatabase":280,"url":95,"indexYears":18,"academicFieldIds":285,"indexDatabaseRanking":18},{"id":82,"createTime":83,"updateTime":84,"relativeEntities":281,"label":282,"description":283,"key":91,"publicationTags":284,"standard":18},[],{"EN":87,"VI":87},{"VI":89,"EN":90},[93,94],[97],{"id":61,"indexDatabase":287,"url":74,"indexYears":75,"academicFieldIds":292,"indexDatabaseRanking":18},{"id":63,"createTime":64,"updateTime":65,"relativeEntities":288,"label":289,"description":290,"key":71,"publicationTags":291,"standard":18},[],{"EN":68,"VI":68},{"EN":68,"VI":70},[73],[77,78],{"impactFactor":19,"impactFactorByYear":294,"i10Index":108,"i10IndexLast5Year":109,"totalPublication":110,"totalPublicationByYear":295,"totalCitation":148,"totalCitationByYear":296,"totalCitationPerPublication":192,"totalCitationPerPublicationByYear":297,"hindexLast5Year":188,"hindex":188},{"2012":100,"2013":101,"2014":102,"2015":103,"2016":100,"2017":104,"2018":102,"2019":100,"2020":105,"2021":106,"2022":107,"2023":105},{"1969":112,"1970":113,"1971":114,"1972":115,"1973":116,"1974":117,"1975":118,"1976":119,"1977":120,"1978":121,"1979":120,"1980":119,"1981":122,"1982":123,"1983":119,"1984":116,"1985":124,"1986":125,"1987":126,"1988":123,"1989":127,"1990":128,"1991":125,"1992":117,"1993":129,"1994":130,"1995":131,"1996":132,"1997":133,"1998":134,"1999":122,"2000":135,"2001":136,"2002":137,"2003":122,"2004":138,"2005":139,"2006":140,"2007":141,"2008":133,"2009":113,"2010":133,"2011":113,"2012":135,"2013":142,"2014":143,"2015":135,"2016":115,"2017":144,"2018":142,"2019":144,"2020":134,"2021":145,"2022":146,"2023":137,"2024":147},{"1969":150,"1970":151,"1971":152,"1972":153,"1973":132,"1974":154,"1975":155,"1976":156,"1977":157,"1978":158,"1979":159,"1980":160,"1981":161,"1982":108,"1983":162,"1984":163,"1985":164,"1986":128,"1987":165,"1988":166,"1989":155,"1990":167,"1991":168,"1992":169,"1993":170,"1994":171,"1995":172,"1996":173,"1997":132,"1998":132,"1999":174,"2000":175,"2003":176,"2004":177,"2005":171,"2006":178,"2007":179,"2008":180,"2009":144,"2010":181,"2011":182,"2012":183,"2013":119,"2014":184,"2015":185,"2016":186,"2017":187,"2018":182,"2019":182,"2020":188,"2021":189,"2022":190,"2023":191},{"1969":194,"1970":195,"1971":196,"1972":197,"1973":198,"1974":199,"1975":200,"1976":201,"1977":202,"1978":203,"1979":204,"1980":205,"1981":206,"1982":207,"1983":208,"1984":209,"1985":210,"1986":211,"1987":212,"1988":201,"1989":213,"1990":214,"1991":215,"1992":216,"1993":217,"1994":218,"1995":200,"1996":219,"1997":203,"1998":211,"1999":220,"2000":221,"2003":222,"2004":223,"2005":224,"2006":225,"2007":226,"2008":205,"2009":227,"2010":228,"2011":229,"2012":194,"2013":230,"2014":231,"2015":232,"2016":195,"2017":233,"2018":234,"2019":235,"2020":236,"2021":237,"2022":194,"2023":104},{"volume":299,"pages":301},{"VOID":300},"92",{"VOID":302},"791-798","1992-07-01",1992,false,{"id":307,"createTime":308,"updateTime":309,"relativeEntities":310,"slug":311,"properties":312,"entityType":257,"verifyStatus":321,"verifyTime":309,"verifyNote":322,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":323,"fullTextUrl":18,"authors":324,"publicationType":269,"publisherRelationship":340,"citationCount":18,"citationInfo":18,"publishDate":373,"publishYear":374,"citationAnalyzeStatus":17,"lastCitationAnalyze":18,"indexDatabases":18,"openAccess":18,"references":18,"isForceReanalyzing":305},"61eec97d-8aaa-40a2-8e4c-34477b81bd4e","2024-01-29T08:54:07.495+00:00","2024-12-23T23:59:30.405+00:00",[],"Stochastic-dynamo-in-critical-situations",{"references":313,"abstract":315,"title":317,"doi":319},{"VOID":314},"L. D. Landau and E. M. Lifshitz, Theoretical Physics [in Russian], Vol. 8, Electrodynamics of Continuous Media, Nauka, Moscow (1992); English transl. prev. ed., Pergamon, Oxford (1960).