Journal of physics A: Mathematical and general最新文献

{"title":"Special issue on Symmetries and Integrability of Difference Equations","authors":"A. Doliwa, R. Korhonen, S. Lafortune","doi":"10.1088/0305-4470/39/42/E01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/42/E01","url":null,"abstract":"This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations, just as differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as: mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete (difference) geometry, etc. Consequently, the aim of the special issue is to benefit from the occasion offered by the SIDE VII meeting to provide a collection of papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. Scope of the special issue The special issue will feature papers which deal with themes that were covered by the SIDE VII Conference. These are •Integrability testing •Discrete geometry and visualization •Laurent phenomena and cluster algebras •Ultra-discrete systems •Random matrix theory •Algebraic-geometric approaches to integrability •Yang–Baxter equations •Quantum and classical integrable systems •Difference Galois theory Editorial policy •The subject of the paper should relate to the subject of the meeting. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic ","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86399408","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}

{"title":"Vector beams as the superposition of cylindrical partial waves in bianisotropic media","authors":"A. Novitsky, L. Barkovsky","doi":"10.1088/0305-4470/39/42/010","DOIUrl":"https://doi.org/10.1088/0305-4470/39/42/010","url":null,"abstract":"The exact solutions for arbitrary electromagnetic beams in bianisotropic media are constructed. The solutions are expressed using tensor Fourier transform whose physical meaning is the superposition of partial waves. We use cylindrical partial waves (vector Bessel beams) and derive exact and paraxial solutions for cylindrically symmetric beams in isotropic, bi-isotropic and bianisotropic media. The comparison of the spatial evolution of vector Bessel–Gauss beams in different media is made.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75964647","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}

{"title":"Coupling, degeneracy breaking and isolation of Weibel modes in relativistic plasmas: I. General theory","authors":"R. Tautz, I. Lerche, R. Schlickeiser, U. Schaefer-Rolffs","doi":"10.1088/0305-4470/39/44/015","DOIUrl":"https://doi.org/10.1088/0305-4470/39/44/015","url":null,"abstract":"A general proof is given that for an asymmetric 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. Starting from the linearized relativistic Vlasov equation it is shown that, unless the asymmetry in the distribution function is precisely zero, the broad ranges of unstable wavenumbers occurring for symmetric distribution functions are reduced to discrete, isolated wavenumbers for which unstable modes can exist. For asymmetric plasmas, electrostatic and electromagnetic wave modes are coupled to each other and the degeneracy of the two electromagnetic wave modes (that holds for symmetric distributions) is therefore broken.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82512855","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}

{"title":"Recent advances in low-dimensional quantum field theories","authors":"P. Dorey, G. Dunne, J. Feinberg","doi":"10.1088/0305-4470/39/41/E01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/41/E01","url":null,"abstract":"Quantum field theory (QFT) is a rich and robust part of mathematical and theoretical physics, with a wide range of applications in statistical physics, condensed matter physics, particle physics and string theory. Many (if not most) of the applications in four space-time dimensions require some sort of systematic approximations. In contrast, quantum field theories in lower dimensions often display special properties which open the door, at least in principle, to their exact solution. In many cases, the methods used to obtain exact solutions are peculiar to low-dimensional space-times, but the exact solutions thus obtained can teach us a great deal about more realistic QFTs in higher dimensions. Thus, lower-dimensional QFTs provide excellent models for exploring deep theoretical and computational issues, in addition to their direct applications to physical processes in reduced dimensions, which include polymers, boundary fluctuations, spin chains, and quantum Hall systems. Such models are also vital testing grounds for fundamental theoretical ideas such as integrability, phase transitions, collective and non-perturbative quantum behaviour, and non-equilibrium statistical mechanics. We should also mention the effective dimensional reduction which occurs in the high temperature limit, or is induced by disorder. Low-dimensional quantum field theory thus sits at a unique intersection point of contemporary mathematics and physics, allowing many of these issues to be addressed rigorously and analytically. Surprising inter-relations continue to arise, from the ubiquitous nature of the Bethe ansatz and Calogero models, to the link between integrable spin chains and the anomalous dimensions of operators in gauge theories. Aspects of the latter connection have been known at least since the 1990s; they have recently received tremendous attention in connection with N=4 supersymmetric Yang--Mills theory (in four space-time dimensions) and the AdS/CFT correspondence. One unifying idea is the Bethe ansatz, whose 75th anniversary we celebrate this year, and whose wide-ranging impact in diverse branches of modern mathematical physics is made abundantly clear in this special issue. In addition, new ideas and techniques of significance to both mathematics and physics have emerged: the recent and spectacular progress on geometrical aspects of phase transitions made possible through the ideas of stochastic (Schramm) Loewner evolution, or SLE, is a particularly noteworthy example. All papers in this special issue are invited, refereed contributions from leading experts. Many are pedagogical reviews, capturing the current state of knowledge in a particular subject, putting the subject in context and outlining open challenges. Others are research papers, reflecting the rapid flux of new ideas and results in this rich and exciting field. Together, they represent a broad sample of the entire field. We would like to take this opportunity to thank all of the authors for thei","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78133319","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}

{"title":"Quantum control by decomposition of SU(1, 1)","authors":"Jianwu Wu, Chunwen Li, R. Wu, T. Tarn, Jing Zhang","doi":"10.1088/0305-4470/39/43/010","DOIUrl":"https://doi.org/10.1088/0305-4470/39/43/010","url":null,"abstract":"Constructive algorithms are presented for controlling quantum systems evolving on the SU(1, 1) Lie group. These procedures are performed via structured decomposition of SU(1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU(1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75285558","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}

