AIM:To investigate the radiation response of various human tumor cells and normal liver cells. METHODS: Cell lines of human hepatoma cells (SMMC-7721), liver cells (L02), melanoma cells (A375) and cervical tumor (HeLa...AIM:To investigate the radiation response of various human tumor cells and normal liver cells. METHODS: Cell lines of human hepatoma cells (SMMC-7721), liver cells (L02), melanoma cells (A375) and cervical tumor (HeLa) were irradiated with 60Co γ-rays. Cell survive was documented by a colony assay. Chromatid breaks were measured by counting the number of chromatid breaks and isochromatid breaks immediately after prematurely chromosome condensed by Calyculin-A. RESULTS: Linear quadratic survival curve was observed in all of four cell lines, and dose-dependent increase in radiation-induced chromatid and isochromatid breaks were observed in GB2B phase. Among these four cell lines, A375 was most sensitive to radiation, while, L02 had the lowest radiosensitivity. For normal liver cells, chromatid breaks were easy to be repaired, isochromatid breaks were difficult to be repaired. CONCLUSION: The results suggest that the y-rays induced chromatid breaks can be possibly used as a good predictor of radiosensitivity, also, unrejoined isochromatid breaks probably tightly related with cell cancerization.展开更多
AIM: Now many countries have developed cancer therapy with heavy ions, especially in GSI (Gesellschaft fur Schwerionenforschung mbH, Darmstadt, Germany),remarkable results have obtained, but due to the complexity of p...AIM: Now many countries have developed cancer therapy with heavy ions, especially in GSI (Gesellschaft fur Schwerionenforschung mbH, Darmstadt, Germany),remarkable results have obtained, but due to the complexity of particle track structure, the basic theory still needs further researching. In this paper, the genotoxic effects of heavy ions irradiation on SMMC-7721 cells were measured using the single cell gel electrophoresis (comet assay). The information about the DNA damage made by other radiations such as X-ray, γ-ray, UV and fast neutron irradiation is very plentiful, while little work have been done on the heavy ions so far. Hereby we tried to detect the reaction of liver cancer cells to heavy ion using comet assay, meanwhile to establish a database for clinic therapy of cancer with the heavy ions.METHODS: The human hepatoma cells were chosen as the test cell line irradiated by 80Mev/u 20Ne10+ on HIRFL (China), the radiation-doses were 0, 0.5, 1, 2, 4 and 8 Gy,and then comet assay was used immediately to detect the DNA damages, 100-150 cells per dose-sample (30-50 cells were randomly observed at constant depth of the gel). The tail length and the quantity of the cells with the tail were put down. EXCEL was used for statistical analysis.RESULTS: We obtained clear images by comet assay and found that SMMC-7721 cells were all damaged apparently from the dose 0.5Gy to 8Gy (t-test: P<0.001, vs control).The tail length and tail moment increased as the doses increased, and the number of cells with tails increased with increasing doses. When doses were higher than 2Gy, nearly 100 % cells were damaged. Furthermore, both tail length and tail moment, showed linear equation.CONCLUSION: From the clear comet assay images, our experiment proves comet assay can be used to measure DNA damages by heavy ions. Meanwhile DNA damages have a positive correlation with the dose changes of heavy ions and SMMC-7721 cells have a great radiosensitivity to 20Ne10+.Different reactions to the change of doses indicate that comet assay is a useful tool to detect DNA damage induced by heavy ions.展开更多
To explore the medical use of a radioactive 9C-ion beam in tumor treatment, which is a double radiation source coming from the external beam itself and the delayed particles emitted internally, some physical experimen...To explore the medical use of a radioactive 9C-ion beam in tumor treatment, which is a double radiation source coming from the external beam itself and the delayed particles emitted internally, some physical experiments are performed at the Secondary Beam Line (SBL) of Heavy Ion Medical Accelerator, Chiba (HIMAC) in Japan be- fore radiobiological research for exhibiting therapeutic value of the 9C beam. Intention of the experiments is for pro- ducing a radioactive 9C-ion beam with higher production rate and purity by means of optimizing the beam line pa- rameters. Finally, a produced 9C beam with the production rate of 9.07×10-6 and purity of 82.88% at full momentum acceptance has been obtained under the optimal conditions of 40 mm-thick beryllium target and 10 mm-thick alumi- num degrader. Both momentum distribution and contaminations for the produced 9C beam under the optimal condi- tions are measured. In order to execute further biological experiments of the 9C beam project, a uniform irradiation field is made with the wobbling magnets and its homogeneity is up to 93.8% inside central area of 20mm in diameter.展开更多
The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvab...The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.展开更多
