A molecular model developed for resonances observed in medium light heavy-ion collisions is described. At high spins in Si + Si (oblate-oblate system), a stable dinuclear configuration is found to be equator-equator touching one. The normal modes around the equilibrium are investigated. These modes are expected to be the origin of a large number of resonances observed. Furthermore, due to the axially asymmetric shape of the stable configuration of Si + Si, the system rotates preferentially around the axis with the largest moment of inertia, which gives rise to wobbling motion (K-mixing). Energy spectra for the normal modes and for the extended model including the wobbling motion are given.
{"title":"Resonances in 28Si + 28Si. I —Dinuclear Molecular Model with Axial Asymmetry—","authors":"E. Uegaki, Y. Abe","doi":"10.1143/PTP.127.831","DOIUrl":"https://doi.org/10.1143/PTP.127.831","url":null,"abstract":"A molecular model developed for resonances observed in medium light heavy-ion collisions is described. At high spins in Si + Si (oblate-oblate system), a stable dinuclear configuration is found to be equator-equator touching one. The normal modes around the equilibrium are investigated. These modes are expected to be the origin of a large number of resonances observed. Furthermore, due to the axially asymmetric shape of the stable configuration of Si + Si, the system rotates preferentially around the axis with the largest moment of inertia, which gives rise to wobbling motion (K-mixing). Energy spectra for the normal modes and for the extended model including the wobbling motion are given.","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"831-876"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.831","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64011483","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 suggest that the Hermitian matrix models with resonant tunneling may exhibit novel criticality. Some features of the proposed criticality are explored. In particular, we argue that the new critical point is connected with the first-order transition.
{"title":"Matrix Model Criticality and Resonant Tunneling","authors":"T. Tada","doi":"10.1143/PTP.128.429","DOIUrl":"https://doi.org/10.1143/PTP.128.429","url":null,"abstract":"We suggest that the Hermitian matrix models with resonant tunneling may exhibit novel criticality. Some features of the proposed criticality are explored. In particular, we argue that the new critical point is connected with the first-order transition.","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"9 1","pages":"429-437"},"PeriodicalIF":0.0,"publicationDate":"2012-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.128.429","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64015345","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}
It is pointed out that the local hidden variables model of Bell and Clauser-Horne-Shimony-Holt (CHSH) gives $||leq 2sqrt{2}$ or $||leq 2$ for the quantum CHSH operator $B={bf a}cdot {bf sigma}otimes ({bf b}+{bf b}^{prime})cdot {bf sigma} +{bf a}^{prime}cdot{bf sigma}otimes ({bf b}-{bf b}^{prime})cdot{bf sigma} $ depending on two different ways of evaluation, when it is applied to a $d=4$ system of two spin-1/2 particles. This is due to the failure of linearity, and it shows that the conventional CHSH inequality $||leq 2$ does not provide a reliable test of the $d=4$ local non-contextual hidden variables model. To achieve $||leq 2$ uniquely, one needs to impose a linearity requirement on the hidden variables model, which in turn adds a von Neumann-type stricture. It is then shown that the local model is converted to a factored product of two non-contextual $d=2$ hidden variables models. This factored product implies pure separable quantum states and satisfies $||leq 2$, but no more a proper hidden variables model in $d=4$. The conventional CHSH inequality $||leq 2$ thus characterizes the pure separable quantum mechanical states but does not test the model of local hidden variables in $d=4$, to be consistent with Gleason's theorem which excludes non-contextual models in $d=4$. This observation is also consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to hidden variables.