\nV. I. Klyatskin, JETP, 109, 1194–1208 (2009).\nV. I. Klyatskin, Phys. Usp., 54, 441–464 (2011).\nA. P. Kazantsev, Sov. Phys. JETP, 26, 1031–1034 (1968).\nYa. B. Zel’dovich, S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. Usp., 28, 307–327 (1985).\nYa. B. Zel’dovich, S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. JETP, 62, 1188–1194 (1985); Sov. Phys. USP, 30, 353–369 (1987).\nYa. B. Zel’dovich and A. A. Ruzmaikin, Sov. Phys. Usp., 30, 494–506 (1987).\nV. I. Klyatskin and O. G. Chkhetiani, JETP, 109, 345–356.\nV. I. Klyatskin, Stochastic Equations through the Eye of the Physicist: Basic Concepts, Exact Results, and Asymptotic Approximations [in Russian], Fizmatlit, Moscow (2001); English transl., Elsevier, Amsterdam (2005); Dynamics of Stochastic Systems [in Russian], Fizmatlit, Moscow (2002); English transl., Elsevier, Amsterdam (2005).\nV. I. Klyatskin, Diffusion and Clustering of a Passive Tracer in Random Hydrodynamic Flows [in Russian], Fizmatlit, Moscow (2005); Stochastic Equations: Theory and Its Applications to Acoustics, Hydrodynamics, and Radio Physics [in Russian], Fizmatlit, Moscow (2008).\nV. I. Klyatskin, Dynamics of Stochastic Systems [in Russian] (A course of lectures), Fizmatlit, Moscow (2002); English transl.: Lectures on Dynamics of Stochastic Systems, Elsevier, Amsterdam (2010).\nV. I. Klyatskin, Izv., Atmos. Ocean. Phys., 44, 18–32 (2008); Phys. Usp., 51, 395–407 (2008); 52, 514–519 (2009).\nL. D. Landau and E. M. Lifshits, Sov. Phys. JETP, 5, 512–513 (1957).\nE. M. Lifshitz and L. P. Pitaevskii, Statistical Physics Part 2 [in Russian], Nauka, Moscow (1978); English transl., Pergamon, Oxford (1980).\nM. L. Levin and S. M. Rytov, Theory of Equilibrium Thermal Fluctuations in Electrodynamics [in Russian], Nauka, Moscow (1967).\nV. I. Klyatskin, Izv., Atmos. Ocean. Phys., 7, 317–321 (1971).\nV. I. Klyatskin, Statistical Description of Dynamical Systems with Fluctuating Parameters [in Russian], Nauka, Moscow (1975).\nV. I. Klyatskin and V. I. Tatarskii, Radiophysics and Quantum Electronics, 14, 1100–1111 (1971).\nS. I. Vainshtein, Ya. B. Zel’dovich, and A. A. Ruzmaikin, The Turbulent Dynamo in Astrophysics [in Russian], Nauka, Moscow (1980).\nN. A. Silant’ev, JETP Lett., 72, 42–45 (2000); JETP, 84, 479–484 (1977); 87, 505–512 (1998); 89, 45–55 (1999); 95, 957–964 (2002); 98, 728–744 (2004).\nS. I. Vainshtein, Sov. Phys. Dokl., 15, 1090–1092 (1970).\nS. I. Vainshtein and Ya. B. Zel’dovich, Sov. Phys. Usp., 15, 159–172 (1972).\nA. P. Kazantsev, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. JETP, 61, 285–289 (1985).",{"EN":316},"Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic parameter of the magnetic field energy vanishes. This implies the absence of structure formation (clustering) in realizations of the magnetic field in that approximation. Critical situations occur in problems of magnetic field diffusion in an equilibrium thermal and random pseudoequilibrium and acoustic (in the absence of dissipation) velocity fields. The sign of the Lyapunov characteristic parameter in the second-order approximation determines the possibility of clustering of the magnetic field energy. We show that energy clustering does not occur in a thermal velocity field. In the cases of pseudoequilibrium and acoustic velocity