Pub Date : 2021-12-10DOI: 10.33581/1561-4085-2021-24-4-326-328
V. Skalozub
In SU(2) gluodynamics, in the background Feynman gauge the effective charge ğ2(A0) is calculated in the presence of the A0 condensate which is spontaneous generated at high temperature. It is determined from a two-loop effective potential W(A0). Temperature dependence in a wide interval is investigated.
{"title":"Effective Color Charge at A0 Background","authors":"V. Skalozub","doi":"10.33581/1561-4085-2021-24-4-326-328","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-4-326-328","url":null,"abstract":"In SU(2) gluodynamics, in the background Feynman gauge the effective charge ğ2(A0) is calculated in the presence of the A0 condensate which is spontaneous generated at high temperature. It is determined from a two-loop effective potential W(A0). Temperature dependence in a wide interval is investigated.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44276268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-222-229
D. Horoshko, S. Kilin
We consider an unambiguous state discrimination attack on the B92 protocol of quantum key distribution, realized on the basis of polarization encoding of photons produced by a single-photon source. We calculate the secure key rate and the maximal tolerable loss for various overlaps between two signal states employed in this protocol. We make also a comparison with a physically impossible attack of perfect quantum cloning, and show that the unambiguous state discrimination is much more dangerous for the B92 protocol, than this attack, demonstrating thus, that the security of quantum key distribution is not always based on the no-cloning theorem.
{"title":"Unambiguous State Discrimination Attack on the B92 Protocol of Quantum Key Distribution with Single Photons","authors":"D. Horoshko, S. Kilin","doi":"10.33581/1561-4085-2021-24-3-222-229","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-222-229","url":null,"abstract":"We consider an unambiguous state discrimination attack on the B92 protocol of quantum key distribution, realized on the basis of polarization encoding of photons produced by a single-photon source. We calculate the secure key rate and the maximal tolerable loss for various overlaps between two signal states employed in this protocol. We make also a comparison with a physically impossible attack of perfect quantum cloning, and show that the unambiguous state discrimination is much more dangerous for the B92 protocol, than this attack, demonstrating thus, that the security of quantum key distribution is not always based on the no-cloning theorem.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43589401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-260-271
E. Ovsiyuk, A. Koral’kov, A. Chichurin, V. Red’kov
The known systems of radial equations describing the relativistic hydrogen atom on the base of the Dirac equation in Lobachevsky hyperbolic space is solved. The relevant 2-nd order differential equation has six regular singular points, its solutions of Frobenius type are constructed explicitly. To produce the quantization rule for energy values we have used the known condition for determination of the transcendental Frobenius solutions. This defines the energy spectrum which is physically interpretable and similar to the spectrum arising for the scalar Klein-Fock-Gordon equation in Lobachevsky space. In the present paper, exact analytical solutions referring to this spectrum are constructed. Convergence of the series involved is proved analytically and numerically. Squared integrability of the solutions is demonstrated numerically. It is shown that the spectrum coincides precisely with that previously found within the semi-classical approximation.
{"title":"Dirac Particle in the Coulomb Field on the Background of Hyperbolic Lobachevsky Model","authors":"E. Ovsiyuk, A. Koral’kov, A. Chichurin, V. Red’kov","doi":"10.33581/1561-4085-2021-24-3-260-271","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-260-271","url":null,"abstract":"The known systems of radial equations describing the relativistic hydrogen atom on the base of the Dirac equation in Lobachevsky hyperbolic space is solved. The relevant 2-nd order differential equation has six regular singular points, its solutions of Frobenius type are constructed explicitly. To produce the quantization rule for energy values we have used the known condition for determination of the transcendental Frobenius solutions. This defines the energy spectrum which is physically interpretable and similar to the spectrum arising for the scalar Klein-Fock-Gordon equation in Lobachevsky space. In the present paper, exact analytical solutions referring to this spectrum are constructed. Convergence of the series involved is proved analytically and numerically. Squared integrability of the solutions is demonstrated numerically. It is shown that the spectrum coincides precisely with that previously found within the semi-classical approximation.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42759032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-230-241
V. Afanasyev, Zhen Keli, A. Kulagin, H. Miao, Y. Ozhigov, Wanshun Lee, N. Victorova
Suggestion of modifications of finite-dimensional quantum-electrodynamic (QED) models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due to quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.
{"title":"About Chemical Modifications of Finite Dimensional QED Models","authors":"V. Afanasyev, Zhen Keli, A. Kulagin, H. Miao, Y. Ozhigov, Wanshun Lee, N. Victorova","doi":"10.33581/1561-4085-2021-24-3-230-241","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-230-241","url":null,"abstract":"Suggestion of modifications of finite-dimensional quantum-electrodynamic (QED) models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due to quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49192385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-280-291
A. Shalyt-Margolin
Based on the results from black hole thermodynamics at all energy scales, this work demonstrates that, both for the discrete QFT previously introduced by the author and for QFT in continuous space-time, there is a natural ultraviolet applicable boundary (cut-off) distant from the Planck scales. It is important that this boundary exists irrespective of the fact in which pattern, perturbative or non-perturbative mode, QFT is studied. Different inferences from the obtained results are discussed, some statements are revised.
