An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byu...An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.展开更多
We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y (sl(2) ) algebras are realized. We derive t...We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y (sl(2) ) algebras are realized. We derive the Hamiltonians of the two models based on the Y(sl(2) ) and the generalized Pauli equation. The energy spectra of the systems are also given in terms of Yangian algebra and quantum mechanics.展开更多
We investigate the properties of A^+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A^+c bound states can exist if the A^+c potential well depth |UA^+c| in nu...We investigate the properties of A^+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A^+c bound states can exist if the A^+c potential well depth |UA^+c| in nuclear matter is less than 10 MeV. If |UA^+c|is less than 20 MeV, A^+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A^+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A^+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.展开更多
It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initial...It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initially in even (odd) coherent states. The nonlinearity of interatomic interactions in the two condensates may lead to the atomic tunneling current and Shapiro-like step between the two condensates. It is found that the interatomic nonlinear interactions can induce the atomic tunneling current and Shapiro-like step between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling. The static atomic tunneling current flows in positive or negative direction, which depends on the phase difference of the two-species condensates.展开更多
Effect of conversion process (≡^-P→AA) on ≡--hypernucleus is studied for ≡^12-Be. It is found that the conversion process has a certain extent effect on properties of low-lying states of the ≡^--hypernuclei.
We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting witha single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is init...We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting witha single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initiallyin a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed thatatoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with twodifferent sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field, both the population difference and the atomic tunnellingcurrent are only a single oscillation. But they will respectively become a superposition of two oscillations with differentoscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one alwayshas an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. Theseconclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of theatomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. lBy properlyselecting the laser field, the expected atomic tunnelling current can be obtained too.展开更多
We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interactio...We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is found that the two condensates may periodically exhibit sub-Poissonian distribution. It is revealed that the correlation between the two condensates can be nonclassical, which means that there exists a violation of Cauchy-Schwartz inequality. The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.展开更多
The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensiono...The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensionof the usual (linear) solutions. In this paper, we not only give a further study on some known set-theoretical solutions(the Venkov's solutions), but also find a new kind of set-theoretical solutions which have a geometric interpretation.Moreover, the new solutions lead to the metahomomorphisms in group theory.展开更多
We have studied the tunneling dynamics of two-species Bose-Einstein condensates. It is shown that the population difference and the Josephson-like tunneling current between the two condensates exhibit oscillation beha...We have studied the tunneling dynamics of two-species Bose-Einstein condensates. It is shown that the population difference and the Josephson-like tunneling current between the two condensates exhibit oscillation behaviors and there exists macroscopic quantum self-trapping, which strongly depends on the initial state, interatomic nonlinear self-interaction, interspecies nonlinear interaction, and the total number of atoms in the two condensates.展开更多
Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU...Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.展开更多
The interaction of N two-level atoms with both a two-mode cavity field and an external classical pumpingfield, and with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are...The interaction of N two-level atoms with both a two-mode cavity field and an external classical pumpingfield, and with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are highlydetuned. This dispersive interaction can be used to generate a large number of important entangled coherent statesconditional on the initial atomic states and state-selective measurements. A dynamical relation is established betweenthe results for the case with continuous pumping and the case without external driving where the coherent field is putin as the initial condition.展开更多
We examine the effect of adding mesons fo(975)and φ(1020)as well as the variety of U(the potential well depth ofin nuclear matter)from -10 MeV to -28 MeV on the extent of the particles participation and the propertie...We examine the effect of adding mesons fo(975)and φ(1020)as well as the variety of U(the potential well depth ofin nuclear matter)from -10 MeV to -28 MeV on the extent of the particles participation and the properties of the neutron star in the relativistic mean field model.We find that considering the contribution of fo and φ mesons,the equation of state of the neutron star turns soft,the maximum mass reduces while the corresponding radius increases.hyperons appear at lower density as Ubecomes deeper,and the variety of Uhas little effect on the equation of state and the properties of the neutron star.展开更多
The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localizati...The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.展开更多
The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In part...The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.展开更多
文摘An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.
