Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is rea...Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.展开更多
Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-fi...Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation（BEC） occurs if and only if the U（1） symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schroedinger eigenvalue equation and using the self-consistent condition.展开更多
Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation r...Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.展开更多
The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings,...The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .展开更多
We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple...We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectr展开更多
Entanglement in quantum theory is a concept that has confused many scientists. This concept implies that the cluster property, which means no relations between sufficiently separated two events, is non-trivial. In the...Entanglement in quantum theory is a concept that has confused many scientists. This concept implies that the cluster property, which means no relations between sufficiently separated two events, is non-trivial. In the works for some quantum spin systems, which have been recently published by the author, extensive and quantitative examinations were made about the violation of cluster property in the correlation function of the spin operator. The previous study of these quantum antiferromagnets showed that this violation is induced by the degenerate states in the systems where the continuous symmetry spontaneously breaks. Since this breaking is found in many materials such as the high temperature superconductors and the superfluidity, it is an important question whether we can observe the violation of the cluster property in them. As a step to answer this question we study a quantum nonlinear sigma model with U(1) symmetry in this paper. It is well known that this model, which has been derived as an effective model of the quantum spin systems, can also be applied to investigations of many materials. Notifying that the existence of the degenerate states is essential for the violation, we made numerical calculations in addition to theoretical arguments to find these states in the nonlinear sigma model. Then, successfully finding the degenerate states in the model, we came to a conclusion that there is a chance to observe the violation of cluster property in many materials to which the nonlinear sigma model applies.展开更多
Many-body localization(MBL)of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half.The von Neumann entanglement entropy Svn is commonly used to detect the MBL p...Many-body localization(MBL)of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half.The von Neumann entanglement entropy Svn is commonly used to detect the MBL phase transition but remains challenging to be directly measured.Based on the U(1)symmetry from the particle number conservation,Svn can be decomposed into the particle number entropy S_(n) and the configuration entropy Sc.In light of the tendency that the eigenstate's S_(c) nears zero in the localized phase,we introduce a quantity describing the deviation of S from the ideal thermalization distribution;finite-size scaling analysis illustrates that it shares the same phase transition point with Sv but displays the better critical exponents.This observation hints that the phase transition to MBL might largely be determined by S and its fluctuations Notably,the recent experiments[A.Lukin,et al.,Science 364,256(2019);J.Leonard,et al.,Nat.Phys.19,481(2023)]demonstrated that this deviation can potentially be measured through the Sn measurement.Furthermore,our investigations reveal that the thermalized states primarily occupy the low-energy section of the spectrum,as indicated by measures of localization length,gap ratio,and energy density distribution.This low-energy spectrum of the Bose model closely resembles the entire spectrum of the Fermi(or spin XXZ)model,accommodating a transition from the thermalized to the localized states.While,owing to the bosonic statistics,the high-energy spectrum of the model allows the formation of distinct clusters of bosons in the random potential background.We analyze the resulting eigenstate properties and briefly summarize the associated dynamics.To distinguish between the phase regions at the low and high energies,a probing quantity based on the structure of S_(VN) is also devised.Our work highlights the importance of symmetry combined with entanglement in the study of MBL.In this regard,for the disordered Heisenberg XXZ chain,the recent pure eigenvalue analyses in[J.S展开更多
We investigate the possibility of detecting the leptophilic gauge boson Z_(x) predicted by the U(1)Le−Lμmodel via the processes e+e−→ℓ^(+)ℓ^(−)Z_(x)(Z_(x)→ℓ^(+)ℓ^(−))and e+e−→ℓ^(+)ℓ^(−)Z_(x)(Z_(x)→νℓ¯νℓ)at...We investigate the possibility of detecting the leptophilic gauge boson Z_(x) predicted by the U(1)Le−Lμmodel via the processes e+e−→ℓ^(+)ℓ^(−)Z_(x)(Z_(x)→ℓ^(+)ℓ^(−))and e+e−→ℓ^(+)ℓ^(−)Z_(x)(Z_(x)→νℓ¯νℓ)at the Circular Electron Positron Collider(CEPC)with a center of mass energy√s=240 GeV and luminosity L=5.6ab^(−1).We provide the expected sensitivities of the CEPC to the parameter space at the 1σ,2σ,3σ,and 5σlevels.展开更多
文摘Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.
