Pub Date : 2006-11-15DOI: 10.1088/0305-4470/39/48/007
Shu-fang Deng
The modified Kadomtsev–Petviashvili I equation with self-consistent sources (mKPIESCS) is derived through the linear problem of the modified Kadomtsev–Petviashvili I (mKPI) system. The bilinear form of the mKPIESCS is given and the N-soliton solutions are obtained through the Hirota method and the Wronskian technique, respectively. The coincidence of these solutions is shown by direct computation.
{"title":"The multisoliton solutions for the mKPI equation with self-consistent sources","authors":"Shu-fang Deng","doi":"10.1088/0305-4470/39/48/007","DOIUrl":"https://doi.org/10.1088/0305-4470/39/48/007","url":null,"abstract":"The modified Kadomtsev–Petviashvili I equation with self-consistent sources (mKPIESCS) is derived through the linear problem of the modified Kadomtsev–Petviashvili I (mKPI) system. The bilinear form of the mKPIESCS is given and the N-soliton solutions are obtained through the Hirota method and the Wronskian technique, respectively. The coincidence of these solutions is shown by direct computation.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80089861","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 : 2006-11-15DOI: 10.1088/0305-4470/39/48/004
A. Ishkhanyan, J. Javanainen, Hiroki Nakamura
The nonlinear Landau–Zener problem for two-mode photoassociation of cold atoms is studied. Based on an exact nonlinear Volterra integral equation for molecular state probability, a limit nonlinear first-order differential equation is applied to construct the first-order approximation to the solution of the problem at a strong coupling limit. An accurate approximate expression for the final transition probability to the molecular state is derived. The non-transition probability turns out to be inversely proportional to the Landau–Zener parameter in contrast to the linear two-state case when the dependence is exponential.
{"title":"Landau–Zener transition in photoassociation of cold atoms: strong interaction limit","authors":"A. Ishkhanyan, J. Javanainen, Hiroki Nakamura","doi":"10.1088/0305-4470/39/48/004","DOIUrl":"https://doi.org/10.1088/0305-4470/39/48/004","url":null,"abstract":"The nonlinear Landau–Zener problem for two-mode photoassociation of cold atoms is studied. Based on an exact nonlinear Volterra integral equation for molecular state probability, a limit nonlinear first-order differential equation is applied to construct the first-order approximation to the solution of the problem at a strong coupling limit. An accurate approximate expression for the final transition probability to the molecular state is derived. The non-transition probability turns out to be inversely proportional to the Landau–Zener parameter in contrast to the linear two-state case when the dependence is exponential.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85585732","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 : 2006-11-15DOI: 10.1088/0305-4470/39/48/R01
Zhong-Qi Ma
The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schrödinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm–Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm–Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced.
{"title":"The Levinson theorem","authors":"Zhong-Qi Ma","doi":"10.1088/0305-4470/39/48/R01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/48/R01","url":null,"abstract":"The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schrödinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm–Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm–Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85958465","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 : 2006-11-10DOI: 10.1088/0305-4470/39/45/021
L. Hu, H. Fan
In three-mode Fock space we construct a new tripartite entangled state |α, γ⟩θλ which makes up a new quantum mechanical representation. The state |α, γ⟩θλ can be generated by using the set-up composed of an asymmetric beam splitter and a parametric down-conversion amplifier. We then show how to use |α, γ⟩θλ to find new squeezing operator and new squeezed state.
{"title":"New tripartite entangled state generated by an asymmetric beam splitter and a parametric down-conversion amplifier","authors":"L. Hu, H. Fan","doi":"10.1088/0305-4470/39/45/021","DOIUrl":"https://doi.org/10.1088/0305-4470/39/45/021","url":null,"abstract":"In three-mode Fock space we construct a new tripartite entangled state |α, γ⟩θλ which makes up a new quantum mechanical representation. The state |α, γ⟩θλ can be generated by using the set-up composed of an asymmetric beam splitter and a parametric down-conversion amplifier. We then show how to use |α, γ⟩θλ to find new squeezing operator and new squeezed state.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77046564","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 : 2006-11-10DOI: 10.1088/0305-4470/39/45/013
M. Koca, M. Al-Ajmi, R. Koc
The vertices of the four-dimensional polytope {3, 3, 5} and its dual {5, 3, 3} admitting the symmetry of the non-crystallographic Coxeter group W(H4) of order 14 400 are represented in terms of quaternions with unit norm where the polytope {3, 3, 5} is represented by the elements of the binaryicosahedral group of quaternions of order 120. We projected the polytopes to three-dimensional Euclidean space where the quaternionic vertices are the orbits of the Coxeter group W(H3), icosahedral group with inversion, where W(H3) × Z2 is one of the maximal subgroups of the Coxeter group W(H4). The orbits of the icosahedral group W(H3) in the polytope {3, 3, 5} are the conjugacy classes of the binary icosahedral group and represent a number of icosahedrons, dodecahedrons and one icosidodecahedron in three dimensions. The 15 orbits of the icosahedral group W(H3) in the polytope {5, 3, 3} represent the dodecahedrons, icosidodecahedrons, small rhombicosidodecahedrons and some convex solids possessing the icosahedral symmetry. One of the convex solids with 60 vertices is very similar to the truncated icosahedron (soccer ball) but with two different edge lengths which can be taken as a realistic model of the C60 molecule at extreme temperature and pressure.