fields, clustering occurs with probability one, i.e., in almost every realization. We evaluate the characteristic time for clustering to be established.",{"EN":318},"Stochastic dynamo in critical situations",{"VOID":320},"10.1007\u002Fs11232-012-0111-9","VERIFIED","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11232-012-0111-9",[325],{"id":326,"sortIndex":19,"researcher":18,"roles":327,"affiliations":328,"properties":337},"1fe33d5c-84c3-4f41-82f5-c18ac461dae3",[264],[329],{"id":18,"sortIndex":19,"affiliation":330,"properties":18},{"id":331,"createTime":332,"updateTime":332,"relativeEntities":333,"slug":18,"properties":334,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"1ccd0620-8570-4b79-b341-bbed976313ce","2024-01-29T08:54:07.569+00:00",[],{"title":335},{"VI":336},"Obukhov Institute for Atmospheric Physics, RAS, Moscow, Russia",{"title":338},{"VI":339},"V. I. 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A. Markov, Pis'ma Zh. Eksp. Teor. Fiz.,36, 214 (1982).\nM. A. Markov, “Problems of perpetually oscillating universe,” Preprint R-0286 [in Russian], Institute for Nuclear Research, USSR Academy of Sciences (1983); Phys. Lett. A,94, 427 (1983).\nB. N. Petrov, I. I. Gol'denblat, G. M. Ulanov, and S. V. Ul'yanov, Problems of the Control of Relativistic and Quantum Dynamical Systems [in Russian], Nauka, Moscow (1982).\nYa. B. Zel'dovich and I. D. Novikov, Structure and Evolution of the Universe [in Russian], Nauka, Moscow (1975).\nL. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th ed., Pergamon Press, Oxford (1975).\nA. A. Starobinskii, Pis'ma Zh. Eksp. Teor. Fiz.,30, 719 (1979); Phys. Lett. B.91, 99 (1980).",{"EN":383},"Oscillating universe in the case p≠0",{"VOID":385},"10.1007\u002FBF01017913","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF01017913",[388,396],{"id":389,"sortIndex":390,"researcher":18,"roles":391,"affiliations":392,"properties":393},"76d0010f-9aa2-4da9-9ba1-efcd4a311aac",1,[264],[],{"title":394},{"VI":395},"M. A. Markov",{"id":397,"sortIndex":19,"researcher":18,"roles":398,"affiliations":399,"properties":408},"7a013576-e194-42ea-aa67-7e11da8aa295",[264],[400],{"id":18,"sortIndex":19,"affiliation":401,"properties":18},{"id":402,"createTime":403,"updateTime":403,"relativeEntities":404,"slug":18,"properties":405,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"eab01bcd-2016-4b54-b174-627a97ad9bb5","2024-01-28T23:58:48.910+00:00",[],{"title":406},{"VI":407},"Department of Theoretical Physics, State University, Irkutsk",{"title":409},{"VI":410},"É. 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Janzing and T. Beth, IEEE Trans. Inform. Theory, 49, 230–240 (2003); arXiv:quant-ph\u002F0112138v2 (2001).\nR. A. Fisher, Proc. Cambridge Philos. Soc, 22, 700–725 (1925).\nC. R. Rao, Bull. Calcutta Math. Soc, 37, 81–91 (1945).\nH. Cramér, Mathematical Methods of Statistics (Princeton Math. Ser., Vol. 9), Princeton Univ. Press, Princeton, N. J. (1946).\nT. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, New York (1991).\nP. J. Huber, Robust Statistics, Wiley, New York (1981).\nE. A. Carlen, J. Funct. Anal, 101, 194–211 (1991).\nA. Kagan and Z. Landsman, Statist. Probab. Lett., 32, 175–179 (1997).\nC. W. Helstrom, Quantum Detection and Estimation Theory, Acad. Press, New York (1976).\nA. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory [in Russian], Nauka, Moscow (1980); English transi. (North-Holland Ser. Statist. Probab., Vol. 1), North-Holland, Amsterdam (1982).\nS. L. Braunstein and C M. Caves, Phys. Rev. Lett., 72, 3439–3443 (1994).