基金0ne of author （Huang H B） was partially supported by the Natural Science Foundation of Jiangsu province, China （Grant No BK2005062）.Acknowledgement We thank Professor Tian G S for discussion
文摘Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation（BEC） occurs if and only if the U（1） symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schroedinger eigenvalue equation and using the self-consistent condition.
文摘Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.
文摘The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .
文摘We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectr
文摘Entanglement in quantum theory is a concept that has confused many scientists. This concept implies that the cluster property, which means no relations between sufficiently separated two events, is non-trivial. In the works for some quantum spin systems, which have been recently published by the author, extensive and quantitative examinations were made about the violation of cluster property in the correlation function of the spin operator. The previous study of these quantum antiferromagnets showed that this violation is induced by the degenerate states in the systems where the continuous symmetry spontaneously breaks. Since this breaking is found in many materials such as the high temperature superconductors and the superfluidity, it is an important question whether we can observe the violation of the cluster property in them. As a step to answer this question we study a quantum nonlinear sigma model with U(1) symmetry in this paper. It is well known that this model, which has been derived as an effective model of the quantum spin systems, can also be applied to investigations of many materials. Notifying that the existence of the degenerate states is essential for the violation, we made numerical calculations in addition to theoretical arguments to find these states in the nonlinear sigma model. Then, successfully finding the degenerate states in the model, we came to a conclusion that there is a chance to observe the violation of cluster property in many materials to which the nonlinear sigma model applies.
基金This work is supported by the Ministry of Science and Technology of China(Grant No.2016YFA0300500)the National Natural Science Foundation of China(No.11974244).
文摘Many-body localization(MBL)of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half.The von Neumann entanglement entropy Svn is commonly used to detect the MBL phase transition but remains challenging to be directly measured.Based on the U(1)symmetry from the particle number conservation,Svn can be decomposed into the particle number entropy S_(n) and the configuration entropy Sc.In light of the tendency that the eigenstate's S_(c) nears zero in the localized phase,we introduce a quantity describing the deviation of S from the ideal thermalization distribution;finite-size scaling analysis illustrates that it shares the same phase transition point with Sv but displays the better critical exponents.This observation hints that the phase transition to MBL might largely be determined by S and its fluctuations Notably,the recent experiments[A.Lukin,et al.,Science 364,256(2019);J.Leonard,et al.,Nat.Phys.19,481(2023)]demonstrated that this deviation can potentially be measured through the Sn measurement.Furthermore,our investigations reveal that the thermalized states primarily occupy the low-energy section of the spectrum,as indicated by measures of localization length,gap ratio,and energy density distribution.This low-energy spectrum of the Bose model closely resembles the entire spectrum of the Fermi(or spin XXZ)model,accommodating a transition from the thermalized to the localized states.While,owing to the bosonic statistics,the high-energy spectrum of the model allows the formation of distinct clusters of bosons in the random potential background.We analyze the resulting eigenstate properties and briefly summarize the associated dynamics.To distinguish between the phase regions at the low and high energies,a probing quantity based on the structure of S_(VN) is also devised.Our work highlights the importance of symmetry combined with entanglement in the study of MBL.In this regard,for the disordered Heisenberg XXZ chain,the recent pure eigenvalue analyses in[J.S
基金the National Natural Science Foundation of China(11875157,12147214)。
文摘We investigate the possibility of detecting the leptophilic gauge boson Z_(x) predicted by the U(1)Le−Lμmodel via the processes e+e−→ℓ^(+)ℓ^(−)Z_(x)(Z_(x)→ℓ^(+)ℓ^(−))and e+e−→ℓ^(+)ℓ^(−)Z_(x)(Z_(x)→νℓ¯νℓ)at the Circular Electron Positron Collider(CEPC)with a center of mass energy√s=240 GeV and luminosity L=5.6ab^(−1).We provide the expected sensitivities of the CEPC to the parameter space at the 1σ,2σ,3σ,and 5σlevels.