{"title":"Quaternionic representation of the Coxeter group W(H4) and the polyhedra","authors":"M. Koca, M. Al-Ajmi, R. Koc","doi":"10.1088/0305-4470/39/45/013","DOIUrl":"https://doi.org/10.1088/0305-4470/39/45/013","url":null,"abstract":"The vertices of the four-dimensional polytope {3, 3, 5} and its dual {5, 3, 3} admitting the symmetry of the non-crystallographic Coxeter group W(H4) of order 14 400 are represented in terms of quaternions with unit norm where the polytope {3, 3, 5} is represented by the elements of the binaryicosahedral group of quaternions of order 120. We projected the polytopes to three-dimensional Euclidean space where the quaternionic vertices are the orbits of the Coxeter group W(H3), icosahedral group with inversion, where W(H3) × Z2 is one of the maximal subgroups of the Coxeter group W(H4). The orbits of the icosahedral group W(H3) in the polytope {3, 3, 5} are the conjugacy classes of the binary icosahedral group and represent a number of icosahedrons, dodecahedrons and one icosidodecahedron in three dimensions. The 15 orbits of the icosahedral group W(H3) in the polytope {5, 3, 3} represent the dodecahedrons, icosidodecahedrons, small rhombicosidodecahedrons and some convex solids possessing the icosahedral symmetry. One of the convex solids with 60 vertices is very similar to the truncated icosahedron (soccer ball) but with two different edge lengths which can be taken as a realistic model of the C60 molecule at extreme temperature and pressure.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/0305-4470/39/45/013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72491656","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 : 2006-11-10DOI: 10.1088/0305-4470/39/45/012
Y. Ishii
In this paper we rigorously prove some statements on the symbolic dynamics for Bernoulli coupled map lattices studied by Kawasaki and Sasa. The advantage of our approach is that it is purely topological and it gives a simultaneous proof for the statements.
{"title":"Note on a paper by Kawasaki and Sasa on Bernoulli coupled map lattices","authors":"Y. Ishii","doi":"10.1088/0305-4470/39/45/012","DOIUrl":"https://doi.org/10.1088/0305-4470/39/45/012","url":null,"abstract":"In this paper we rigorously prove some statements on the symbolic dynamics for Bernoulli coupled map lattices studied by Kawasaki and Sasa. The advantage of our approach is that it is purely topological and it gives a simultaneous proof for the statements.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76905031","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 : 2006-11-10DOI: 10.1088/0305-4470/39/45/024
F. Tanaka
The classical Gaussian model, a parametric family of the Gaussian distribution, is known to be a space of constant negative curvature if one regards the Fisher information on the model as a Riemannian metric. Constant curvature reflects the scale invariance of the classical Gaussian model, which is well known in information geometry. However, it is shown that if the Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model is adopted as a Riemannian metric, then this scale invariance on the Gaussian model is broken due to the quantum effect. In the present study, the connection between the geometry of the classical Gaussian model and its quantum counterpart is clarified using the Taylor expansion with respect to the Planck constant. It is further shown that such a method is not applicable to a finite-dimensional system such as the spin system.
{"title":"Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance","authors":"F. Tanaka","doi":"10.1088/0305-4470/39/45/024","DOIUrl":"https://doi.org/10.1088/0305-4470/39/45/024","url":null,"abstract":"The classical Gaussian model, a parametric family of the Gaussian distribution, is known to be a space of constant negative curvature if one regards the Fisher information on the model as a Riemannian metric. Constant curvature reflects the scale invariance of the classical Gaussian model, which is well known in information geometry. However, it is shown that if the Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model is adopted as a Riemannian metric, then this scale invariance on the Gaussian model is broken due to the quantum effect. In the present study, the connection between the geometry of the classical Gaussian model and its quantum counterpart is clarified using the Taylor expansion with respect to the Planck constant. It is further shown that such a method is not applicable to a finite-dimensional system such as the spin system.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82060465","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 : 2006-11-10DOI: 10.1088/0305-4470/39/45/007
J. Matthews, K. Hopcraft, E. Jakeman, G B Siviour
We investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined. The model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events. This leads to a scale-free discrete random process where customary measures, such as mean value and variance, do not exist. However, converting the number of events occurring in fixed time intervals to a 1-bit ‘clipped’ process allows the construction of well-behaved statistics that still retain vestiges of the original power-law and fluctuation properties. These statistics include the clipped mean and correlation function, from measurements of which both the power-law index of the distribution of events and the time constant of its fluctuations can be deduced. We report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process. This indicates that, for a fixed experiment time, the error on measurements of the sample mean is minimized by an optimum choice of the number of samples. It is shown furthermore that this choice is sensitive to the power-law index and that the approach to Poisson statistics is dominated by rare events or ‘outliers’. Our results are supported by numerical simulation.