文摘We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y (sl(2) ) algebras are realized. We derive the Hamiltonians of the two models based on the Y(sl(2) ) and the generalized Pauli equation. The energy spectra of the systems are also given in terms of Yangian algebra and quantum mechanics.
文摘We investigate the properties of A^+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A^+c bound states can exist if the A^+c potential well depth |UA^+c| in nuclear matter is less than 10 MeV. If |UA^+c|is less than 20 MeV, A^+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A^+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A^+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.
文摘It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initially in even (odd) coherent states. The nonlinearity of interatomic interactions in the two condensates may lead to the atomic tunneling current and Shapiro-like step between the two condensates. It is found that the interatomic nonlinear interactions can induce the atomic tunneling current and Shapiro-like step between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling. The static atomic tunneling current flows in positive or negative direction, which depends on the phase difference of the two-species condensates.
文摘Effect of conversion process (≡^-P→AA) on ≡--hypernucleus is studied for ≡^12-Be. It is found that the conversion process has a certain extent effect on properties of low-lying states of the ≡^--hypernuclei.
文摘We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting witha single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initiallyin a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed thatatoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with twodifferent sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field, both the population difference and the atomic tunnellingcurrent are only a single oscillation. But they will respectively become a superposition of two oscillations with differentoscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one alwayshas an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. Theseconclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of theatomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. lBy properlyselecting the laser field, the expected atomic tunnelling current can be obtained too.
文摘We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is found that the two condensates may periodically exhibit sub-Poissonian distribution. It is revealed that the correlation between the two condensates can be nonclassical, which means that there exists a violation of Cauchy-Schwartz inequality. The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.
文摘The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensionof the usual (linear) solutions. In this paper, we not only give a further study on some known set-theoretical solutions(the Venkov's solutions), but also find a new kind of set-theoretical solutions which have a geometric interpretation.Moreover, the new solutions lead to the metahomomorphisms in group theory.
文摘We have studied the tunneling dynamics of two-species Bose-Einstein condensates. It is shown that the population difference and the Josephson-like tunneling current between the two condensates exhibit oscillation behaviors and there exists macroscopic quantum self-trapping, which strongly depends on the initial state, interatomic nonlinear self-interaction, interspecies nonlinear interaction, and the total number of atoms in the two condensates.
文摘Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.
基金The project supported by National Natural Science Foundation of China
文摘The interaction of N two-level atoms with both a two-mode cavity field and an external classical pumpingfield, and with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are highlydetuned. This dispersive interaction can be used to generate a large number of important entangled coherent statesconditional on the initial atomic states and state-selective measurements. A dynamical relation is established betweenthe results for the case with continuous pumping and the case without external driving where the coherent field is putin as the initial condition.
基金The project supported in part by the Postdoctoral Science Foundation of China under Grant No.2002032169+2 种基金National Natural Science Foundation of China under Grant No.10275037the Foundation for Doctorate Training Program of China under Grant No.2001005
文摘We examine the effect of adding mesons fo(975)and φ(1020)as well as the variety of U(the potential well depth ofin nuclear matter)from -10 MeV to -28 MeV on the extent of the particles participation and the properties of the neutron star in the relativistic mean field model.We find that considering the contribution of fo and φ mesons,the equation of state of the neutron star turns soft,the maximum mass reduces while the corresponding radius increases.hyperons appear at lower density as Ubecomes deeper,and the variety of Uhas little effect on the equation of state and the properties of the neutron star.
基金Project supported by the Cheung-Kong Scholarshipthe Key Laboratory of Pure MathematicsCombinatorics of the Ministry of Education of Chinathe 973 Project of the Ministry of Science and Technology of China.
文摘The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.
基金Project supported by the National Natural Science Foundation of China the Cheung-Kong Scholarship of the Ministry of Education of China the Qiu Shi Foundation and the 973 Project of the Ministry of Science and Technology of China.
文摘The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.