The self-absorption of γ-ray emitted from cylindrical fissile materials, such as 235 U and 239 Pu, does not possess spherical symmetry. The analytical formulae of self-absorption for γ-ray throughout the cylinder ha...The self-absorption of γ-ray emitted from cylindrical fissile materials, such as 235 U and 239 Pu, does not possess spherical symmetry. The analytical formulae of self-absorption for γ-ray throughout the cylinder have been obtained. The intensity of γ-ray is a function of γ-ray outgoing directions and cylindrical configurations, accordingly one can acquire the information about geometrical configuration of cylindrical fissile materials through multi-location measurements. Further more, the method is given in this article. The result can be applied to the fissile material safe- guard, such as nuclear monitoring and verifying.展开更多
N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the gen...The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.展开更多
A systematic overview on the characteristics of super heavy nuclei from Z = 101 to Z = 130 based on the data by P. Moller et al. is presented. The nuclei which have the biggest mean binding energy in each of their iso...A systematic overview on the characteristics of super heavy nuclei from Z = 101 to Z = 130 based on the data by P. Moller et al. is presented. The nuclei which have the biggest mean binding energy in each of their isotope chain show systematic regular behavior, indicating that the mean binding energy is a good criterion to classify super heavy nuclei by their stabilities. Further investigation on the nuclear data at and after Z=127 has been suggested.展开更多
For any classical Lie algebra , we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers . The universal form of the Lax pair, equations of motion, Hamiltonian as well a...For any classical Lie algebra , we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers . The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for with are also given. For all , it is shown that the dynamics of the - and the -Toda chains are natural reductions of that of the -chain, and for , there is also a family of symmetrically reduced Toda systems, the -Toda systems, which are also integrable. In the quantum case, all -Toda systems with 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_12.gif'/> or 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_13.gif'/> describe the dynamics of standard Toda variables coupled to noncommutative variables. Except for the symmetrically reduced cases, the integrability for all -Toda systems survive after quantization.展开更多
The relation between one-to-one correspondent orthonormal eigenstates of H0 and H(λ) = H0 + λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local ...The relation between one-to-one correspondent orthonormal eigenstates of H0 and H(λ) = H0 + λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local destruction due to nonlinear resonance. Numerical results are given to show such possibility with a special Jacobi diagonalization method. The conclusions show that for the system H(λ) belonging to the same class as H0, the relation between one-to-one correspondent orthonormal eigenstates |φi(λ)> and|φ0m(i)>can be expressed as an analytical unitary matrix which can be identified to the relevant quantum canonical transformation. But for the system H(λ) violated dynamical symmetry, the relation between one-to-one correspondent orthonormal eigenstates cannot be expressed as an analytical unitary matrix. Such a kind of unitary matrix cannot be taken as a quantum canonical transformation to define quantum mechanical quantities. This is a key point for studying the quantum chaos with the help of dynamical symmetry theory.展开更多
After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations b...After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schr?dinger equation as a concrete example, the method is recommended in detail.展开更多
We measured the visible light spectral lines of sputtering atoms from solid surfaces orAl, Ti, Ni, Ta and Au which are impacted by 150 keV 126Xeq+ (6 ≤q ≤ 30). It is found that intensities of the light spectral line...We measured the visible light spectral lines of sputtering atoms from solid surfaces orAl, Ti, Ni, Ta and Au which are impacted by 150 keV 126Xeq+ (6 ≤q ≤ 30). It is found that intensities of the light spectral lines are greatly and suddenly enhanced when the charge state of the ion is raised up to a critical value. If assuming that potential energy released from the incident ion due to capturing one electron is enough to excite a surface plasmon, we can estimate the critical charge states and obtain the results very well consistent with the measurements for the above-mentioned target materials. This means that a surface plasmon induced by one electron capture can enhance the excitation of atomic visible light spectral lines in the impact of a highly charged ion on a solid surface.展开更多