{"title":"Accuracy analysis of measurements on a stable power-law distributed series of events","authors":"J. Matthews, K. Hopcraft, E. Jakeman, G B Siviour","doi":"10.1088/0305-4470/39/45/007","DOIUrl":"https://doi.org/10.1088/0305-4470/39/45/007","url":null,"abstract":"We investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined. The model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events. This leads to a scale-free discrete random process where customary measures, such as mean value and variance, do not exist. However, converting the number of events occurring in fixed time intervals to a 1-bit ‘clipped’ process allows the construction of well-behaved statistics that still retain vestiges of the original power-law and fluctuation properties. These statistics include the clipped mean and correlation function, from measurements of which both the power-law index of the distribution of events and the time constant of its fluctuations can be deduced. We report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process. This indicates that, for a fixed experiment time, the error on measurements of the sample mean is minimized by an optimum choice of the number of samples. It is shown furthermore that this choice is sensitive to the power-law index and that the approach to Poisson statistics is dominated by rare events or ‘outliers’. Our results are supported by numerical simulation.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90079117","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 : 2006-11-08DOI: 10.1088/0305-4470/39/47/018
R. Tautz, I. Lerche
Recently, a general proof was given (Tautz et al 2006 J. Phys. A: Math. Gen. 39 13831) that for an asymmetric relativistic particle phase-space distribution function, and in the absence of a homogeneous background magnetic field, any unstable linear Weibel modes are isolated, i.e. restricted to discrete wavenumbers. In this paper, for a specific distribution function consisting of mono-energetic counterstreaming electron and positron beams, growth rates and associated wavenumbers for the isolated modes are calculated, proving the existence of discrete values for unstable wavenumbers. Furthermore, electrostatic and electromagnetic Weibel modes are investigated for monoenergetic counterstreaming plasmas, yielding constraints to the momentum components that have to be fulfilled in order to have unstable wave modes.
最近，给出了一个一般的证明(Tautz et al . 2006 J. Phys.)。答:数学。(Gen. 39 13831)，对于不对称相对论性粒子相空间分布函数，在没有均匀背景磁场的情况下，任何不稳定的线性Weibel模都是孤立的，即限制为离散波数。本文对由单能逆流电子束和正电子束组成的特定分布函数，计算了孤立模的增长率和相关波数，证明了不稳定波数的离散值的存在性。此外，对单能量逆流等离子体的静电和电磁威贝尔模式进行了研究，得出了为了具有不稳定的波模式而必须满足的动量分量的约束。
{"title":"Coupling, degeneracy breaking and isolation of Weibel modes in relativistic plasmas: II. Specific examples","authors":"R. Tautz, I. Lerche","doi":"10.1088/0305-4470/39/47/018","DOIUrl":"https://doi.org/10.1088/0305-4470/39/47/018","url":null,"abstract":"Recently, a general proof was given (Tautz et al 2006 J. Phys. A: Math. Gen. 39 13831) that for an asymmetric relativistic particle phase-space distribution function, and in the absence of a homogeneous background magnetic field, any unstable linear Weibel modes are isolated, i.e. restricted to discrete wavenumbers. In this paper, for a specific distribution function consisting of mono-energetic counterstreaming electron and positron beams, growth rates and associated wavenumbers for the isolated modes are calculated, proving the existence of discrete values for unstable wavenumbers. Furthermore, electrostatic and electromagnetic Weibel modes are investigated for monoenergetic counterstreaming plasmas, yielding constraints to the momentum components that have to be fulfilled in order to have unstable wave modes.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85980172","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}
We present and investigate a general nonlinear growth network model which incorporates accelerated growth of nodes and edges, where the growth rates of edges and nodes are all time-dependent power-law functions. The acceleration of edges determines the proportion of the internal edges to the external edges, which play a key role influencing the structure of the network. On the other hand, the effects of the acceleration of nodes on the topology of the network are discussed in the present work. This model predicts an observable two-regime scale-free degree distribution, where the scaling exponents are γ1 < 2 and γ2 ≈ 3, respectively. The crossover point kcross of the degree distribution is adjusted by the growth rates of nodes and edges. The nontrivial clustering coefficient and degree assortativity coefficient are relevant to the acceleration of nodes and edges.
{"title":"The topology of an accelerated growth network","authors":"Xiao-ling Yu, Zhihao Li, Duan-ming Zhang, Fang Liang, X. Wang, Xiao Wu","doi":"10.1088/0305-4470/39/46/007","DOIUrl":"https://doi.org/10.1088/0305-4470/39/46/007","url":null,"abstract":"We present and investigate a general nonlinear growth network model which incorporates accelerated growth of nodes and edges, where the growth rates of edges and nodes are all time-dependent power-law functions. The acceleration of edges determines the proportion of the internal edges to the external edges, which play a key role influencing the structure of the network. On the other hand, the effects of the acceleration of nodes on the topology of the network are discussed in the present work. This model predicts an observable two-regime scale-free degree distribution, where the scaling exponents are γ1 < 2 and γ2 ≈ 3, respectively. The crossover point kcross of the degree distribution is adjusted by the growth rates of nodes and edges. The nontrivial clustering coefficient and degree assortativity coefficient are relevant to the acceleration of nodes and edges.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81047429","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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