{"title":"Does CHSH Inequality Test the Model of Local Hidden Variables","authors":"K. Fujikawa","doi":"10.1143/PTP.127.975","DOIUrl":"https://doi.org/10.1143/PTP.127.975","url":null,"abstract":"It is pointed out that the local hidden variables model of Bell and Clauser-Horne-Shimony-Holt (CHSH) gives $||leq 2sqrt{2}$ or $||leq 2$ for the quantum CHSH operator $B={bf a}cdot {bf sigma}otimes ({bf b}+{bf b}^{prime})cdot {bf sigma} +{bf a}^{prime}cdot{bf sigma}otimes ({bf b}-{bf b}^{prime})cdot{bf sigma} $ depending on two different ways of evaluation, when it is applied to a $d=4$ system of two spin-1/2 particles. This is due to the failure of linearity, and it shows that the conventional CHSH inequality $||leq 2$ does not provide a reliable test of the $d=4$ local non-contextual hidden variables model. To achieve $||leq 2$ uniquely, one needs to impose a linearity requirement on the hidden variables model, which in turn adds a von Neumann-type stricture. It is then shown that the local model is converted to a factored product of two non-contextual $d=2$ hidden variables models. This factored product implies pure separable quantum states and satisfies $||leq 2$, but no more a proper hidden variables model in $d=4$. The conventional CHSH inequality $||leq 2$ thus characterizes the pure separable quantum mechanical states but does not test the model of local hidden variables in $d=4$, to be consistent with Gleason's theorem which excludes non-contextual models in $d=4$. This observation is also consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to hidden variables.","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"975-987"},"PeriodicalIF":0.0,"publicationDate":"2012-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.975","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64011208","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 noncontextual hidden variables models in $d=2$, such as the ones constructed by Bell and by Kochen and Specker, have difficulties in accounting for the conditional measurement of two non-orthogonal projectors. An idea of branching in the hidden variables space, which provides a means to realize the notion of reduction effectively and describe the state preparation, is suggested as a way to resolve the difficulties associated with the conditional measurement.
{"title":"Conditional Measurement in Noncontextual Hidden-Variable Models","authors":"K. Fujikawa","doi":"10.1143/PTP.127.989","DOIUrl":"https://doi.org/10.1143/PTP.127.989","url":null,"abstract":"The noncontextual hidden variables models in $d=2$, such as the ones constructed by Bell and by Kochen and Specker, have difficulties in accounting for the conditional measurement of two non-orthogonal projectors. An idea of branching in the hidden variables space, which provides a means to realize the notion of reduction effectively and describe the state preparation, is suggested as a way to resolve the difficulties associated with the conditional measurement.","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"989-996"},"PeriodicalIF":0.0,"publicationDate":"2012-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.989","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64011314","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}
It is known that some of the traversable wormhole can exist in General Relativity only if its throat contains some exotic matter. In this paper, we obtain (2 + 1)-dimensional horizonless charged magnetic brane without curvature singularity. Then, we consider a nontrivial local transformation to endow a global rotation to spacetime. After that, we generalize magnetic brane to higher dimensional solutions and use the cut-and-paste method to construct higher dimensional charged BTZ-like rotating wormholes in such a way that they reduce to charged magnetic BTZ solution in three dimensions, exactly. We also show that charged BTZ-like wormhole supported by the exotic matter at its throat r = r+. Finally, we calculate the conserved quantities of the charged BTZ-like wormhole such as mass, angular momentum and electric charge density, and show that the electric charge depends on the rotation parameters and the static wormhole does not have a net electric charge density. Subject Index: 450, 453
{"title":"Higher Dimensional Charged BTZ-Like Wormhole","authors":"S. H. Hendi","doi":"10.1143/PTP.127.907","DOIUrl":"https://doi.org/10.1143/PTP.127.907","url":null,"abstract":"It is known that some of the traversable wormhole can exist in General Relativity only if its throat contains some exotic matter. In this paper, we obtain (2 + 1)-dimensional horizonless charged magnetic brane without curvature singularity. Then, we consider a nontrivial local transformation to endow a global rotation to spacetime. After that, we generalize magnetic brane to higher dimensional solutions and use the cut-and-paste method to construct higher dimensional charged BTZ-like rotating wormholes in such a way that they reduce to charged magnetic BTZ solution in three dimensions, exactly. We also show that charged BTZ-like wormhole supported by the exotic matter at its throat r = r+. Finally, we calculate the conserved quantities of the charged BTZ-like wormhole such as mass, angular momentum and electric charge density, and show that the electric charge depends on the rotation parameters and the static wormhole does not have a net electric charge density. Subject Index: 450, 453","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"907-919"},"PeriodicalIF":0.0,"publicationDate":"2012-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.907","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64011399","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}
M. Eto, T. Fujimori, M. Nitta, K. Ohashi, N. Sakai
We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general nonlinear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four derivative corrections to the effective sigma model on the moduli space C×CP N−1 . We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that YangMills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.