In the present paper, latent track formation in yttrium iron garnet (YIG) produced by high energy Ar ions is briefly reported at first. Then, in the framework of thermal spike model, a phenomenological parameter descr...In the present paper, latent track formation in yttrium iron garnet (YIG) produced by high energy Ar ions is briefly reported at first. Then, in the framework of thermal spike model, a phenomenological parameter describing the effective energy transfer from excited electrons to lattice atoms, effective energy deposition Qeff, is deduced. Qeff is a function of ion velocity, electronic energy loss (Se) and mean free path λ of excited electrons in the matter, and is a time moderate term initialized by Waligorski’s function of spatial energy deposition of secondary electrons ejected by incident ions. Size of ion latent track is proportional to Qeff value. From Qeff obtained by use of realistic λ values, the sizes of latent tracks in SiO2, YIG, Ti and Zr produced by given swift heavy ion irradiations are deduced and com- pared with experimental results. It is found that, from the fits to experimental results, the best λ values for SiO2, YIG, Ti and Zr are (6±1), (8±2), (6.1±1.0) and (9.6±1.0) nm, respectively. Moreover, the relationship between experimental damage and Qeff is discussed.展开更多
For the Bariey model for correlated hopping in one dimension under open boundary conditions, the Bethe ansatz equations are analyzed for both a repulsive and an attractive interaction in several limiting cases, i.e., ...For the Bariey model for correlated hopping in one dimension under open boundary conditions, the Bethe ansatz equations are analyzed for both a repulsive and an attractive interaction in several limiting cases, i.e., the ground state, the weak and strong coupling limits. The contributions of the boundary fields to both the magnetic susceptibility and the specific heat are obtained.展开更多
Thick gold targets were bombarded with 47 MeV/nucleon C ions and the radioactive isotopes of iridium 12 and platinum were produced through the multi-nucleon transfer reactions. The production cross-sections of iridium...Thick gold targets were bombarded with 47 MeV/nucleon C ions and the radioactive isotopes of iridium 12 and platinum were produced through the multi-nucleon transfer reactions. The production cross-sections of iridium isotopes in the reactions have been determined by a combination of radiochemical separation and off-line γ-ray spec- troscopy technique. The obtained Ir isotope distribution was compared with those obtained in other experiment as well as calculated by the statistical model.展开更多
We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenval...We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenvalue of the free fermion Dirac operator as same as the result by [Hajime Aoki, Satoshi Iso, and Kelichi Nagao, Phys. Rev.D67 (2003) 065018]. Meanwhile, we also give the eigenvalue of Dirac operator with U(1) Dirac monopole background.展开更多
For each of the Lie algebras gln and gl~n., we construct a family of integrable generalizations of the Toda chains characterized by two integers m+ and m-. The Lax matrices and the equations of motion are given expli...For each of the Lie algebras gln and gl~n., we construct a family of integrable generalizations of the Toda chains characterized by two integers m+ and m-. The Lax matrices and the equations of motion are given explicitly, and the integrals of motion can be calculated in terms of the trace of powers of the Lax matrix L. For the case of m+ = m-,we find a symmetric reduction for each generalized Toda chain we found, and the solution to the initial value problems of the reduced systems is outlined. We also studied the spectral curves of the periodic (m+,m-)-Toda chains, which turns out to be very different for different pairs of m+ and m-. Finally we also obtain thenonabelian generalizations of the (m+, m-)-Toda chains in an explicit form.展开更多
基金Supported by the National Natural Science Foundation of China, No. 10335050Ministry of Science and Technology of the People's Republic of China, No. 2003CCB00200
文摘AIM:To investigate the radiation response of various human tumor cells and normal liver cells. METHODS: Cell lines of human hepatoma cells (SMMC-7721), liver cells (L02), melanoma cells (A375) and cervical tumor (HeLa) were irradiated with 60Co γ-rays. Cell survive was documented by a colony assay. Chromatid breaks were measured by counting the number of chromatid breaks and isochromatid breaks immediately after prematurely chromosome condensed by Calyculin-A. RESULTS: Linear quadratic survival curve was observed in all of four cell lines, and dose-dependent increase in radiation-induced chromatid and isochromatid breaks were observed in GB2B phase. Among these four cell lines, A375 was most sensitive to radiation, while, L02 had the lowest radiosensitivity. For normal liver cells, chromatid breaks were easy to be repaired, isochromatid breaks were difficult to be repaired. CONCLUSION: The results suggest that the y-rays induced chromatid breaks can be possibly used as a good predictor of radiosensitivity, also, unrejoined isochromatid breaks probably tightly related with cell cancerization.