\nD. Petz, Linear Algebra Appl, 244, 81–96 (1996).\nE. P. Wigner and M. M. Yanase, Proc. Natl. Acad. Sci. USA, 49, 910–918 (1963).\nP. Gibilisco and T. Isola, J. Math. Phys., 44, 3752–3762 (2003); arXiv:math\u002F0304170v1 (2003).\nS. Luo, Proc. Amer. Math. Soc, 132, 885–890 (2004).\nS. Luo and Q. Zhang, Phys. Rev. A, 69, 032106 (2004).\nS. Luo and Q. Zhang, IEEE Trans. Inform. Theory, 50, 1778–1782 (2004); 51, 4432 (2005).\nP. Chen and S. Luo, Front. Math. China, 2, 359–381 (2007).\nF. Hansen, Proc. Natl. Acad. Sci. USA, 105, 9909–9916 (2008); arXiv:math-ph\u002F0607049v6 (2006).\nL. Cai, N. Li, and S. Luo, J. Phys. A, 41, 135301 (2008).\nE. H. Lieb, Adv. Math., 11, 267–288 (1973).\nE. H. Lieb and M. B. Ruskai, Phys. Rev. Lett., 30, 434–436 (1973).\nA. Uhlmann, Comm. Math. Phys., 54, 21–32 (1977).\nH. Kosaki, Comm. Math. Phys., 87, 315–329 (1982).\nM. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge (2000).\nF. Hansen, J. Stat. Phys., 126, 643–648 (2007); arXiv:math-ph\u002F0609019v2 (2006).\nS. Luo, J. Stat. Phys., 128, 1177–1188 (2007).",{"EN":456},"In a broad sense, any parametric family of quantum states can be viewed as a quantum clock. The time, which is the parameter, is encoded in the corresponding quantum states. The quality of such a clock depends on how precisely we can distinguish the states or, equivalently, estimate the parameter. In view of the quantum Cramér—Rao inequalities, the quality of quantum clocks can be characterized by the quantum Fisher information. We address the issue of quantum clock synchronization in terms of quantum Fisher information and demonstrate its fundamental difference from the classical paradigm. The key point is the superadditivity of Fisher information, which always holds in the classical case but can be violated in quantum mechanics. The violation can occur for both pure and mixed states. Nevertheless, we establish the superadditivity of quantum Fisher information for any classical-quantum state. We also demonstrate an alternative form of superadditivity and propose a weak form of superadditivity. The violation of superadditivity can be exploited to enhance quantum clock synchronization.",{"EN":458},"Clocks and fisher information",{"VOID":460},"10.1007\u002Fs11232-010-0129-9","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs11232-010-0129-9",[463,480],{"id":464,"sortIndex":19,"researcher":18,"roles":465,"affiliations":466,"properties":477},"8c1aee42-3fb7-457f-b80e-4f2e01daf669",[264],[467],{"id":18,"sortIndex":19,"affiliation":468,"properties":18},{"id":469,"createTime":470,"updateTime":471,"relativeEntities":472,"slug":473,"properties":474,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"6e040bb6-7791-46dc-92a1-a3c9d5efa458","2024-01-13T17:41:16.513+00:00","2024-10-15T21:16:05.348+00:00",[],"Department-of-Economics-University-of-Melbourne-Melbourne-Australia",{"title":475},{"VI":476},"Department of Economics, University of Melbourne, Melbourne, Australia",{"title":478},{"VI":479},"Ping Chen",{"id":481,"sortIndex":390,"researcher":18,"roles":482,"affiliations":483,"properties":492},"f9f8ca17-9b0b-4b52-b9e3-05c785b7ebd8",[264],[484],{"id":18,"sortIndex":19,"affiliation":485,"properties":18},{"id":486,"createTime":487,"updateTime":487,"relativeEntities":488,"slug":18,"properties":489,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"b9c3cb07-a7f2-4a41-9077-8f58bd87eeab","2023-12-20T08:58:28.410+00:00",[],{"title":490},{"VI":491},"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. 