Pub Date : 2006-11-30DOI: 10.1088/0305-4470/39/50/009
A. Frolov
The new approach to the analysis of four-body systems and computation of various four-body integrals is proposed. The approach is based on the use of six perimetric coordinates which can be introduced for an arbitrary four-body system. The proper (i.e. non-conflicting) definition of the four-body perimetric coordinates is given for an arbitrary four-body system. It is shown that these six internal perimetric coordinates describe all possible configurations in an arbitrary four-body system and can be used to simplify computations of many four-body integrals written in the relative coordinates r12, r13, r23, r14, r24 and r34. In addition to this, a number of new, very effective procedures for variational computation of different four-body systems can now be developed.
{"title":"Four-body perimetric coordinates","authors":"A. Frolov","doi":"10.1088/0305-4470/39/50/009","DOIUrl":"https://doi.org/10.1088/0305-4470/39/50/009","url":null,"abstract":"The new approach to the analysis of four-body systems and computation of various four-body integrals is proposed. The approach is based on the use of six perimetric coordinates which can be introduced for an arbitrary four-body system. The proper (i.e. non-conflicting) definition of the four-body perimetric coordinates is given for an arbitrary four-body system. It is shown that these six internal perimetric coordinates describe all possible configurations in an arbitrary four-body system and can be used to simplify computations of many four-body integrals written in the relative coordinates r12, r13, r23, r14, r24 and r34. In addition to this, a number of new, very effective procedures for variational computation of different four-body systems can now be developed.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89268482","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 : 2006-11-24DOI: 10.1088/0305-4470/39/47/003
P. Oprocha
It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J Smítal (1994 Trans. Am. Math. Soc. 344 737–54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models.
{"title":"A quantum harmonic oscillator and strong chaos","authors":"P. Oprocha","doi":"10.1088/0305-4470/39/47/003","DOIUrl":"https://doi.org/10.1088/0305-4470/39/47/003","url":null,"abstract":"It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J Smítal (1994 Trans. Am. Math. Soc. 344 737–54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77178686","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 : 2006-11-24DOI: 10.1088/0305-4470/39/47/006
E. Moskovchenko, V. Kotlyarov
The Riemann–Hilbert problem proposed in [2] for the integrable stimulated Raman scattering (SRS) model was shown to be solvable under an additional condition: the boundary data have to be chosen in such a way that a corresponding spectral problem has no spectral singularities. In the general case, it can be shown that a spectral singularity occurs at k = 0. On the other hand, the initial boundary value (IBV) problem for the SRS equations is known to be well posed: using PDE techniques, this has been established in [3]. Therefore, it seems natural to try to find a new RH problem that is solvable in the presence of arbitrary spectral singularities. The formulation of such a RH problem is the main aim of the paper. Then the solution of the nonlinear initial boundary value problem for the SRS equations is expressed in terms of the solution of a linear problem which is the Riemann–Hilbert problem for a sectionally analytic matrix function.
{"title":"A new Riemann–Hilbert problem in a model of stimulated Raman Scattering","authors":"E. Moskovchenko, V. Kotlyarov","doi":"10.1088/0305-4470/39/47/006","DOIUrl":"https://doi.org/10.1088/0305-4470/39/47/006","url":null,"abstract":"The Riemann–Hilbert problem proposed in [2] for the integrable stimulated Raman scattering (SRS) model was shown to be solvable under an additional condition: the boundary data have to be chosen in such a way that a corresponding spectral problem has no spectral singularities. In the general case, it can be shown that a spectral singularity occurs at k = 0. On the other hand, the initial boundary value (IBV) problem for the SRS equations is known to be well posed: using PDE techniques, this has been established in [3]. Therefore, it seems natural to try to find a new RH problem that is solvable in the presence of arbitrary spectral singularities. The formulation of such a RH problem is the main aim of the paper. Then the solution of the nonlinear initial boundary value problem for the SRS equations is expressed in terms of the solution of a linear problem which is the Riemann–Hilbert problem for a sectionally analytic matrix function.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/0305-4470/39/47/006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72451189","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 : 2006-11-21DOI: 10.1088/0305-4470/39/49/008
G. Furman
Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. An extremely important role of the non-diagonal part of zeroth-order coherence in the construction of the pseudopure state has been shown. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4-nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule) and a double ring (cyclopentane molecule)) open the way to experimental NMR testing of the obtained results. The proposed method could be considered as a fruitful technology for quantum computation.
