Pub Date : 2006-09-05DOI: 10.1088/0305-4470/39/38/013
C. Jia, A. de, Souza Dutra
We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1+1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrödinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrödinger-like equation problem with the Rosen–Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.
{"title":"Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials","authors":"C. Jia, A. de, Souza Dutra","doi":"10.1088/0305-4470/39/38/013","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/013","url":null,"abstract":"We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1+1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrödinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrödinger-like equation problem with the Rosen–Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.","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":"74471503","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: 10.1088/0305-4470/39/38/014
Guqiang Li
We use the Parikh–Wilczek method to study the tunnelling radiation from the event of the black string, which is asymptotically anti-de Sitter and possesses cylindrical symmetry. We show that higher corrections to the semi-classical rate which are caused by energy conservation and angular momentum conservation exist and the emission rate has completely the same functional form as that for spherically symmetric or axisymmetric black holes.
{"title":"Black string's tunnelling radiation","authors":"Guqiang Li","doi":"10.1088/0305-4470/39/38/014","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/014","url":null,"abstract":"We use the Parikh–Wilczek method to study the tunnelling radiation from the event of the black string, which is asymptotically anti-de Sitter and possesses cylindrical symmetry. We show that higher corrections to the semi-classical rate which are caused by energy conservation and angular momentum conservation exist and the emission rate has completely the same functional form as that for spherically symmetric or axisymmetric black holes.","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":"82336850","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: 10.1088/0305-4470/39/38/003
Lali Barrière, F. Comellas, C. Dalfó
Although some real networks exhibit self-similarity, there is no standard definition of fractality in graphs. On the other hand, the small-world phenomenon is one of the most important common properties of real interconnection networks. In this paper we relate these two properties. In order to do so, we focus on the family of Sierpinski networks. For the Sierpinski gasket, the Sierpinski carpet and the Sierpinski tetra, we give the basic properties and we calculate the box-counting dimension as a measure of their fractality. We also define a deterministic family of graphs, which we call small-world Sierpinski graphs. We show that our construction preserves the structure of Sierpinski graphs, including its box-counting dimension, while the small-world phenomenon arises. Thus, in this family of graphs, fractality and small-world effect are simultaneously present.
{"title":"Fractality and the small-world effect in Sierpinski graphs","authors":"Lali Barrière, F. Comellas, C. Dalfó","doi":"10.1088/0305-4470/39/38/003","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/003","url":null,"abstract":"Although some real networks exhibit self-similarity, there is no standard definition of fractality in graphs. On the other hand, the small-world phenomenon is one of the most important common properties of real interconnection networks. In this paper we relate these two properties. In order to do so, we focus on the family of Sierpinski networks. For the Sierpinski gasket, the Sierpinski carpet and the Sierpinski tetra, we give the basic properties and we calculate the box-counting dimension as a measure of their fractality. We also define a deterministic family of graphs, which we call small-world Sierpinski graphs. We show that our construction preserves the structure of Sierpinski graphs, including its box-counting dimension, while the small-world phenomenon arises. Thus, in this family of graphs, fractality and small-world effect are simultaneously present.","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":"75834933","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: 10.1088/0305-4470/39/38/011
Chang-yong Chen, K. Gao, M. Feng
We propose an analytical treatment method of generation of multipartite W-type states with a single-resonant interaction of the atoms with the cavity mode in cavity QED, under the consideration of very weak decay from the excited atomic level and from the cavity mode. By manipulating different coupling strengths between the atoms and the cavity mode, we show how to deterministically produce W states, including the standard W state and the one with arbitrary coefficients. The corresponding analytical expressions are given, indicating that the detrimental influence from the atomic spontaneous emission is three times that from the cavity decay. The experimental feasibility of our scheme is also discussed by using current cavity QED techniques.
{"title":"Analytical treatment of W-state preparation in cavity QED in the presence of very weak dissipation","authors":"Chang-yong Chen, K. Gao, M. Feng","doi":"10.1088/0305-4470/39/38/011","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/011","url":null,"abstract":"We propose an analytical treatment method of generation of multipartite W-type states with a single-resonant interaction of the atoms with the cavity mode in cavity QED, under the consideration of very weak decay from the excited atomic level and from the cavity mode. By manipulating different coupling strengths between the atoms and the cavity mode, we show how to deterministically produce W states, including the standard W state and the one with arbitrary coefficients. The corresponding analytical expressions are given, indicating that the detrimental influence from the atomic spontaneous emission is three times that from the cavity decay. The experimental feasibility of our scheme is also discussed by using current cavity QED techniques.","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":"75466062","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: 10.1088/0305-4470/39/38/008
M. Guasti
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
{"title":"Attainable conditions and exact invariant for the time-dependent harmonic oscillator","authors":"M. Guasti","doi":"10.1088/0305-4470/39/38/008","DOIUrl":"https://doi.org/10.1088/0305-4470/39/38/008","url":null,"abstract":"The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.","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":"73758078","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 : 2006-09-01DOI: 10.1088/0305-4470/39/35/007
E. Khalil
We propose a scheme for generating a nonlinear finite-dimensional pair coherent state of the vibrational motion of an ion in a two-dimensional trap. It is a type of the correlated two-mode states but in finite dimensions. Based on the resonant ion–cavity interaction, we propose a scheme to generate these states revealing their connection with the converter type of interaction and investigate some of their nonclassical properties.