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Bayen, M. Flato, C. Fronsdal, A. Lichnerowich, and D. Sternheimer, Ann. Phys., 111, 61 (1978).\nF. Bayen, M. Flato, C. Fronsdal, A. Lichnerowich, and D. Sternheimer, Ann. Phys., 111, 111 (1978).\nM. V. Karasev and V. P. Maslov, Nonlinear Poisson Brackets: Geometry and Quantization [in Russian], Nauka, Moscow (1991); English transl., Am. Math. Soc., Providence (1993).\nB. Fedosov, Deformation Quantization and Index Theory, Akademie, Berlin (1996).\nM. Kontsevich, “Deformation quantization of Poisson manifolds: I,” q-alg\u002F9709040 (1997).\nJ. E. Moyal, Proc. Cambridge Philos. Soc., 45, 99 (1949).",{"EN":540},"The general form of the *-commutator on the Grassmann algebra treated as a deformation of the conventional Poisson bracket is investigated. It is shown that in addition to the Moyal *-commutator, there exist other deformations of the Poisson bracket on the Grassman algebra (one additional deformation for even and odd n, where n is the number of the Grassmann algebra generators) that are not reducible to the Moyal *-commutator by a similarity transformation.",{"EN":542},"General Form of the *-Commutator on the Grassmann Algebra",{"VOID":544},"10.1023\u002FA:1012320121612","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1023\u002FA:1012320121612",[547],{"id":548,"sortIndex":19,"researcher":18,"roles":549,"affiliations":550,"properties":560},"bb5a3185-2816-422e-9e46-54112730e602",[264],[551],{"id":18,"sortIndex":19,"affiliation":552,"properties":18},{"id":553,"createTime":554,"updateTime":554,"relativeEntities":555,"slug":556,"properties":557,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"9157d804-c74a-44c9-be5e-996293df71e3","2024-04-16T06:16:26.846+00:00",[],"Lebedev-Physical-Institute-RAS-Moscow-Russia",{"title":558},{"EN":559},"Lebedev Physical Institute, RAS, Moscow, Russia",{"title":561},{"VI":562},"I. 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M. Perelomov, Commun. Math. Phys.,26, 222 (1972);44, 197 (1975).",{"doi":680},"10.1007\u002FBF01645091",{"id":18,"text":682,"url":18,"identifiers":683},"Coherent States in Quantum Theory [Russian translation], Mir (1972).",{},{"id":18,"text":685,"url":18,"identifiers":686},"A. M. Perelomov, Usp. Fiz. Nauk,123, 23 (1977); Teor. Mat. Fiz.,19, 83 (1974).",{"doi":687},"10.3367\u002FUFNr.0123.197709b.0023",{"id":18,"text":689,"url":18,"identifiers":690},"F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A,6, 2211 (1972).",{"doi":691},"10.1103\u002FPhysRevA.6.2211",{"id":18,"text":693,"url":18,"identifiers":694},"V. V. Zverev, Teor. Mat. Fiz.,26, 401 (1976).",{},{"id":18,"text":696,"url":18,"identifiers":697},"R. H. Dicke, Phys. Rev.,93, 99 (1954).",{"doi":698},"10.1103\u002FPhysRev.93.99",{"id":18,"text":700,"url":18,"identifiers":701},"L. A. Shelepin, Zh. Eksp. Teor. Fiz.,54, 1963 (1968); T. M. Makhviladze and L. A. Shelepin, Tr. Fiz. Inst. Akad. Nauk SSSR,70, 120 (1973); É. Sh. Teplitskii, Teor. Mat. Fiz.,2, 399 (1970).",{},{"id":18,"text":703,"url":18,"identifiers":704},"J. M. Radcliffe, J. Phys. A,4, 313 (1971).",{"doi":705},"10.1088\u002F0305-4470\u002F4\u002F3\u002F009",{"id":18,"text":707,"url":18,"identifiers":708},"V. P. Karasev, P. P. Karasev, and L. A. Shelepin, Teor. Mat. Fiz.,34, 185 (1978); V. P. Karasev and L. A. Shelepin, Teor. Mat. Fiz.,36, 2979 (1978).",{"doi":709},"10.1007\u002FBF01028029",{"id":18,"text":711,"url":18,"identifiers":712},"J. Bellissard and R. Holtz., J. Math. Phys.,15, 1275 (1974).",{"doi":713},"10.1063\u002F1.1666806",{"id":18,"text":715,"url":18,"identifiers":716},"V. P. Karasev