{"title":"The pseudopure state in homonuclear dipolar coupling spin systems","authors":"G. Furman","doi":"10.1088/0305-4470/39/49/008","DOIUrl":"https://doi.org/10.1088/0305-4470/39/49/008","url":null,"abstract":"Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. An extremely important role of the non-diagonal part of zeroth-order coherence in the construction of the pseudopure state has been shown. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4-nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule) and a double ring (cyclopentane molecule)) open the way to experimental NMR testing of the obtained results. The proposed method could be considered as a fruitful technology for quantum computation.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75775168","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 : 2006-11-21DOI: 10.1088/0305-4470/39/49/014
H. Tan
Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the transition amplitude defined between two coherent states of mean position coordinates. In our approach, we invoke solely a representation of the noncommutative algebra in terms of commutative variables. The kernel expression for a general Hamiltonian was found to contain Gaussian-like damping terms, and it is non-perturbative in the sense that it does not reduce to the commutative theory in the limit of vanishing θ—the noncommutative parameter. As an example, we studied the free particle's propagator which turned out to be oscillating with period being the product of its mass and θ. Further, it satisfies the Pauli equation for a charged particle with its spin aligned to a constant, orthogonal B field in the ordinary Landau problem, thus providing an interesting evidence of how noncommutativity can induce spin-like effects at the quantum mechanical level.
{"title":"A coherent-state-based path integral for quantum mechanics on the Moyal plane","authors":"H. Tan","doi":"10.1088/0305-4470/39/49/014","DOIUrl":"https://doi.org/10.1088/0305-4470/39/49/014","url":null,"abstract":"Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the transition amplitude defined between two coherent states of mean position coordinates. In our approach, we invoke solely a representation of the noncommutative algebra in terms of commutative variables. The kernel expression for a general Hamiltonian was found to contain Gaussian-like damping terms, and it is non-perturbative in the sense that it does not reduce to the commutative theory in the limit of vanishing θ—the noncommutative parameter. As an example, we studied the free particle's propagator which turned out to be oscillating with period being the product of its mass and θ. Further, it satisfies the Pauli equation for a charged particle with its spin aligned to a constant, orthogonal B field in the ordinary Landau problem, thus providing an interesting evidence of how noncommutativity can induce spin-like effects at the quantum mechanical level.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87929244","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 : 2006-11-21DOI: 10.1088/0305-4470/39/49/001
Haiming Deng, Wenhua Hai, Qianquan Zhu
Based on the idea of balance between the internal and external potentials, it is shown that for a two-component Bose–Einstein condensate (BEC) confined in an optical lattice the presence of a spacetime periodic laser field can induce a family of exact Floquet states (EFSs). The atomic-number densities of the EFSs are illustrated and the atomic current, phase blowing-up and the quantum reflection are investigated. The balance conditions and blowing-up region on parameter space are found, and the influences of phase blowing-up to the velocity fields, flow densities are revealed. It is demonstrated that the BEC motions can be controlled by adjusting the laser frequency, wave vector and amplitude.
{"title":"Exact Floquet states of a two-component Bose–Einstein condensate induced by a laser standing wave","authors":"Haiming Deng, Wenhua Hai, Qianquan Zhu","doi":"10.1088/0305-4470/39/49/001","DOIUrl":"https://doi.org/10.1088/0305-4470/39/49/001","url":null,"abstract":"Based on the idea of balance between the internal and external potentials, it is shown that for a two-component Bose–Einstein condensate (BEC) confined in an optical lattice the presence of a spacetime periodic laser field can induce a family of exact Floquet states (EFSs). The atomic-number densities of the EFSs are illustrated and the atomic current, phase blowing-up and the quantum reflection are investigated. The balance conditions and blowing-up region on parameter space are found, and the influences of phase blowing-up to the velocity fields, flow densities are revealed. It is demonstrated that the BEC motions can be controlled by adjusting the laser frequency, wave vector and amplitude.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89071320","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 : 2006-11-17DOI: 10.1088/0305-4470/39/46/010
N. Baddour
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging.
