Pub Date : 2006-09-19DOI: 10.1088/0305-4470/39/40/004
Y. Kubota, T. Odagaki
The transmission of a single soliton is investigated numerically across an interface between two Toda lattices, which are connected by a harmonic lattice. The soliton transmission coefficient is used as a measure of transmission. When the spring constant (κ) of the harmonic spring is small and the number of harmonic springs is greater than or equal to 2, a delay in the transmission of the soliton is found for proper κ. It is shown that the delay in the soliton transmission is due to the existence of the quasi-localization of the wave in the harmonic lattice and the agreement of the time scale of the motion between the two springs.
{"title":"Delay in a soliton transmission across an interface between two Toda lattices","authors":"Y. Kubota, T. Odagaki","doi":"10.1088/0305-4470/39/40/004","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/004","url":null,"abstract":"The transmission of a single soliton is investigated numerically across an interface between two Toda lattices, which are connected by a harmonic lattice. The soliton transmission coefficient is used as a measure of transmission. When the spring constant (κ) of the harmonic spring is small and the number of harmonic springs is greater than or equal to 2, a delay in the transmission of the soliton is found for proper κ. It is shown that the delay in the soliton transmission is due to the existence of the quasi-localization of the wave in the harmonic lattice and the agreement of the time scale of the motion between the two springs.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85502352","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 : 2006-09-19DOI: 10.1088/0305-4470/39/40/015
A. Janutka
The polarization of a multi-component vector soliton (of the Manakov type) can be thought of as a state vector of a system of qubits (a register of quantum information). A change of this state on demand via colliding the register pulse with other solitons is shown to be possible with arbitrary accuracy. The parameters (polarization, pulse width, velocity) of the register-switching solitons corresponding to the computationally universal set of quantum gates are found. Physical realizations of information processing using effects of the self-focusing of optical media or of the self-induced transparency are considered.
{"title":"Simulation of quantum logic via collisions of vector solitons","authors":"A. Janutka","doi":"10.1088/0305-4470/39/40/015","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/015","url":null,"abstract":"The polarization of a multi-component vector soliton (of the Manakov type) can be thought of as a state vector of a system of qubits (a register of quantum information). A change of this state on demand via colliding the register pulse with other solitons is shown to be possible with arbitrary accuracy. The parameters (polarization, pulse width, velocity) of the register-switching solitons corresponding to the computationally universal set of quantum gates are found. Physical realizations of information processing using effects of the self-focusing of optical media or of the self-induced transparency are considered.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74279840","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 : 2006-09-19DOI: 10.1088/0305-4470/39/40/013
E. D. Prunelé
A one-particle non-relativistic quantum mechanical solvable model in two-dimensional space is given. The Hamiltonian is the sum of kinetic and interaction parts. Interactions are separable and can be centred at n arbitrary points of the plane. Conditions for the existence and for the number of bound states in finite linear chains are formulated in terms of the parameters of the interactions and intercentre distances. Scattering problems are also considered. Finally, when the interactions are centred in a single centre, it is shown that the model remains solvable in the presence of a uniform magnetic field of arbitrary intensity.
{"title":"Solvable quantum mechanical model in two-dimensional space","authors":"E. D. Prunelé","doi":"10.1088/0305-4470/39/40/013","DOIUrl":"https://doi.org/10.1088/0305-4470/39/40/013","url":null,"abstract":"A one-particle non-relativistic quantum mechanical solvable model in two-dimensional space is given. The Hamiltonian is the sum of kinetic and interaction parts. Interactions are separable and can be centred at n arbitrary points of the plane. Conditions for the existence and for the number of bound states in finite linear chains are formulated in terms of the parameters of the interactions and intercentre distances. Scattering problems are also considered. Finally, when the interactions are centred in a single centre, it is shown that the model remains solvable in the presence of a uniform magnetic field of arbitrary intensity.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81996303","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 : 2006-09-15DOI: 10.1088/0305-4470/39/37/003
A A T Smith, I W Stewart
Theoretical work based on the Freedericksz transition in a wedge of smectic C liquid crystal is presented. Continuum theory is employed in order to mathematically model the two-way interaction between the anisotropic fluid and an applied electric field. Asymptotic methods are used to obtain concise and informative explicit solutions for limiting regimes where (a) the applied voltage is just above threshold, and (b) a high voltage is applied. As is anticipated, in the case of a small dielectric anisotropy, the solution reduces to that obtained when the two-way interaction is neglected. Nevertheless, at voltages close to threshold, this interaction can have a significant effect upon the director profile. Realistic material, geometry and field parameters are adopted in order to display these solutions. By comparing them with those obtained using a numerical method, a high degree of accuracy can be found within the above regimes.