and L. A. Shelepin, Kratk. Soobshch. Fiz., No.6, 14 (1978).",{},{"id":18,"text":718,"url":18,"identifiers":719},"M. Hongoh, Rep. Math. Phys.,13, 305 (1978).",{"doi":720},"10.1016\u002F0034-4877(78)90057-5",{"id":18,"text":722,"url":18,"identifiers":723},"V. P. Karasev and L. A. Shelepin, Kratk. Soobshch. Fiz., No.5, 20 (1979).",{},{"id":18,"text":725,"url":18,"identifiers":726},"J. Schwinger, On Angular Momentum, U.S. Atomic Energy Commission, NYO-3071 (1952).",{"doi":727},"10.2172\u002F4389568",{"id":18,"text":729,"url":18,"identifiers":730},"J. D. Louck, Amer. J. Phys.,38, 3 (1970).",{"doi":731},"10.1119\u002F1.1976225",{"id":18,"text":733,"url":18,"identifiers":734},"V. Bargmann, Rev. Mod. Phys.,34, 829 (1962).",{"doi":735},"10.1103\u002FRevModPhys.34.829",{"id":18,"text":737,"url":18,"identifiers":738},"V. P. Karasev, P. P. Karasev, and L. A. Shelepin, Kratk. Soobshch. Fiz., No.12, 27 (1977).",{},{"id":18,"text":740,"url":18,"identifiers":741},"T. M. Makhviladze and L. A. Shelepin, Kratk. Soobshch. Fiz., No.7, 3 (1971).",{},{"id":743,"createTime":744,"updateTime":745,"relativeEntities":746,"slug":747,"properties":748,"entityType":257,"verifyStatus":321,"verifyTime":745,"verifyNote":322,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":757,"fullTextUrl":18,"authors":758,"publicationType":269,"publisherRelationship":776,"citationCount":18,"citationInfo":18,"publishDate":809,"publishYear":810,"citationAnalyzeStatus":17,"lastCitationAnalyze":18,"indexDatabases":18,"openAccess":18,"references":18,"isForceReanalyzing":305},"1880932d-6f18-436f-a350-7a00ddb66072","2023-11-27T16:04:13.640+00:00","2025-01-27T23:57:38.499+00:00",[],"Perturbation-theory-series-in-quantum-mechanics-Phase-transition-and-exact-asymptotic-forms-for-the-expansion-coefficients",{"references":749,"abstract":751,"title":753,"doi":755},{"VOID":750},"J. Glimm and A. Jaffe, Quantum Physics: A Functional Integral Point of View, Springer, New York (1981).\nH.-O. Georgii, Gibbs Measures and Phase Transitions (De Gruyter Stud. Math., Vol. 9), de Gruyter, Berlin (2011).\nV. I. Piterbarg and V. R. Fatalov, Russ. Math. Surveys, 50, 1151–1239 (1995).\nV. R. Fatalov, Theor. Math. Phys., 168, 1112–1149 (2011).\nM. Reed and B. Simon, Methods of Modern Mathematical Physics, Vols. 1, 2, and 4, Acad. Press, New York (1978).\nR. P. Feynman, “Space-time approach to nonrelativistic quantum mechanics,” Rev. Modern Phys., 20, 367–387 (1948).\nV. R. Fatalov, “On the Laplace method for Gaussian measures in a Banach space,” Theory Probab. Appl. (to appear).\nV. R. Fatalov, Izv. Math., 75, 837–868 (2011).\nV. R. Fatalov, Theory Probab. Appl., 53, 13–36 (2009).\nS. Albeverio, V. Fatalov, and V. Piterbarg, J. Math. Sci. Univ. Tokyo, 16, 55–93 (2009).\nV. R. Fatalov, Izv. Math., 75, 837–868 (2011).\nV. R. Fatalov, “Exact asymptotics of probability distributions and functional integrals: Laplace method [in Russian],” Doctoral dissertation, Moscow State Univ., Moscow (2009).\nB. Simon, Functional Integration and Quantum Physics (Pure Appl. Math., Vol. 86), Acad. Press, New York (1979).\nW. Janke and A. Pelster, eds., Path Integrals: New Trends and Perspectives (Proc. 9th Intl. Conf., Dresden, 23–28 September 2007), World Scientific, Hackensack, N. J. (2008).\nJ. Zinn-Justin, “Functional integrals in physics: The main achievements,” in: Path Integrals: New Trends and Perspectives (Proc. 9th Intl. Conf., Dresden, 23–28 September 2007, W. Janke and A. Pelster, eds.), World Scientific, Hackensack, N. J. (2008), pp. 251–260.