The classical and quanta! dynamics of non-hydrogenic Rydberg atoms in magnetic fields are investigated. Previous attempts to infer classical behaviour from quantum properties produced conflicting results: at low scaled energies (c:= -0.5) the nearest-neighbour statistics (NNS) were found to be at the chaotic (Wigner) limit while quantum phase-space distribu tions suggested a high degree of regularity. Here the classical limit is investigated directly by solving the equations of motion of the Diamagnetic Kepler problem (DKP) with an additional non-Coulombic model potential. It is found that typically trajectories are, over a long time-scale, ergodic. However over a shorter time-scale-in between collisions with the core-classical trajectories remain confined on the tori of the DKP. The origin of a well-known resonance in the NNS of hydrogen at c:= -0.316 is clarified by the comparison with the non-hydrogenic behaviour. However, the classical model only partially explains the quantum behaviour. The difficulties of quantizing such a system are discussed.
{"title":"Non-Hydrogenic Rydberg Atoms in Magnetic Fields","authors":"P. Dando, T. S. Monteiro, W. Jans, W. Schweizer","doi":"10.1143/PTPS.116.403","DOIUrl":"https://doi.org/10.1143/PTPS.116.403","url":null,"abstract":"The classical and quanta! dynamics of non-hydrogenic Rydberg atoms in magnetic fields are investigated. Previous attempts to infer classical behaviour from quantum properties produced conflicting results: at low scaled energies (c:= -0.5) the nearest-neighbour statistics (NNS) were found to be at the chaotic (Wigner) limit while quantum phase-space distribu tions suggested a high degree of regularity. Here the classical limit is investigated directly by solving the equations of motion of the Diamagnetic Kepler problem (DKP) with an additional non-Coulombic model potential. It is found that typically trajectories are, over a long time-scale, ergodic. However over a shorter time-scale-in between collisions with the core-classical trajectories remain confined on the tori of the DKP. The origin of a well-known resonance in the NNS of hydrogen at c:= -0.316 is clarified by the comparison with the non-hydrogenic behaviour. However, the classical model only partially explains the quantum behaviour. The difficulties of quantizing such a system are discussed.","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"116 1","pages":"403-416"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64726724","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}
We present microscopic calculations of the Interacting Boson Model (IBM) based on the shell model interaction by using the OAI mapping approach. We determine the col lective pairs, which correspond to the IBM bosons, by the number conserved Hartree-Fock Bogoluibov (HFB) and the proton-neutron Tamm-Dancoff methods, and we take into consid eration couplings to the non-collective degrees of freedom. The present realistic calculations are carried out for the Te, Xe and Ba isotopes. Among them, the Xe isotopes are known by numerous phenomenological works to show the 0(6) symmetry. We present the clear 0(6) symmetry in the spectra and the wave function which are microscopically obtained. Low-lying spectra of medium and medium-heavy nuclei show simple and regular structures, although these nuclei consist of many interacting protons and neutrons and their dynamics is intrinsically very complicate. This is known to be the collec tive motion. Especially, in the case of even-even nuclei, there are quite simpler and common features in energy levels and electro-magnetic transitions. The understand ing of them has been one of the main problems in nuclear structure. Many theories have been advocated, developed and extended. Among them, the Interacting Boson Model (IBM), l)- 6 ) which was first introduced by Arima and Iachello in the 1970's, has shown to be rather successful. In the IBM, nucleon collective pairs are approximated in terms of bosons. This notion can simplify the treatment of the nucleon many-body system. Furthermore this ansatz facilitates the group theoretical treatment. Originally s and d bosons, which are counterparts of S(J = 0) and D(J = 2) nucleon pairs, are introduced as the building blocks of the IBM. Because these bosons do not distinguish the proton and neutron degrees of freedom, the nucleon pair counterparts of these bosons are ambiguous. But, the s and d bosons span a U(6) space and its group chains containing the 0(3) subgroup correspond physically to vibrational, rotational and '"'( unstable nuclei as limiting cases. These group chains are U(5), SU(3) and 0(6) limits. Unlike to other collective models, the IBM can give us a clear description of the 0(6) nuclei besides the U(5) and SU(3) nuclei. There are many nuclei, the spectra of which show the pattern of these group theoretical limits. Furthermore the intermediate situations between three limits are easily tractable by diagonalization of the Hamiltonian because the dimension of the original IBM space is at most about one hundred. At this stage, many phenomenological works were carried out, which showed that the low-lying states of many even-even nuclei can be explained by using six parameters of the IBM in a unified way. These parameters are considered to