基金President Special Foundation of Chinese Academy of Sciences,grant No.TB990601
文摘AIM: Now many countries have developed cancer therapy with heavy ions, especially in GSI (Gesellschaft fur Schwerionenforschung mbH, Darmstadt, Germany),remarkable results have obtained, but due to the complexity of particle track structure, the basic theory still needs further researching. In this paper, the genotoxic effects of heavy ions irradiation on SMMC-7721 cells were measured using the single cell gel electrophoresis (comet assay). The information about the DNA damage made by other radiations such as X-ray, γ-ray, UV and fast neutron irradiation is very plentiful, while little work have been done on the heavy ions so far. Hereby we tried to detect the reaction of liver cancer cells to heavy ion using comet assay, meanwhile to establish a database for clinic therapy of cancer with the heavy ions.METHODS: The human hepatoma cells were chosen as the test cell line irradiated by 80Mev/u 20Ne10+ on HIRFL (China), the radiation-doses were 0, 0.5, 1, 2, 4 and 8 Gy,and then comet assay was used immediately to detect the DNA damages, 100-150 cells per dose-sample (30-50 cells were randomly observed at constant depth of the gel). The tail length and the quantity of the cells with the tail were put down. EXCEL was used for statistical analysis.RESULTS: We obtained clear images by comet assay and found that SMMC-7721 cells were all damaged apparently from the dose 0.5Gy to 8Gy (t-test: P<0.001, vs control).The tail length and tail moment increased as the doses increased, and the number of cells with tails increased with increasing doses. When doses were higher than 2Gy, nearly 100 % cells were damaged. Furthermore, both tail length and tail moment, showed linear equation.CONCLUSION: From the clear comet assay images, our experiment proves comet assay can be used to measure DNA damages by heavy ions. Meanwhile DNA damages have a positive correlation with the dose changes of heavy ions and SMMC-7721 cells have a great radiosensitivity to 20Ne10+.Different reactions to the change of doses indicate that comet assay is a useful tool to detect DNA damage induced by heavy ions.
文摘To explore the medical use of a radioactive 9C-ion beam in tumor treatment, which is a double radiation source coming from the external beam itself and the delayed particles emitted internally, some physical experiments are performed at the Secondary Beam Line (SBL) of Heavy Ion Medical Accelerator, Chiba (HIMAC) in Japan be- fore radiobiological research for exhibiting therapeutic value of the 9C beam. Intention of the experiments is for pro- ducing a radioactive 9C-ion beam with higher production rate and purity by means of optimizing the beam line pa- rameters. Finally, a produced 9C beam with the production rate of 9.07×10-6 and purity of 82.88% at full momentum acceptance has been obtained under the optimal conditions of 40 mm-thick beryllium target and 10 mm-thick alumi- num degrader. Both momentum distribution and contaminations for the produced 9C beam under the optimal condi- tions are measured. In order to execute further biological experiments of the 9C beam project, a uniform irradiation field is made with the wobbling magnets and its homogeneity is up to 93.8% inside central area of 20mm in diameter.
文摘The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.