{"title":"Asymptotic solutions for an electrically induced Freedericksz transition in a wedge of smectic C liquid crystal","authors":"A A T Smith, I W Stewart","doi":"10.1088/0305-4470/39/37/003","DOIUrl":"https://doi.org/10.1088/0305-4470/39/37/003","url":null,"abstract":"Theoretical work based on the Freedericksz transition in a wedge of smectic C liquid crystal is presented. Continuum theory is employed in order to mathematically model the two-way interaction between the anisotropic fluid and an applied electric field. Asymptotic methods are used to obtain concise and informative explicit solutions for limiting regimes where (a) the applied voltage is just above threshold, and (b) a high voltage is applied. As is anticipated, in the case of a small dielectric anisotropy, the solution reduces to that obtained when the two-way interaction is neglected. Nevertheless, at voltages close to threshold, this interaction can have a significant effect upon the director profile. Realistic material, geometry and field parameters are adopted in order to display these solutions. By comparing them with those obtained using a numerical method, a high degree of accuracy can be found within the above regimes.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89399784","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 : 2006-09-13DOI: 10.1088/0305-4470/39/39/S10
A. Ramani, Y. Ohta, B. Grammaticos
We present discrete Painlevé equations which can be obtained as contiguity relations of the solutions of the continuous Painlevé VI. The derivation is based on the geometry of the affine Weyl group D(1)4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau–Ablowitz–Fokas equation, which is a Miura transformed, ‘modified’, PVI.
{"title":"Discrete systems related to the sixth Painlevé equation","authors":"A. Ramani, Y. Ohta, B. Grammaticos","doi":"10.1088/0305-4470/39/39/S10","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/S10","url":null,"abstract":"We present discrete Painlevé equations which can be obtained as contiguity relations of the solutions of the continuous Painlevé VI. The derivation is based on the geometry of the affine Weyl group D(1)4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau–Ablowitz–Fokas equation, which is a Miura transformed, ‘modified’, PVI.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82970833","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 : 2006-09-13DOI: 10.1088/0305-4470/39/39/S12
A. Tongas, F. Nijhoff
A symmetry reduction of the lattice modified Boussinesq system is studied. The full group of Lie point symmetries of the relevant system is retrieved and certain group invariant solutions are considered by using an accessional generalized symmetry. It is demonstrated that the symmetry reduction leads to a coupled set of second-order nonlinear non-autonomous ordinary difference equations involving six free parameters, generalizing to higher order some of the known discrete analogues of the Painlevé VI equation. The corresponding isomonodromic deformation problem is constructed through the symmetry reduction as well.
{"title":"A discrete Garnier type system from symmetry reduction on the lattice","authors":"A. Tongas, F. Nijhoff","doi":"10.1088/0305-4470/39/39/S12","DOIUrl":"https://doi.org/10.1088/0305-4470/39/39/S12","url":null,"abstract":"A symmetry reduction of the lattice modified Boussinesq system is studied. The full group of Lie point symmetries of the relevant system is retrieved and certain group invariant solutions are considered by using an accessional generalized symmetry. It is demonstrated that the symmetry reduction leads to a coupled set of second-order nonlinear non-autonomous ordinary difference equations involving six free parameters, generalizing to higher order some of the known discrete analogues of the Painlevé VI equation. The corresponding isomonodromic deformation problem is constructed through the symmetry reduction as well.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75958208","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 : 2006-09-08DOI: 10.1088/0305-4470/39/36/003
M. Romero-Bastida, J F Aguilar
In this work, we numerically study the dynamical evolution and heat transport properties of a system that consists of two time-reversible thermostats connected either by a one-dimensional Fermi–Pasta–Ulam or a Frenkel–Kontorova oscillator lattice, which are representative models of momentum-conserving and nonconserving systems, respectively. The thermostats were described by a chain of variables, Nosé–Hoover chains, which enhances the ergodicity of the thermostats in comparison to the Nosé–Hoover method. The time evolution of both lattices is not significantly altered by the dynamics of the thermostats. The temperature profile and heat flux of the Fermi–Pasta–Ulam model are more sensitive to the dynamics of the extended variables than those corresponding to the Frenkel–Kontorova model. Nevertheless we reproduce the scaling properties of the thermal conductivity with system size obtained by other authors.