{"title":"Microscopic Calculations for O(6) Nuclei by the Interacting Boson Model","authors":"T. Mizusaki, T. Otsuka","doi":"10.1143/PTPS.125.97","DOIUrl":"https://doi.org/10.1143/PTPS.125.97","url":null,"abstract":"We present microscopic calculations of the Interacting Boson Model (IBM) based on the shell model interaction by using the OAI mapping approach. We determine the col lective pairs, which correspond to the IBM bosons, by the number conserved Hartree-Fock Bogoluibov (HFB) and the proton-neutron Tamm-Dancoff methods, and we take into consid eration couplings to the non-collective degrees of freedom. The present realistic calculations are carried out for the Te, Xe and Ba isotopes. Among them, the Xe isotopes are known by numerous phenomenological works to show the 0(6) symmetry. We present the clear 0(6) symmetry in the spectra and the wave function which are microscopically obtained. Low-lying spectra of medium and medium-heavy nuclei show simple and regular structures, although these nuclei consist of many interacting protons and neutrons and their dynamics is intrinsically very complicate. This is known to be the collec tive motion. Especially, in the case of even-even nuclei, there are quite simpler and common features in energy levels and electro-magnetic transitions. The understand ing of them has been one of the main problems in nuclear structure. Many theories have been advocated, developed and extended. Among them, the Interacting Boson Model (IBM), l)- 6 ) which was first introduced by Arima and Iachello in the 1970's, has shown to be rather successful. In the IBM, nucleon collective pairs are approximated in terms of bosons. This notion can simplify the treatment of the nucleon many-body system. Furthermore this ansatz facilitates the group theoretical treatment. Originally s and d bosons, which are counterparts of S(J = 0) and D(J = 2) nucleon pairs, are introduced as the building blocks of the IBM. Because these bosons do not distinguish the proton and neutron degrees of freedom, the nucleon pair counterparts of these bosons are ambiguous. But, the s and d bosons span a U(6) space and its group chains containing the 0(3) subgroup correspond physically to vibrational, rotational and '\"'( unstable nuclei as limiting cases. These group chains are U(5), SU(3) and 0(6) limits. Unlike to other collective models, the IBM can give us a clear description of the 0(6) nuclei besides the U(5) and SU(3) nuclei. There are many nuclei, the spectra of which show the pattern of these group theoretical limits. Furthermore the intermediate situations between three limits are easily tractable by diagonalization of the Hamiltonian because the dimension of the original IBM space is at most about one hundred. At this stage, many phenomenological works were carried out, which showed that the low-lying states of many even-even nuclei can be explained by using six parameters of the IBM in a unified way. These parameters are considered to","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"125 1","pages":"97-150"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTPS.125.97","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64739256","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":"Non-Gaussian Parameter and Heterogeneity of Amorphous Polymers","authors":"T. Kanaya, I. Tsukushi, K. Kaji","doi":"10.1143/PTPS.126.133","DOIUrl":"https://doi.org/10.1143/PTPS.126.133","url":null,"abstract":"","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"126 1","pages":"133-140"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64739879","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":"Aging in Glasses: Traps and Mode-Coupling Theory","authors":"J. Bouchaud, M. Mézard","doi":"10.1143/PTPS.126.181","DOIUrl":"https://doi.org/10.1143/PTPS.126.181","url":null,"abstract":"","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"126 1","pages":"181-184"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64740265","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":"Models of Molecular Cooperativity in Liquids near the Glass Transition","authors":"J. Jäckle","doi":"10.1143/PTPS.126.53","DOIUrl":"https://doi.org/10.1143/PTPS.126.53","url":null,"abstract":"","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"126 1","pages":"53-60"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64743348","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}
The nature of Bi in molten Bi-Biia mixtures and In in molten In-Inia mixtures is surveyed on the basis of static properties and macroscopic transport coefficient (phase diagram and d.c. conductivity). It is shown that information at the microscopic level due to techniques of pulsed neutron scattering, Raman scattering and NMR can account for their nature. From pulsed neutron scattering data preferred Bi-Bi pair-correlation or polybismuth species is proposed for Bi..It-z melts even at the I-rich side below about 40 at% Bi. The localized electronic states around the Fermi level may be established and conduction takes place via hopping of electrons from one trapping site to another for these solutions. The strong concentrationdependence of the first peak distance, which is related to preferred Bi-Bi distance and observed over the range of 0.4
