Pub Date : 2006-10-04DOI: 10.1088/0305-4470/39/42/006
K. Górska, A. Makowski, S. Dembinski
We study the connections between some specially entangled stationary states and the classical periodic trajectories of two non-interacting oscillators. The latter are well-known Lissajous figures, which are shown to run precisely over the apogees of their corresponding probability distributions in the above states. We propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images. Finally, our results are successfully applied to the interpretation of some experimentally observed wave patterns.
{"title":"Correspondence between some wave patterns and Lissajous figures","authors":"K. Górska, A. Makowski, S. Dembinski","doi":"10.1088/0305-4470/39/42/006","DOIUrl":"https://doi.org/10.1088/0305-4470/39/42/006","url":null,"abstract":"We study the connections between some specially entangled stationary states and the classical periodic trajectories of two non-interacting oscillators. The latter are well-known Lissajous figures, which are shown to run precisely over the apogees of their corresponding probability distributions in the above states. We propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images. Finally, our results are successfully applied to the interpretation of some experimentally observed wave patterns.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77120193","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 : 2006-09-29DOI: 10.1088/0305-4470/39/39/S17
M. Shah, N. Woodhouse
We show that Okamoto's classical solutions to PVI constructed from a seed solution of Gauss' hypergeometric equation can be derived very simply from the Ward ansätze for ASDYM connections.
{"title":"Painlevé VI, hypergeometric hierarchies and Ward ansätze","authors":"M. Shah, N. Woodhouse","doi":"10.1088/0305-4470/39/39/S17","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/S17","url":null,"abstract":"We show that Okamoto's classical solutions to PVI constructed from a seed solution of Gauss' hypergeometric equation can be derived very simply from the Ward ansätze for ASDYM connections.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82408969","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 : 2006-09-29DOI: 10.1088/0305-4470/39/39/S01
C. Cosgrove
We examine two sets of second-degree Painlevé equations derived by Chazy in 1909, denoted by systems (II) and (III). The last member of each set is a second-degree version of the Painlevé-VI equation, and there are no other second-order second-degree Painlevé equations in the polynomial class with this property. We map the last member of system (II) into the Fokas–Yortsos equation and demonstrate how both Schlesinger and Okamoto transformations for Painlevé-VI can be read off the Chazy equation. The 24 fundamental Schlesinger transformations were known to Garnier in 1943 while the 64 Okamoto transformations date from 1987. In an appendix, we gather together the solutions of the five members of system (II). System (III) is better known, being equivalent to Jimbo and Miwa's equations for the logarithmic derivatives of the tau functions of the six Painlevé transcendents. The last member, known to Painlevé in 1906, was written in a manifestly symmetric form by Jimbo and Miwa, suggesting many induced symmetries for Painlevé-VI. In particular, Schlesinger and Okamoto transformations for Painlevé-VI can be read off immediately.
{"title":"Chazy's second-degree Painlevé equations","authors":"C. Cosgrove","doi":"10.1088/0305-4470/39/39/S01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/S01","url":null,"abstract":"We examine two sets of second-degree Painlevé equations derived by Chazy in 1909, denoted by systems (II) and (III). The last member of each set is a second-degree version of the Painlevé-VI equation, and there are no other second-order second-degree Painlevé equations in the polynomial class with this property. We map the last member of system (II) into the Fokas–Yortsos equation and demonstrate how both Schlesinger and Okamoto transformations for Painlevé-VI can be read off the Chazy equation. The 24 fundamental Schlesinger transformations were known to Garnier in 1943 while the 64 Okamoto transformations date from 1987. In an appendix, we gather together the solutions of the five members of system (II). System (III) is better known, being equivalent to Jimbo and Miwa's equations for the logarithmic derivatives of the tau functions of the six Painlevé transcendents. The last member, known to Painlevé in 1906, was written in a manifestly symmetric form by Jimbo and Miwa, suggesting many induced symmetries for Painlevé-VI. In particular, Schlesinger and Okamoto transformations for Painlevé-VI can be read off immediately.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78031084","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 : 2006-09-29DOI: 10.1088/0305-4470/39/39/S09
S. Shimomura
Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N = 2.
{"title":"A family of solutions of a higher order PVI equation near a regular singularity","authors":"S. Shimomura","doi":"10.1088/0305-4470/39/39/S09","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/S09","url":null,"abstract":"Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N = 2.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72679593","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 : 2006-09-29DOI: 10.1088/0305-4470/39/39/E01
P. Clarkson, N. Joshi, M. Mazzocco, F. Nijhoff, M. Noumi
For preface, please see PDF.
