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Journal of physics A: Mathematical and general最新文献

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The inverse of a singular linear transformation and some applications in constrained mechanics 奇异线性变换的逆及其在约束力学中的一些应用
Journal of physics A: Mathematical and general Pub Date : 2006-08-09 DOI: 10.1088/0305-4470/39/34/011
J. Cariñena, J. Fernández-Núñez
{"title":"The inverse of a singular linear transformation and some applications in constrained mechanics","authors":"J. Cariñena, J. Fernández-Núñez","doi":"10.1088/0305-4470/39/34/011","DOIUrl":"https://doi.org/10.1088/0305-4470/39/34/011","url":null,"abstract":"We extend the notion of the Moore–Penrose inverse of a matrix to the case of a morphism between vector bundles and a more general concept is used to develop the geometric theory of Udwadia and Kalaba's approach to constrained Lagrangian mechanics.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76962787","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}
引用次数: 3
Weyl correspondence and P-representation as operator Fredholm equations and their solutions 算子Fredholm方程的Weyl对应和p -表示及其解
Journal of physics A: Mathematical and general Pub Date : 2006-08-09 DOI: 10.1088/0305-4470/39/34/016
H. Fan, J. Klauder
{"title":"Weyl correspondence and P-representation as operator Fredholm equations and their solutions","authors":"H. Fan, J. Klauder","doi":"10.1088/0305-4470/39/34/016","DOIUrl":"https://doi.org/10.1088/0305-4470/39/34/016","url":null,"abstract":"Using the technique of integration within an ordered product of operators we construct operator Fredholm equations, which can help us to re-formulize the Weyl correspondence and P-representation. We then search for their solutions which present new formulae for deriving quantum operators' Weyl classical correspondence and P-representation. As the application, we deduce some new relations about the two-variable Hermite polynomials.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90720826","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}
引用次数: 2
Multidimensional maps of QRT type QRT类型的多维映射
Journal of physics A: Mathematical and general Pub Date : 2006-08-09 DOI: 10.1088/0305-4470/39/34/012
A. Fordy, P. Kassotakis
{"title":"Multidimensional maps of QRT type","authors":"A. Fordy, P. Kassotakis","doi":"10.1088/0305-4470/39/34/012","DOIUrl":"https://doi.org/10.1088/0305-4470/39/34/012","url":null,"abstract":"We consider a class of multidimensional maps which naturally generalize the QRT map of the plane. Our 2n-dimensional maps are volume preserving and have n rational invariants, but we do not generally have a symplectic form. However, many specializations and reductions are integrable, some of which we present. Included in these are some new four-dimensional generalizations of the McMillan map.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89608453","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}
引用次数: 12
Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei 可积系统中的单态和激发态量子相变:原子核的集体振动
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/L01
P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobeš
{"title":"Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei","authors":"P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobeš","doi":"10.1088/0305-4470/39/31/L01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/L01","url":null,"abstract":"Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90635071","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}
引用次数: 78
Wavefunction of a pair coherent state in the entangled state representation as an eigenfunction of a type of Fokker–Planck differential operator 用一类Fokker-Planck微分算子的特征函数表示纠缠态中的对相干态的波函数
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/012
H. Fan, Xu-bing Tang
{"title":"Wavefunction of a pair coherent state in the entangled state representation as an eigenfunction of a type of Fokker–Planck differential operator","authors":"H. Fan, Xu-bing Tang","doi":"10.1088/0305-4470/39/31/012","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/012","url":null,"abstract":"We find that the wavefunction of a pair coherent state (or SU(1,1) coherent state) in the entangled state representation is just the eigenfunction of a type of Fokker–Planck differential operator. The relationship between these two states is discussed.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81917432","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}
引用次数: 5
Complex positive maps and quaternionic unitary evolution 复正映射与四元数酉演化
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/005
M. Asorey, G. Scolarici
{"title":"Complex positive maps and quaternionic unitary evolution","authors":"M. Asorey, G. Scolarici","doi":"10.1088/0305-4470/39/31/005","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/005","url":null,"abstract":"The complex projection of any n-dimensional quaternionic unitary dynamics defines a one-parameter positive semigroup dynamics. We show that the converse is also true, i.e. that any one-parameter positive semigroup dynamics of complex density matrices with maximal rank can be obtained as the complex projection of suitable quaternionic unitary dynamics.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90045417","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}
引用次数: 8
Comments on the approximating Hamiltonian method for imperfect boson gas 关于不完全玻色子气体的近似哈密顿方法的评述
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/N01
Thomas Jaeck