{"title":"Higher Derivative Corrections to Non-Abelian Vortex Effective Theory","authors":"M. Eto, T. Fujimori, M. Nitta, K. Ohashi, N. Sakai","doi":"10.1143/PTP.128.67","DOIUrl":"https://doi.org/10.1143/PTP.128.67","url":null,"abstract":"We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general nonlinear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four derivative corrections to the effective sigma model on the moduli space C×CP N−1 . We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that YangMills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"128 1","pages":"67-103"},"PeriodicalIF":0.0,"publicationDate":"2012-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.128.67","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64015594","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 lowest scalar and pseudoscalar glueball masses are evaluated by means of the timedependent variational approach to the Yang-Mills gauge theory without fermions in the Hamiltonian formalism within a Gaussian wavefunctional approximation. The glueball mass is calculated as a pole of the propagator for a composite glueball field which consists of two massless gluons. The glueball propagator is here evaluated by using the linear response theory for the composite external glueball field. As a result, a finite glueball mass is obtained through the interaction between two massless gluons, in which the glueball mass depends on the QCD coupling constant g in the nonperturbative form.
{"title":"Scalar and Pseudoscalar Glueball Masses within a Gaussian Wavefunctional Approximation","authors":"Y. Tsue","doi":"10.1143/PTP.128.373","DOIUrl":"https://doi.org/10.1143/PTP.128.373","url":null,"abstract":"The lowest scalar and pseudoscalar glueball masses are evaluated by means of the timedependent variational approach to the Yang-Mills gauge theory without fermions in the Hamiltonian formalism within a Gaussian wavefunctional approximation. The glueball mass is calculated as a pole of the propagator for a composite glueball field which consists of two massless gluons. The glueball propagator is here evaluated by using the linear response theory for the composite external glueball field. As a result, a finite glueball mass is obtained through the interaction between two massless gluons, in which the glueball mass depends on the QCD coupling constant g in the nonperturbative form.","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"128 1","pages":"373-396"},"PeriodicalIF":0.0,"publicationDate":"2012-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.128.373","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64015366","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 study the equation of states of symmetric and pure neutron matter in the SkyrmeHartree-Fock (SHF) model with tensor corrections. We are aware now that the pion exchange interaction has a significant contribution to nuclear structure in light nuclei. The pion generates a strong tensor interaction between two nucleons, which cannot be treated within the Hartree-Fock framework for the spin-saturated system such as homogeneous nuclear matter. Therefore, we study the role of the tensor interaction based on the SHF model, in which we extend it by explicitly introducing two-particle-two-hole (2p-2h) excitations for the treatment of the tensor interaction in symmetric nuclear matter and pure neutron matter. We are able to describe infinite matter very well using the SHF model with tensor corrections. We also discuss the connection between the symmetry energy and the tensor interaction in this framework. Subject Index: 201
{"title":"Skyrme-Hartree-Fock plus Tensor Correction for Nuclear Matter","authors":"Yannan Wang, Jinniu Hu, H. Toki, Hong Shen","doi":"10.1143/PTP.127.739","DOIUrl":"https://doi.org/10.1143/PTP.127.739","url":null,"abstract":"We study the equation of states of symmetric and pure neutron matter in the SkyrmeHartree-Fock (SHF) model with tensor corrections. We are aware now that the pion exchange interaction has a significant contribution to nuclear structure in light nuclei. The pion generates a strong tensor interaction between two nucleons, which cannot be treated within the Hartree-Fock framework for the spin-saturated system such as homogeneous nuclear matter. Therefore, we study the role of the tensor interaction based on the SHF model, in which we extend it by explicitly introducing two-particle-two-hole (2p-2h) excitations for the treatment of the tensor interaction in symmetric nuclear matter and pure neutron matter. We are able to describe infinite matter very well using the SHF model with tensor corrections. We also discuss the connection between the symmetry energy and the tensor interaction in this framework. Subject Index: 201","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"739-749"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.739","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64010699","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}