\nI. M. Koval’chik and L. A. Yanovich, The Generalized Wiener Integral and Some of its Applications [in Russian], Nauka i Tekhnika, Minsk (1989).\nR. S. Ellis and J. S. Rosen, Comm. Math. Phys., 82, 153–181 (1981).\nR. S. Ellis and J. S. Rosen, Trans. Amer. Math. 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Belokurov and D. V. Shirkov, Theory of the Interaction of Particles [in Russian], Nauka, Moscow (1986).\nV. V. Belokurov, Yu. P. Solov’ev, and E. T. Shavgulidze, “Method for constructing a quantum field theory of perturbations with convergent series [in Russian],” Preprint Sci.-Res. Inst. Nucl. Phys. 95-31\u002F395, Moscow State Univ., Moscow (1995).\nJ. Zinn-Justin, Phys. Rep., 70, 109–167 (1981).\nS. G. Krein, ed., Functional Analysis [in Russian], Nauka, Moscow (1972); English transl., Wolters-Noordhoff, Groningen (1972).\nB. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, Princeton, N. J. (1974).\nT. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1995).\nB. Simon, Ann. Phys., 58, 76–136 (1970).\nE. Lieb, Bull. Amer. Math. Soc., 82, 751–753 (1976).\nN. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes (North-Holland Math. Library, Vol. 24), North-Holland, Amsterdam (1981).\nT. Hida, Brownian Motion (Appl. Math., Vol. 11), Springer, New York (1980).\nA. N. Borodin and P. Salminen, Handbook of Brownian motion [in Russian], Lan’, St. Petersburg (2000); English transl., Birkhäuser, Basel (2002).\nH.-H. Kuo, Gaussian Measures in Banach Spaces (Lect. Notes Math., Vol. 463), Springer, Berlin (1975).\nN. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions on Banach Spaces [in Russian], Nauka, Moscow (1985); English transl. (Math. Appl. Soviet Ser., Vol. 14), Reidel, Dordrecht (1987).\nM. A. Lifshits, Gaussian Random Functions [in Russian], TViMS, Kiev (1995); English transl. (Math. Appl., Vol. 322), Kluwer, Dordrecht (1995).\nV. I. Bogachev, Gaussian Measures [in Russian], Fizmatlit, Moscow (1997); English transl. (Math. Surv. Monogr., Vol. 62), Amer. Math. Soc., Providence, R. I. (1998).\nS. R. S. Varadhan, Comm. Pure Appl. Math., 19, 261–286 (1996).\nS. R. S. Varadhan, Lett. Math. Phys., 88, 175–185 (2009).\nE. Olivieri and M. E. 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Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1979); English transl., Consultants Bureau, New York (1987).\nX. M. Fernique, “La régularité des trajectoires des fonctions aléatoires gaussiennes,” in: Ecole d’Ete de Probabilites de Saint-Flour IV — 1974 (Lect. Notes Math., Vol. 480, P.-L. Hennequin, ed.), Springer, Berlin (1975), pp. 1–96.\nE. Kamke, Differentialgleichungen, Lösunsmethoden, und Lösungen, Academie, Leipzig (1959).\nA. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Elementary Functions [in Russian], Nauka, Moscow (1981); English transl., Gordon and Breach, New York (1986).",{"EN":752},"We consider the model of a harmonic oscillator with a power-law potential and derive new asymptotic formulas for the coefficients of the perturbation theory series in powers of the coupling constant in the case of a power-law perturbing potential |x|p, p > 0. We prove the existence of a critical value p\n                  0\n                 and compute it. It is a threshold in the sense that the asymptotic forms of the studied coefficients for 0 \u003C p \u003C p\n                  0\n                 and for p > p\n                  0\n                 differ qualitatively. We note that the considered physical system undergoes a phase transition at p = p\n                  0\n                . 