{"title":"On the Nature of Bi in Molten Bi-BiI3 Mixtures and In in Molten In-InI3 Mixtures","authors":"K. Ichikawa","doi":"10.1143/PTPS.72.156","DOIUrl":"https://doi.org/10.1143/PTPS.72.156","url":null,"abstract":"The nature of Bi in molten Bi-Biia mixtures and In in molten In-Inia mixtures is surveyed on the basis of static properties and macroscopic transport coefficient (phase diagram and d.c. conductivity). It is shown that information at the microscopic level due to techniques of pulsed neutron scattering, Raman scattering and NMR can account for their nature. From pulsed neutron scattering data preferred Bi-Bi pair-correlation or polybismuth species is proposed for Bi..It-z melts even at the I-rich side below about 40 at% Bi. The localized electronic states around the Fermi level may be established and conduction takes place via hopping of electrons from one trapping site to another for these solutions. The strong concentrationdependence of the first peak distance, which is related to preferred Bi-Bi distance and observed over the range of 0.4<x<0.6, means substantial change of the structural and bonding pattern in polybismuth clusters. Since delocalization of valence electrons concerns the chemical bonding in these clusters consisting of Bi, the continuous MNM transition as well as microscopic inhomogeneity can be observed over the range of 0.4<x<0.6. For Inzit-z melts there exist two distinct valence-states In• and In\"+, over the range of 0.25:s;;x:s;;0.5. The existence of two stable ionic-states causes short-range order associated with ionic or unlike configuration and thus these solutions are of conduction-electron deficient insulator.","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"72 1","pages":"156-168"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64897958","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":"t-Matrix Approximation to Two-Dimensional Hubbard Model","authors":"H. Fukuyama, Y. Hasegawa","doi":"10.1143/PTPS.101.441","DOIUrl":"https://doi.org/10.1143/PTPS.101.441","url":null,"abstract":"","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"101 1","pages":"441-452"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64704780","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":"Structure and Representations of the W ∞ Algebra","authors":"I. Bakas, E. Kiritsis","doi":"10.1143/PTPS.102.15","DOIUrl":"https://doi.org/10.1143/PTPS.102.15","url":null,"abstract":"","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"102 1","pages":"15-37"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTPS.102.15","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64705965","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}
One of the principal goals of the theory of 2D gravity is making sense of the formal expression $$Zleft( {mu ,kappa ;{t_i}} right) = sumlimits_h {{{int_{ME{T_h}} {dge} }^{mu int {sqrt g + kint {sqrt g } + k} }}} {Z_{QFTleft( {{t_i}} right)}}left[ g right]$$(1.1)where we integrate over metrics g on surfaces with h handles with a weight defined by the Einstein-Hilbert action (μ is the cosmological constant and κ is Newton’s constant, or, equivalently, the string coupling) together with the partition function of some 2D quantum field theory, QFT(t i ). The parameters t i are coordinates on a subspace of the space of 2D field theories, or, equivalently, coordinates for a space of string backgrounds.
二维引力理论的主要目标之一是使形式表达式$$Zleft( {mu ,kappa ;{t_i}} right) = sumlimits_h {{{int_{ME{T_h}} {dge} }^{mu int {sqrt g + kint {sqrt g } + k} }}} {Z_{QFTleft( {{t_i}} right)}}left[ g right]$$(1.1)有意义，其中我们在带有h柄的曲面上对度量g进行积分，积分权由爱因斯坦-希尔伯特作用(μ是宇宙学常数，κ是牛顿常数，或者等价地，弦耦合)和某些二维量子场理论的配分函数QFT(t i)定义。参数t i是二维场论空间的一个子空间上的坐标，或者，等价地，是弦背景空间的坐标。
{"title":"Matrix Models of 2D Gravity and Isomonodromic Deformation","authors":"G. Moore","doi":"10.1143/PTPS.102.255","DOIUrl":"https://doi.org/10.1143/PTPS.102.255","url":null,"abstract":"One of the principal goals of the theory of 2D gravity is making sense of the formal expression $$Zleft( {mu ,kappa ;{t_i}} right) = sumlimits_h {{{int_{ME{T_h}} {dge} }^{mu int {sqrt g + kint {sqrt g } + k} }}} {Z_{QFTleft( {{t_i}} right)}}left[ g right]$$(1.1)where we integrate over metrics g on surfaces with h handles with a weight defined by the Einstein-Hilbert action (μ is the cosmological constant and κ is Newton’s constant, or, equivalently, the string coupling) together with the partition function of some 2D quantum field theory, QFT(t i ). The parameters t i are coordinates on a subspace of the space of 2D field theories, or, equivalently, coordinates for a space of string backgrounds.","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"102 1","pages":"255-285"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTPS.102.255","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64706239","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}
The Anderson orthogonality exponents K + for introducing a localized perturbation into an electron gas and K(a) for displacing the localized potential by a vector a are discussed for one- and two-dimensional systems. It is shown that the smoothness of the potential enters very differently in the exponents K + and K(a). The controversial point of the boundedness of the two exponents is clarified
{"title":"Orthogonality Exponents in Low-Dimensional Metals","authors":"K. Schönhammer","doi":"10.1143/PTPS.106.147","DOIUrl":"https://doi.org/10.1143/PTPS.106.147","url":null,"abstract":"The Anderson orthogonality exponents K + for introducing a localized perturbation into an electron gas and K(a) for displacing the localized potential by a vector a are discussed for one- and two-dimensional systems. It is shown that the smoothness of the potential enters very differently in the exponents K + and K(a). The controversial point of the boundedness of the two exponents is clarified","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"36 1","pages":"147-156"},"PeriodicalIF":0.0,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64712696","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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