{"title":"Comments on the approximating Hamiltonian method for imperfect boson gas","authors":"Thomas Jaeck","doi":"10.1088/0305-4470/39/31/N01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/N01","url":null,"abstract":"In the recent paper (Pulé J V and Zagrebnov V A 2004 The approximating Hamiltonian method for the imperfect boson gas J. Phys. A: Math. Gen. 45 3565–83) the pressure for the imperfect (mean field) boson gas is derived by a method based on the approximating Hamiltonian argument. We give some comments about this derivation.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86144359","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}
引用次数: 2
A new type of modulation instability of Stokes waves in the framework of an extended NSE system with mean flow 具有平均流量的扩展NSE系统框架下Stokes波的一种新型调制不稳定性
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/L03
Y. Sedletsky
{"title":"A new type of modulation instability of Stokes waves in the framework of an extended NSE system with mean flow","authors":"Y. Sedletsky","doi":"10.1088/0305-4470/39/31/L03","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/L03","url":null,"abstract":"Stokes waves on the surface of a layer of an ideal fluid are studied. The nonlinear Schrodinger equation (NSE) for the envelope of the first harmonic and the equation for zero harmonic are extended with allowance for full linear dispersion. To investigate modulational instability (MI) of Stokes waves, we derive a quartic equation for the perturbation frequency without the traditional approximation for the motion of mean current with a group speed on the frequency of fast filling. The interaction of the four roots of this equation is shown to result in the occurrence of MI bands not described by the NSE. The analysis of the obtained expressions demonstrates that the limit kh = 1.363 (where h is the fluid depth and k is the wave number) found by Benjamin and Feir (and also by Whitham and then by Hasimoto and Ono) for the transition between the states of modulationally stable and unstable liquid is valid only in the limiting case of small amplitudes of unperturbed waves and small wave numbers of the perturbation wave.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83078020","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}
引用次数: 4
Critical behaviour of continuous phase transitions with infinitely many absorbing states 具有无限多吸收态的连续相变的临界行为
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/001
D. Hua, Lie-yan Wang, Ting Chen
{"title":"Critical behaviour of continuous phase transitions with infinitely many absorbing states","authors":"D. Hua, Lie-yan Wang, Ting Chen","doi":"10.1088/0305-4470/39/31/001","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/001","url":null,"abstract":"A lattice gas model is proposed for the A2 + 2B2 → 2B2A reaction system with particle diffusion. In the model, A2 dissociates in the random dimer-filling mechanism and B2 dissociation is in the end-on dimer-filling mechanism. A reactive window appears and the system exhibits a continuous phase transition from a reactive state to a covered state with infinitely many absorbing states. When the diffusion of particle A and AB is included, there are still infinitely many absorbing states for the continuous phase transition, but it is found that the critical behaviour changes from the directed percolation (DP) class to the pair contact process with diffusion (PCPD) class.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87005460","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}
引用次数: 4
Constructive definition of functional derivatives in density-functional theory 密度泛函理论中泛函导数的构造定义
Journal of physics A: Mathematical and general Pub Date : 2006-08-04 DOI: 10.1088/0305-4470/39/31/008
Ji Luo
{"title":"Constructive definition of functional derivatives in density-functional theory","authors":"Ji Luo","doi":"10.1088/0305-4470/39/31/008","DOIUrl":"https://doi.org/10.1088/0305-4470/39/31/008","url":null,"abstract":"It is shown that the functional derivatives in density-functional theory (DFT) can be explicitly defined within the domain of electron densities restricted by the electron number, and a constructive definition of such restricted derivatives is suggested. With this definition, Kohn–Sham (KS) equations can be established for an N-electron system without extending the functional domain and introducing a Lagrange multiplier. This may clarify some of the fundamental questions raised by Nesbet (1998 Phys. Rev. A 58 R12). The definition naturally leads to the fact that the KS effective potential is determined only to within an additive constant, thus the KS levels can shift freely and the relation between the highest occupied molecular orbital (HOMO) energy and the ionization potential of the system depends on the choice of the constant. On the other hand, if the domain of functionals is indeed extended beyond the electron number restriction, conclusions depend on whether the extended functionals have unrestricted derivatives or not. It is shown that the ensemble extension of DFT to open systems of mixed states (Perdew et al 1982 Phys. Rev. Lett. 49 1691) leads to an energy functional which has no unrestricted derivative at integer electron numbers. Hence after this extension, the relation between the HOMO energy and the ionization potential for an N-electron system is still uncertain. Besides, there are different extensions of the energy functional to a domain of densities unrestricted by the integer electron number, resulting in different unrestricted derivatives and electron systems with different chemical potentials. Even for the exact exchange-correlation potential, there is still an undetermined constant, whether it is a restricted or unrestricted derivative.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/0305-4470/39/31/008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72412756","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}
引用次数: 0
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