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Martínez Alonso and A. B. Shabat, Phys. Lett. A, 300, 58 (2002).\nL. Martínez Alonso and A. B. Shabat, J. Nonlinear Math. Phys., 10, 229 (2003); “On the prolongation of a hierarchy of hydrodynamic chains,” in: New Trends in Integrability and Partial Solvability (NATO Sci. Ser.,Vol. 132, A. B. Shabat et al., eds.), Kluwer, Dordrecht, p. 263.\nA. B. Shabat, Theor. Math. Phys., 136, 1066 (2003).\nV. G. Mikhalev, Funct. Anal. Appl., 26, 140 (1992).\nM. Jaulent and I. Miodek, Lett. Math. Phys., 1, 243 (1976); Lett. Nuovo Cimento, 20, 655 (1977); L. Martínez Alonso, J. Math. Phys., 21, 2342 (1980); M. Antonowicz and A. P. Fordy, Phys. D, 28, 345 (1987); A. N.W. Hone, Phys. Lett. A, 249, 46(1998).\nR. Camassa and D. Holm, Phys. Rev. Lett.,71, 1661 (1993).\nJ. Gibbons and Y. Kodama, Phys. Lett. A , 135, 167 (1989); J. Gibbons and S. P. Tsarev, Phys. Lett. A, 211, 19 (1996); 258, 263 (1999); M. Mñas, L. Martínez Alonso, and E. Medina, J. Phys.A, 35, 401 (2002).\nE. V. Ferapontov and K. R. Khusnutdinova, “On integrability of (2+1)-dimensional quasilinear systems,” nlin.SI\u002F0305044 (2003).\nM. V. Pavlov, “Integrable hydrodynamic chains,” nlin.SI\u002F0301010 (2003).\nS. P. Tsarev, Izv. Akad. Nauk USSR, Ser. Mat., 37, 397 (1991).",{"EN":821},"We investigate the diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains and analyze their compatibility with previously introduced reductions of differential type.",{"EN":823},"Hydrodynamic Reductions and Solutions of a Universal Hierarchy",{"VOID":825},"10.1023\u002FB:TAMP.0000036538.41884.57","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1023\u002FB:TAMP.0000036538.41884.57",[828,843],{"id":829,"sortIndex":19,"researcher":18,"roles":830,"affiliations":831,"properties":840},"04325c03-561d-4082-97cf-daa72b207fdc",[264],[832],{"id":18,"sortIndex":19,"affiliation":833,"properties":18},{"id":834,"createTime":835,"updateTime":835,"relativeEntities":836,"slug":18,"properties":837,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"3674aebf-cd04-4a98-a84f-bac82c6b6160","2024-01-15T02:29:56.954+00:00",[],{"title":838},{"VI":839},"Departamento de Física Teórica II, Universidad Complutense, Madrid, Spain",{"title":841},{"VI":842},"L. 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Phys., 85, 1096 (1990).\nYu. A. Tserkovnikov, Theor. Math. Phys., 118, 85 (1999).\nYu. A. Tserkovnikov, Theor. Math. Phys., 119, 511 (1999).\nI. M. Mryglod and A. M. Hachkevych, Cond. Matter Phys., No. 5, 105 (1995).\nG. O. Balabanyan, Theor. Math. Phys., 82, 317 (1990).\nG. O. Balabanyan, Theor. Math. Phys., 85, 1081 (1990).",{"EN":904},"We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics.",{"EN":906},"Nonequilibrium statistical operator in the generalized molecular hydrodynamics of fluids",{"VOID":908},"10.1007\u002Fs11232-008-0007-x","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs11232-008-0007-x",[911,926,938],{"id":912,"sortIndex":390,"researcher":18,"roles":913,"affiliations":914,"properties":923},"15e640a3-f810-47ab-8d1c-784244c0124c",[264],[915],{"id":18,"sortIndex":19,"affiliation":916,"properties":18},{"id":917,"createTime":918,"updateTime":918,"relativeEntities":919,"slug":18,"properties":920,"entityType":45,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"99205a38-5c37-4638-a181-bfb6e1837c59","2023-12-06T07:42:44.049+00:00",[],{"title":921},{"VI":922},"Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lvov, Ukraine",{"title":924},{"VI":925},"I. 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