In this paper the inverse scattering method is applied to the Vakhnenko-Parkes equation. We describe a procedure for using the inverse scattering transform to find the solutions that are associated with both the bound state spectrum and continuous spectrum of the spectral problem. The suggested special form of the singularity function gives rise to the multi-mode periodic solutions. Sufficient conditions are obtained in order that the solutions become real functions. The interaction of the solitons and multi-mode periodic waves is studied. The procedure is illustrated by considering a number of examples. Subject Index: 010, 011
{"title":"Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation","authors":"V. O. Vakhnenko, E. Parkes","doi":"10.1143/PTP.127.593","DOIUrl":"https://doi.org/10.1143/PTP.127.593","url":null,"abstract":"In this paper the inverse scattering method is applied to the Vakhnenko-Parkes equation. We describe a procedure for using the inverse scattering transform to find the solutions that are associated with both the bound state spectrum and continuous spectrum of the spectral problem. The suggested special form of the singularity function gives rise to the multi-mode periodic solutions. Sufficient conditions are obtained in order that the solutions become real functions. The interaction of the solitons and multi-mode periodic waves is studied. The procedure is illustrated by considering a number of examples. Subject Index: 010, 011","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"593-613"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.593","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64010340","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}
Taking the Rubin model for the one-dimensional Brownian motion and the chaotic Kuramoto-Sivashinsky equation for the one-dimensional turbulence, we derive a generalized Langevin equation in terms of the projection operator formalism, and then investigate the decay forms of the time correlation function Uk(t) and its memory function Γk(t )f or a normal mode uk(t) of the system with a wavenumber k .L etτ (u) k and τ (γ) k be the decay times of Uk(t )a ndΓk(t), respectively, with τ (u) k ≥ τ (γ) k . Here, τ (u) k is a macroscopic time scale if k � 1, but a microscopic time scale if k & 1, whereas τ (γ) k is always a microscopic time scale. Changing the length scale k −1 and the time scales τ (u) k , τ (γ) k , we can obtain various aspects of
{"title":"Decay Forms of the Time Correlation Functions for Turbulence and Chaos","authors":"H. Mori, M. Okamura","doi":"10.1143/PTP.127.615","DOIUrl":"https://doi.org/10.1143/PTP.127.615","url":null,"abstract":"Taking the Rubin model for the one-dimensional Brownian motion and the chaotic Kuramoto-Sivashinsky equation for the one-dimensional turbulence, we derive a generalized Langevin equation in terms of the projection operator formalism, and then investigate the decay forms of the time correlation function Uk(t) and its memory function Γk(t )f or a normal mode uk(t) of the system with a wavenumber k .L etτ (u) k and τ (γ) k be the decay times of Uk(t )a ndΓk(t), respectively, with τ (u) k ≥ τ (γ) k . Here, τ (u) k is a macroscopic time scale if k � 1, but a microscopic time scale if k & 1, whereas τ (γ) k is always a microscopic time scale. Changing the length scale k −1 and the time scales τ (u) k , τ (γ) k , we can obtain various aspects of","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"127 1","pages":"615-629"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.127.615","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64010423","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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