{"title":"The Discrete and Continuous Quantum Field Theories and Natural Ultraviolet Cutting-off","authors":"A. Shalyt-Margolin","doi":"10.33581/1561-4085-2021-24-3-280-291","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-280-291","url":null,"abstract":"Based on the results from black hole thermodynamics at all energy scales, this work demonstrates that, both for the discrete QFT previously introduced by the author and for QFT in continuous space-time, there is a natural ultraviolet applicable boundary (cut-off) distant from the Planck scales. It is important that this boundary exists irrespective of the fact in which pattern, perturbative or non-perturbative mode, QFT is studied. Different inferences from the obtained results are discussed, some statements are revised.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48543910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-292-300
E. Kokoulina, N. Barlykov, V. Dudin, A. Gribovsky, V. Dunin, V. Nikitin, V. Popov, A. Kutov, V. Ryadovikov, R. Shulyakovsky
The latest results on the search for collective phenomena in proton interactions at the U-70 accelerator at IHEP (Protvino) are presented. This long-term experiment has been carried at the SVD-2 setup. Our study was aimed at a high multiplicity region where the series of collective phenomena is predicted. We have received an evidence of the formation of a pion (Bose-Einstein) condensate. We have observed two noticeable peaks in the angular distribution of charged pions interpreted as Cherenkov radiation of gluons by quarks and others phenomena.
{"title":"Collective Behavior of Secondary Particles in the Region of high Multiplicity in pp Interactions at 50 GeV/c","authors":"E. Kokoulina, N. Barlykov, V. Dudin, A. Gribovsky, V. Dunin, V. Nikitin, V. Popov, A. Kutov, V. Ryadovikov, R. Shulyakovsky","doi":"10.33581/1561-4085-2021-24-3-292-300","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-292-300","url":null,"abstract":"The latest results on the search for collective phenomena in proton interactions at the U-70 accelerator at IHEP (Protvino) are presented. This long-term experiment has been carried at the SVD-2 setup. Our study was aimed at a high multiplicity region where the series of collective phenomena is predicted. We have received an evidence of the formation of a pion (Bose-Einstein) condensate. We have observed two noticeable peaks in the angular distribution of charged pions interpreted as Cherenkov radiation of gluons by quarks and others phenomena.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43287489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-242-259
V. Trofimov, M. Loginova, V. Egorenkov
We consider a problem of laser pulse interaction with a nonlinear medium which is accompanied by different nonlinear phenomena. Among them, we highlight the laser pulse self-action, optical bistability realization, formation of laser-induced complicated spatio-temporal structures. For computer modeling of these strongly nonlinear effects, using robust conservative numerical methods is required. Well-known, there are two widely applied approaches for the construction of numerical method: the conservative finite-difference schemes and additive finite-difference schemes (the split-step methods or decomposition methods). The first ones are non-economic, as a rule, while the second type of the methods is economic ones, however they possess well-known disadvantages. In our study, we joint advantages of both approaches by developing an original multi-stage iterative process for the conservative finite-difference scheme realization. Using computer simulation results, we demonstrate the feasibility of the proposed approach for investigating certain nonlinear optical phenomena.
{"title":"Multi-Stages Iterative Process for Conservative Economic Finite-Difference Schemes Realization for the Problem of Nonlinear Laser Pulse Interaction with a Medium","authors":"V. Trofimov, M. Loginova, V. Egorenkov","doi":"10.33581/1561-4085-2021-24-3-242-259","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-242-259","url":null,"abstract":"We consider a problem of laser pulse interaction with a nonlinear medium which is accompanied by different nonlinear phenomena. Among them, we highlight the laser pulse self-action, optical bistability realization, formation of laser-induced complicated spatio-temporal structures. For computer modeling of these strongly nonlinear effects, using robust conservative numerical methods is required. Well-known, there are two widely applied approaches for the construction of numerical method: the conservative finite-difference schemes and additive finite-difference schemes (the split-step methods or decomposition methods). The first ones are non-economic, as a rule, while the second type of the methods is economic ones, however they possess well-known disadvantages. In our study, we joint advantages of both approaches by developing an original multi-stage iterative process for the conservative finite-difference scheme realization. Using computer simulation results, we demonstrate the feasibility of the proposed approach for investigating certain nonlinear optical phenomena.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42204342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-301-310
N. V. Harbachova, N. Kuzmina, N. Kulich, S. Yatsko, J. A. Korchova
In this paper, natural (geological and hydrological) and climatic impact conditions on the influence zone for two different sites of radioactive waste disposals have been studied. Probabilistic approach to assessment of the groundwater vulnerability from radionuclide contamination during disposal of radioactive waste is developed. As to climatic conditions, an effective numerical and analytical methods for annual precipitation rates assessment of rare recurrence have been proposed which allow to take into account uncertainties of rare events as well.