前言请见PDF。
{"title":"One hundred years of PVI, the Fuchs–Painlevé equation","authors":"P. Clarkson, N. Joshi, M. Mazzocco, F. Nijhoff, M. Noumi","doi":"10.1088/0305-4470/39/39/E01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/E01","url":null,"abstract":"For preface, please see PDF.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86234889","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 : 2006-09-29DOI: 10.1088/0305-4470/39/39/S08
Y. Ohyama, S. Okumura
We revise Garnier–Okamoto's coalescent diagram of isomonodromic deformations and give a possible coalescent diagram from the viewpoint of isomonodromic deformations. We have ten types of isomonodromic deformations and two of them give the same type of Painlevé equation. We can naturally put the 34th Painlevé equation in our diagram, which corresponds to the Flaschka–Newell form of the second Painlevé equation.
{"title":"A coalescent diagram of the Painlevé equations from the viewpoint of isomonodromic deformations","authors":"Y. Ohyama, S. Okumura","doi":"10.1088/0305-4470/39/39/S08","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/S08","url":null,"abstract":"We revise Garnier–Okamoto's coalescent diagram of isomonodromic deformations and give a possible coalescent diagram from the viewpoint of isomonodromic deformations. We have ten types of isomonodromic deformations and two of them give the same type of Painlevé equation. We can naturally put the 34th Painlevé equation in our diagram, which corresponds to the Flaschka–Newell form of the second Painlevé equation.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72846024","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 : 2006-09-27DOI: 10.1088/0305-4470/39/41/S02
J. Minahan
We give a brief introduction to the application of the Bethe ansatz to the study of planar super-Yang–Mills. The emphasis is on one-loop integrability in the SU(2) sector. We use the Bethe ansatz to find the anomalous dimensions for certain operators and compare these results with string theory predictions based on the AdS/CFT correspondence.
{"title":"A brief introduction to the Bethe ansatz in super-Yang–Mills","authors":"J. Minahan","doi":"10.1088/0305-4470/39/41/S02","DOIUrl":"https://doi.org/10.1088/0305-4470/39/41/S02","url":null,"abstract":"We give a brief introduction to the application of the Bethe ansatz to the study of planar super-Yang–Mills. The emphasis is on one-loop integrability in the SU(2) sector. We use the Bethe ansatz to find the anomalous dimensions for certain operators and compare these results with string theory predictions based on the AdS/CFT correspondence.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84975333","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 : 2006-09-22DOI: 10.1088/0305-4470/39/38/019
Lei Wu, Qin Yang, Jie-Fang Zhang
In this paper, the inhomogeneous damped nonlinear Schrödinger equation (NLS) which describes wave propagation in plasmas is investigated. Based on Husimi's transformation and lens-type transformation, we reduce the inhomogeneous NLS equation to the standard NLS equation and thus the bright soliton solutions on a continuous wave (cw) background are constructed and discussed. Besides, we also consider the inhomogeneous NLS equation with different damping coefficients. Based on the perturbation theory for bright solitons, the approximate bright soliton solutions for such an equation are obtained, which are in good agreements with direct numerical simulations.
{"title":"Bright solitons on a continuous wave background for the inhomogeneous nonlinear Schrödinger equation in plasma","authors":"Lei Wu, Qin Yang, Jie-Fang Zhang","doi":"10.1088/0305-4470/39/38/019","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/019","url":null,"abstract":"In this paper, the inhomogeneous damped nonlinear Schrödinger equation (NLS) which describes wave propagation in plasmas is investigated. Based on Husimi's transformation and lens-type transformation, we reduce the inhomogeneous NLS equation to the standard NLS equation and thus the bright soliton solutions on a continuous wave (cw) background are constructed and discussed. Besides, we also consider the inhomogeneous NLS equation with different damping coefficients. Based on the perturbation theory for bright solitons, the approximate bright soliton solutions for such an equation are obtained, which are in good agreements with direct numerical simulations.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75864187","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 : 2006-09-22DOI: 10.1088/0305-4470/39/38/015
K. Thylwe
A relation between a multi-state complex angular momentum (CAM) pole residue and the corresponding CAM-state wavefunction is derived for a real symmetric potential matrix. The result generalizes a residue formula available for single-channel atomical collision systems and it is based on a diagonalization of the S matrix together with the use of exact Wronskian relations.
{"title":"Multi-state complex angular momentum residues","authors":"K. Thylwe","doi":"10.1088/0305-4470/39/38/015","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/015","url":null,"abstract":"A relation between a multi-state complex angular momentum (CAM) pole residue and the corresponding CAM-state wavefunction is derived for a real symmetric potential matrix. The result generalizes a residue formula available for single-channel atomical collision systems and it is based on a diagonalization of the S matrix together with the use of exact Wronskian relations.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84482938","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 : 2006-09-22DOI: 10.1088/0305-4470/39/38/018
R. Léandre, A. Rogers
Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.
{"title":"Equivariant cohomology, Fock space and loop groups","authors":"R. Léandre, A. Rogers","doi":"10.1088/0305-4470/39/38/018","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/018","url":null,"abstract":"Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74544269","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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