{"title":"Generation and some nonclassical properties of a nonlinear finite-dimensional pair coherent state","authors":"E. Khalil","doi":"10.1088/0305-4470/39/35/007","DOIUrl":"https://doi.org/10.1088/0305-4470/39/35/007","url":null,"abstract":"We propose a scheme for generating a nonlinear finite-dimensional pair coherent state of the vibrational motion of an ion in a two-dimensional trap. It is a type of the correlated two-mode states but in finite dimensions. Based on the resonant ion–cavity interaction, we propose a scheme to generate these states revealing their connection with the converter type of interaction and investigate some of their nonclassical properties.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78798446","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 : 2006-09-01DOI: 10.1088/0305-4470/39/35/012
O. Shrier, Joe Khachan, S. G. Bosi
A Markov chain method is presented as an alternative approach to Monte Carlo simulations of charge exchange collisions by an energetic hydrogen ion beam with a cold background hydrogen gas. This method was used to determine the average energy of the resulting energetic neutrals along the path of the beam. A comparison with Monte Carlo modelling showed a good agreement but with the advantage that it required much less computing time and produced no numerical noise. In particular, the Markov chain method works well for monotonically increasing or decreasing electrostatic potentials. Finally, a good agreement is obtained with experimental results from Doppler shift spectroscopy on energetic beams from a hollow cathode discharge. In particular, the average energy of ions that undergo charge exchange reaches a plateau that can be well below the full energy that might be expected from the applied voltage bias, depending on the background gas pressure. For example, pressures of ≈20 mTorr limit the ion energy to ≈20% of the applied voltage.
{"title":"A Markov chain approach to modelling charge exchange processes of an ion beam in monotonically increasing or decreasing potentials","authors":"O. Shrier, Joe Khachan, S. G. Bosi","doi":"10.1088/0305-4470/39/35/012","DOIUrl":"https://doi.org/10.1088/0305-4470/39/35/012","url":null,"abstract":"A Markov chain method is presented as an alternative approach to Monte Carlo simulations of charge exchange collisions by an energetic hydrogen ion beam with a cold background hydrogen gas. This method was used to determine the average energy of the resulting energetic neutrals along the path of the beam. A comparison with Monte Carlo modelling showed a good agreement but with the advantage that it required much less computing time and produced no numerical noise. In particular, the Markov chain method works well for monotonically increasing or decreasing electrostatic potentials. Finally, a good agreement is obtained with experimental results from Doppler shift spectroscopy on energetic beams from a hollow cathode discharge. In particular, the average energy of ions that undergo charge exchange reaches a plateau that can be well below the full energy that might be expected from the applied voltage bias, depending on the background gas pressure. For example, pressures of ≈20 mTorr limit the ion energy to ≈20% of the applied voltage.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81761181","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 : 2006-09-01DOI: 10.1088/0305-4470/39/35/002
Z. Bai
The Fourier spectral density of the Thue–Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Rényi) dimension and f(α) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. αq at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.
{"title":"Multifractal analysis of the spectral measure of the Thue–Morse sequence: a periodic orbit approach","authors":"Z. Bai","doi":"10.1088/0305-4470/39/35/002","DOIUrl":"https://doi.org/10.1088/0305-4470/39/35/002","url":null,"abstract":"The Fourier spectral density of the Thue–Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Rényi) dimension and f(α) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. αq at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79826794","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 : 2006-08-25DOI: 10.1088/0305-4470/39/34/L01
J. Killingbeck, A. Grosjean, G. Jolicard
Complex hypervirial perturbation theory (HVPT) is applied to the problem of a harmonic oscillator with a perturbation gx3exp(iφ), for which the traditional Rayleigh–Schodinger perturbation theory has to be supplemented by hyperasymptotics for obtaining accurate resonance energies in the negative φ region. Complex HVPT gives accurate results for positive φ and for negative φ up to about . The case of a quartic perturbed oscillator is also treated.
{"title":"Complex HVPT and hyperasymptotics","authors":"J. Killingbeck, A. Grosjean, G. Jolicard","doi":"10.1088/0305-4470/39/34/L01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/34/L01","url":null,"abstract":"Complex hypervirial perturbation theory (HVPT) is applied to the problem of a harmonic oscillator with a perturbation gx3exp(iφ), for which the traditional Rayleigh–Schodinger perturbation theory has to be supplemented by hyperasymptotics for obtaining accurate resonance energies in the negative φ region. Complex HVPT gives accurate results for positive φ and for negative φ up to about . The case of a quartic perturbed oscillator is also treated.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83536476","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 : 2006-08-25DOI: 10.1088/0305-4470/39/34/022
L. Carvalho, R M Cavalcanti, M. V. Cougo-Pinto, C. Farina
We obtain the magnetic properties of the Dirac vacuum confined between two parallel plates. The confinement is implemented by MIT boundary conditions on the Dirac field and the properties are described by corrections to the Euler–Heisenberg effective Lagrangian. When the plates are separated by a distance in the range from nanometres to micrometres the new term associates with the vacuum a magnetic susceptibility of the same order of that of hydrogen or nitrogen at room temperature and atmospheric pressure.
{"title":"Magnetic permeability of the Dirac vacuum under confining boundary conditions","authors":"L. Carvalho, R M Cavalcanti, M. V. Cougo-Pinto, C. Farina","doi":"10.1088/0305-4470/39/34/022","DOIUrl":"https://doi.org/10.1088/0305-4470/39/34/022","url":null,"abstract":"We obtain the magnetic properties of the Dirac vacuum confined between two parallel plates. The confinement is implemented by MIT boundary conditions on the Dirac field and the properties are described by corrections to the Euler–Heisenberg effective Lagrangian. When the plates are separated by a distance in the range from nanometres to micrometres the new term associates with the vacuum a magnetic susceptibility of the same order of that of hydrogen or nitrogen at room temperature and atmospheric pressure.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79659510","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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