{"title":"Heat conduction in one-dimensional oscillator lattices using Nosé–Hoover chain thermostats","authors":"M. Romero-Bastida, J F Aguilar","doi":"10.1088/0305-4470/39/36/003","DOIUrl":"https://doi.org/10.1088/0305-4470/39/36/003","url":null,"abstract":"In this work, we numerically study the dynamical evolution and heat transport properties of a system that consists of two time-reversible thermostats connected either by a one-dimensional Fermi–Pasta–Ulam or a Frenkel–Kontorova oscillator lattice, which are representative models of momentum-conserving and nonconserving systems, respectively. The thermostats were described by a chain of variables, Nosé–Hoover chains, which enhances the ergodicity of the thermostats in comparison to the Nosé–Hoover method. The time evolution of both lattices is not significantly altered by the dynamics of the thermostats. The temperature profile and heat flux of the Fermi–Pasta–Ulam model are more sensitive to the dynamics of the extended variables than those corresponding to the Frenkel–Kontorova model. Nevertheless we reproduce the scaling properties of the thermal conductivity with system size obtained by other authors.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84666877","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 : 2006-09-08DOI: 10.1088/0305-4470/39/36/004
E J Janse van Rensburg, J. Ma
We examine partitions and their natural three-dimensional generalizations, plane partitions, as models of vesicles undergoing an inflation–deflation transition. The phase diagrams of these models include a critical point corresponding to an inflation–deflation transition, and exhibits multicritical scaling in the vicinity of a multicritical point located elsewhere on the critical curve. We determine the locations of the multicritical points by analysing the generating functions using analytic and numerical means. In addition, we determine the numerical values of the multicritical scaling exponents associated with the multicritical scaling regimes in these models.
{"title":"Plane partition vesicles","authors":"E J Janse van Rensburg, J. Ma","doi":"10.1088/0305-4470/39/36/004","DOIUrl":"https://doi.org/10.1088/0305-4470/39/36/004","url":null,"abstract":"We examine partitions and their natural three-dimensional generalizations, plane partitions, as models of vesicles undergoing an inflation–deflation transition. The phase diagrams of these models include a critical point corresponding to an inflation–deflation transition, and exhibits multicritical scaling in the vicinity of a multicritical point located elsewhere on the critical curve. We determine the locations of the multicritical points by analysing the generating functions using analytic and numerical means. In addition, we determine the numerical values of the multicritical scaling exponents associated with the multicritical scaling regimes in these models.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84679194","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 : 2006-09-05DOI: 10.1088/0305-4470/39/38/007
F. Calogero, F. Leyvraz
Hamiltonians linear in the momenta and yielding (in the classical context) trajectories isochronous in configuration space are considered. It is shown that their motions are completely periodic in phase space as well, with the same common period as the orbits in configuration space. Moreover, it is shown that for this particular class of Hamiltonians the semiclassical quantization prescription is exact, so that to the isochronous character of their classical dynamics there corresponds in the quantized context an equidistant spectrum, for a broad range of ordering prescriptions, including non-symmetrical ones. Examples illustrating these findings are presented.
{"title":"On a class of Hamiltonians with (classical) isochronous motions and (quantal) equi-spaced spectra","authors":"F. Calogero, F. Leyvraz","doi":"10.1088/0305-4470/39/38/007","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/007","url":null,"abstract":"Hamiltonians linear in the momenta and yielding (in the classical context) trajectories isochronous in configuration space are considered. It is shown that their motions are completely periodic in phase space as well, with the same common period as the orbits in configuration space. Moreover, it is shown that for this particular class of Hamiltonians the semiclassical quantization prescription is exact, so that to the isochronous character of their classical dynamics there corresponds in the quantized context an equidistant spectrum, for a broad range of ordering prescriptions, including non-symmetrical ones. Examples illustrating these findings are presented.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78935641","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 : 2006-09-05DOI: 10.1088/0305-4470/39/38/001
M. Gorzelańczyk
We find the resolvent at the Kirkwood–Salsburg integral operator in a finite volume for hard core potentials. We also construct the resolvent at the Kirkwood–Salsburg operator in the thermodynamical limit for values of chemical activity and for non-negative potentials. Therefore the phase transition does not occur for these values of chemical activity.
{"title":"Analytic properties of gas hard core spheres in a continuous system of statistical classical mechanics","authors":"M. Gorzelańczyk","doi":"10.1088/0305-4470/39/38/001","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/001","url":null,"abstract":"We find the resolvent at the Kirkwood–Salsburg integral operator in a finite volume for hard core potentials. We also construct the resolvent at the Kirkwood–Salsburg operator in the thermodynamical limit for values of chemical activity and for non-negative potentials. Therefore the phase transition does not occur for these values of chemical activity.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77130486","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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