{"title":"Path-integral quantization of the electromagnetic field in the Hopfield dielectric beyond dipole approximation","authors":"A. Bechler","doi":"10.1088/0305-4470/39/43/011","DOIUrl":"https://doi.org/10.1088/0305-4470/39/43/011","url":null,"abstract":"The paper contains an application of the path-integration method to the quantization of the electromagnetic field in a linear material medium modelled as the Hopfield dielectric. Except for the frequency dispersion of the medium, non-dipole effects are included leading to the wave vector dependence of the dielectric function. Starting from a local microscopic Lagrangian, the elimination of the matter degrees of freedom leads to the effective action describing dynamics of the classical field in the medium, from which the classical constitutive relation, non-local, both in time and space variables, could be determined. Full quantization of the model is achieved by integration over all fields with source terms included into the Lagrangian, and taking into account the constraint and gauge fixing term, characteristic for a quantized gauge theory. This gives the generating functional from which quantum propagators could be constructed. Operators of effective quantum electromagnetic and polarization fields were further retrieved from the propagators. The quantum constitutive equation containing the absorption noise term was also determined. The canonical equal time commutation rules are examined using both the BJL-limiting procedure and using explicit expressions for the field operators—the results in both cases are the same.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74073035","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}

{"title":"Schwinger representation approach to the Lipkin model","authors":"M. Yamamura, C. Providência, J. da Providência, S. Nishiyama, F. Cordeiro, Y. Tsue","doi":"10.1088/0305-4470/39/40/012","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/012","url":null,"abstract":"The Schwinger representation and the Marumori–Yamamura–Tokunaga boson expansion are used to describe the Lipkin model in terms of generalized coherent states. The groundstate, first excited state and RPA energies are obtained within several variant types of coherent states. It has been found that generalized coherent states defined in consonance with the parity symmetry of the model describe particularly well the transition from weak to strong coupling, providing a remarkable improvement of the mean-field description of the transition zone.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73124757","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}

{"title":"Important developments in Journal of Physics A: Mathematical and General","authors":"C. Bender, Neil Scriven","doi":"10.1088/0305-4470/39/40/E01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/E01","url":null,"abstract":"There will be two important changes in the structure of this journal. From the first issue in January 2007 the name of the journal will be Journal of Physics A: Mathematical and Theoretical. Also, there will be a new section entitled `Fast Track Communications: Short Innovative Papers'. Letters to the Editor will no longer be published in the journal. Change of journal name. The new name, Journal of Physics A: Mathematical and Theoretical, is an accurate description of the content, nature and spirit of the journal as described in the scope statement on the inside front cover: `A major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.' The word `General' is no longer appropriate for the scope of this journal. This name change will have no effect on the subject material of the papers the journal publishes. Fast Track Communications: Short Innovative Papers. Beginning with issue 1 of the 2007 volume, the journal will publish a new article type, Fast Track Communications. Fast Track Communications (FTCs) are defined as outstanding short papers reporting new and timely developments in mathematical and theoretical physics. These high-quality articles will be of importance to readers of Journal of Physics A: Mathematical and Theoretical but are not expected to meet any criterion of `general interest'. Conjectural articles are welcomed. FTCs will be processed quickly and are available free to readers in the electronic journal. To facilitate a fast review process we urge authors of FTCs to restrict the length of their article to eight journal pages (5000 words). The key criteria for acceptance will be quality, novelty and timeliness. FTCs will be published at the front of the journal and will be free to readers through IOPSelect. Submissions are welcomed from 1 October 2006. For details of how to submit an FTC please visit the journal homepage, www.iop.org/journals/jphysa. For further information please contact the journal at jphysa@iop.org.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85346540","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}

{"title":"Algebraic structure of a generalized coupled dispersionless system","authors":"K. K. Victor, B. Thomas, T. Kofané","doi":"10.1088/0305-4470/39/40/005","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/005","url":null,"abstract":"We study a physical model of the O(3)-invariant coupled integrable dispersionless equations that describes the dynamic of a focused system within the background of a plane gravitational field. The investigation is carried out both numerically and analytically, and realized beneath some assumptions superseding the structure constant with the structure function implemented in Lie algebra and quasigroup theory, respectively. The energy density and topological structures such as loop soliton are examined.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86872221","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}

{"title":"Nonlinear Fokker–Planck–Landau integral propagator (II): transport far from equilibrium","authors":"J M Donoso, J J Salgado","doi":"10.1088/0305-4470/39/40/021","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/021","url":null,"abstract":"We present a time evolving path-integral method for solving the Landau–Fokker–Planck equation to compute kinetic transport coefficients in a fully ionized plasma. The electron distribution function is advanced in time by means of the conservative short-time propagators, which we previously obtained. The validated integral operator takes into account both electron–electron and electron–ion collisions without linearizing the original Fokker–Planck collisional operator. The resulting integral formulation in velocity space is applied here to evaluate the local transport coefficients if inhomogeneities in configuration space appear. We define an effective source term through a flux particle balance in a thin slab of plasma, which leads to a nonhomogeneous Fokker–Planck equation. Hence, this new term locally models the so-called Vlasov term appearing in the general kinetic equation. Arbitrary departures from Maxwellian equilibrium can be dealt with this effective source term that preserves the positiveness of the electron distribution function, even in the runaway limit. For small perturbations of the equilibrium, the classical Spitzer and Harm transport coefficients are recovered, while a very strong reduction of the heat flux takes place for large temperature gradients, as predicted by some authors in different theories.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83512194","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}