{"title":"Influence of Natural and Climatic Factors on Water Horizons Protection Degree in Site Evaluation for Radioactive Waste Disposal","authors":"N. V. Harbachova, N. Kuzmina, N. Kulich, S. Yatsko, J. A. Korchova","doi":"10.33581/1561-4085-2021-24-3-301-310","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-301-310","url":null,"abstract":"In this paper, natural (geological and hydrological) and climatic impact conditions on the influence zone for two different sites of radioactive waste disposals have been studied. Probabilistic approach to assessment of the groundwater vulnerability from radionuclide contamination during disposal of radioactive waste is developed. As to climatic conditions, an effective numerical and analytical methods for annual precipitation rates assessment of rare recurrence have been proposed which allow to take into account uncertainties of rare events as well.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42356833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-272-279
N. V. Gerasimenko, F. M. Trukhachev, E. Gusakov, L. Simonchik, A. V. Tomov
A numerical one-dimensional model of convective parametric instability of inhomogeneous plasma is developed. By using this model, a numerical solution describing spatial and temporal characteristics of interacting waves is obtained. The results obtained are in a good agreement with known analytical models and substantially generalize them. In particular, an important advantage of the proposed model is the possibility of varying initial conditions, analyzing behavior of the system in the presence of incident wave fluctuations that is important for the future study of the absolute instability mode. The model is also provides possibility to simulate absolute parametric instability with a wide range of controllable parameters, as well as to study interacting wave transients.
{"title":"One-Dimensional Nonlinear Parametric Instability of Inhomogeneous Plasma: Time Domain Problem","authors":"N. V. Gerasimenko, F. M. Trukhachev, E. Gusakov, L. Simonchik, A. V. Tomov","doi":"10.33581/1561-4085-2021-24-3-272-279","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-272-279","url":null,"abstract":"A numerical one-dimensional model of convective parametric instability of inhomogeneous plasma is developed. By using this model, a numerical solution describing spatial and temporal characteristics of interacting waves is obtained. The results obtained are in a good agreement with known analytical models and substantially generalize them. In particular, an important advantage of the proposed model is the possibility of varying initial conditions, analyzing behavior of the system in the presence of incident wave fluctuations that is important for the future study of the absolute instability mode. The model is also provides possibility to simulate absolute parametric instability with a wide range of controllable parameters, as well as to study interacting wave transients.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43338270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.33581/1561-4085-2021-24-3-207-221
K. Khadiev, Vladislav Remidovskii
We study algorithms for solving the problem of assembling a text (long string) from a dictionary (a sequence of small strings). The problem has an application in bioinformatics and has a connection with the sequence assembly method for reconstructing a long deoxyribonucleic-acid (DNA) sequence from small fragments. The problem is assembling a string t of length n from strings s1,...,sm. Firstly, we provide a classical (randomized) algorithm with running time Õ(nL0.5 + L) where L is the sum of lengths of s1,...,sm. Secondly, we provide a quantum algorithm with running time Õ(nL0.25 + √mL). Thirdly, we show the lower bound for a classical (randomized or deterministic) algorithm that is Ω(n+L). So, we obtain the quadratic quantum speed-up with respect to the parameter L; and our quantum algorithm have smaller running time comparing to any classical (randomized or deterministic) algorithm in the case of non-constant length of strings in the dictionary.
{"title":"Classical and Quantum Algorithms for Assembling a Text from a Dictionary","authors":"K. Khadiev, Vladislav Remidovskii","doi":"10.33581/1561-4085-2021-24-3-207-221","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-3-207-221","url":null,"abstract":"We study algorithms for solving the problem of assembling a text (long string) from a dictionary (a sequence of small strings). The problem has an application in bioinformatics and has a connection with the sequence assembly method for reconstructing a long deoxyribonucleic-acid (DNA) sequence from small fragments. The problem is assembling a string t of length n from strings s1,...,sm. Firstly, we provide a classical (randomized) algorithm with running time Õ(nL0.5 + L) where L is the sum of lengths of s1,...,sm. Secondly, we provide a quantum algorithm with running time Õ(nL0.25 + √mL). Thirdly, we show the lower bound for a classical (randomized or deterministic) algorithm that is Ω(n+L). So, we obtain the quadratic quantum speed-up with respect to the parameter L; and our quantum algorithm have smaller running time comparing to any classical (randomized or deterministic) algorithm in the case of non-constant length of strings in the dictionary.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42495692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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