{"title":"Fourier diffraction theorem for diffusion-based thermal tomography","authors":"N. Baddour","doi":"10.1088/0305-4470/39/46/010","DOIUrl":"https://doi.org/10.1088/0305-4470/39/46/010","url":null,"abstract":"There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84121637","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 : 2006-11-17DOI: 10.1088/0305-4470/39/46/018
A. Wonderen, K. Lendi
Starting from a prescribed Hamiltonian, we construct a non-Markovian evolution equation for a non-relativistic quantum system that exchanges energy with a large reservoir. In order to create sufficient mathematical freedom, the density operator is replaced by a more flexible entity that depends on two times. If these times are chosen equal, the density operator is recovered. In deriving a non-Markovian integral equation for our bitemporal operator, it is assumed that initially system and reservoir are completely uncorrelated. Furthermore, in employing Wick's theorem for factorization of reservoir correlation functions, only those Wick contractions between reservoir potentials are retained that belong to a generalized nearest-neighbour class. The latter is established by subjecting the set of plain nearest-neighbour contractions to any cyclic permutation of reservoir potentials. Through generalizing the notion of nearest-neighbour contraction, it is ensured that the trace of the density operator is conserved. By construction, our bitemporal evolution equation agrees with the Kraus map for quantum dissipation. Moreover, a sound Markovian limit exists that reproduces the complete van Hove–Davies theory. By making use of a rotating-wave approximation and Laplace transformation, the density operator of a damped N-level atom can be computed. For large times and moderate coupling to the reservoir, the atom ends up near the state of thermal equilibrium. At zero temperature, our non-Markovian integral equation gives an exact solution for the atomic density operator.
{"title":"Ab initio construction of an analytically tractable Kraus map for non-Markovian quantum dissipation","authors":"A. Wonderen, K. Lendi","doi":"10.1088/0305-4470/39/46/018","DOIUrl":"https://doi.org/10.1088/0305-4470/39/46/018","url":null,"abstract":"Starting from a prescribed Hamiltonian, we construct a non-Markovian evolution equation for a non-relativistic quantum system that exchanges energy with a large reservoir. In order to create sufficient mathematical freedom, the density operator is replaced by a more flexible entity that depends on two times. If these times are chosen equal, the density operator is recovered. In deriving a non-Markovian integral equation for our bitemporal operator, it is assumed that initially system and reservoir are completely uncorrelated. Furthermore, in employing Wick's theorem for factorization of reservoir correlation functions, only those Wick contractions between reservoir potentials are retained that belong to a generalized nearest-neighbour class. The latter is established by subjecting the set of plain nearest-neighbour contractions to any cyclic permutation of reservoir potentials. Through generalizing the notion of nearest-neighbour contraction, it is ensured that the trace of the density operator is conserved. By construction, our bitemporal evolution equation agrees with the Kraus map for quantum dissipation. Moreover, a sound Markovian limit exists that reproduces the complete van Hove–Davies theory. By making use of a rotating-wave approximation and Laplace transformation, the density operator of a damped N-level atom can be computed. For large times and moderate coupling to the reservoir, the atom ends up near the state of thermal equilibrium. At zero temperature, our non-Markovian integral equation gives an exact solution for the atomic density operator.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89015641","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 : 2006-11-17DOI: 10.1088/0305-4470/39/46/L01
M. Andrecut, S A Kauffman
We present a simple method for ‘reverse engineering’ causal networks, based on mutual information, as a correlation measure. The goal of our method is not to recover all the causal interactions in a network but rather to recover some causal interactions with a very high confidence. For this purpose, we derive an ‘exact’ theoretical result for the statistical significance of mutual information. Also, we give some numerical simulation results, obtained for random Boolean networks, as an idealized model of genetic regulatory networks.
{"title":"A simple method for reverse engineering causal networks","authors":"M. Andrecut, S A Kauffman","doi":"10.1088/0305-4470/39/46/L01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/46/L01","url":null,"abstract":"We present a simple method for ‘reverse engineering’ causal networks, based on mutual information, as a correlation measure. The goal of our method is not to recover all the causal interactions in a network but rather to recover some causal interactions with a very high confidence. For this purpose, we derive an ‘exact’ theoretical result for the statistical significance of mutual information. Also, we give some numerical simulation results, obtained for random Boolean networks, as an idealized model of genetic regulatory networks.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80806889","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 : 2006-11-17DOI: 10.1088/0305-4470/39/46/016
A B Klimov, C. Muñoz, J. L. Romero
We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.
{"title":"Geometrical approach to the discrete Wigner function in prime power dimensions","authors":"A B Klimov, C. Muñoz, J. L. Romero","doi":"10.1088/0305-4470/39/46/016","DOIUrl":"https://doi.org/10.1088/0305-4470/39/46/016","url":null,"abstract":"We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/0305-4470/39/46/016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72402660","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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