文摘The self-absorption of γ-ray emitted from cylindrical fissile materials, such as 235 U and 239 Pu, does not possess spherical symmetry. The analytical formulae of self-absorption for γ-ray throughout the cylinder have been obtained. The intensity of γ-ray is a function of γ-ray outgoing directions and cylindrical configurations, accordingly one can acquire the information about geometrical configuration of cylindrical fissile materials through multi-location measurements. Further more, the method is given in this article. The result can be applied to the fissile material safe- guard, such as nuclear monitoring and verifying.
文摘N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.
文摘The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
基金国家自然科学基金,the Major Basic Research Development Program,中国科学院知识创新工程项目,中国科学院"百人计划",support from DFG of Germany
文摘A systematic overview on the characteristics of super heavy nuclei from Z = 101 to Z = 130 based on the data by P. Moller et al. is presented. The nuclei which have the biggest mean binding energy in each of their isotope chain show systematic regular behavior, indicating that the mean binding energy is a good criterion to classify super heavy nuclei by their stabilities. Further investigation on the nuclear data at and after Z=127 has been suggested.
基金The project supported in part by National Natural Science Foundation of China
文摘For any classical Lie algebra , we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers . The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for with are also given. For all , it is shown that the dynamics of the - and the -Toda chains are natural reductions of that of the -chain, and for , there is also a family of symmetrically reduced Toda systems, the -Toda systems, which are also integrable. In the quantum case, all -Toda systems with 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_12.gif'/> or 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_13.gif'/> describe the dynamics of standard Toda variables coupled to noncommutative variables. Except for the symmetrically reduced cases, the integrability for all -Toda systems survive after quantization.
文摘The relation between one-to-one correspondent orthonormal eigenstates of H0 and H(λ) = H0 + λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local destruction due to nonlinear resonance. Numerical results are given to show such possibility with a special Jacobi diagonalization method. The conclusions show that for the system H(λ) belonging to the same class as H0, the relation between one-to-one correspondent orthonormal eigenstates |φi(λ)> and|φ0m(i)>can be expressed as an analytical unitary matrix which can be identified to the relevant quantum canonical transformation. But for the system H(λ) violated dynamical symmetry, the relation between one-to-one correspondent orthonormal eigenstates cannot be expressed as an analytical unitary matrix. Such a kind of unitary matrix cannot be taken as a quantum canonical transformation to define quantum mechanical quantities. This is a key point for studying the quantum chaos with the help of dynamical symmetry theory.
基金国家自然科学基金,浙江省自然科学基金,Foundation of State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation (PLN 0104),the Foundation of Educational Commission,浙江省宁波市博士基金
文摘After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schr?dinger equation as a concrete example, the method is recommended in detail.
文摘We measured the visible light spectral lines of sputtering atoms from solid surfaces orAl, Ti, Ni, Ta and Au which are impacted by 150 keV 126Xeq+ (6 ≤q ≤ 30). It is found that intensities of the light spectral lines are greatly and suddenly enhanced when the charge state of the ion is raised up to a critical value. If assuming that potential energy released from the incident ion due to capturing one electron is enough to excite a surface plasmon, we can estimate the critical charge states and obtain the results very well consistent with the measurements for the above-mentioned target materials. This means that a surface plasmon induced by one electron capture can enhance the excitation of atomic visible light spectral lines in the impact of a highly charged ion on a solid surface.
基金Supported by NSFC (Projects 10125522 10175084 10475102) and the Chinese Academy of Sciences.
文摘In the present paper, latent track formation in yttrium iron garnet (YIG) produced by high energy Ar ions is briefly reported at first. Then, in the framework of thermal spike model, a phenomenological parameter describing the effective energy transfer from excited electrons to lattice atoms, effective energy deposition Qeff, is deduced. Qeff is a function of ion velocity, electronic energy loss (Se) and mean free path λ of excited electrons in the matter, and is a time moderate term initialized by Waligorski’s function of spatial energy deposition of secondary electrons ejected by incident ions. Size of ion latent track is proportional to Qeff value. From Qeff obtained by use of realistic λ values, the sizes of latent tracks in SiO2, YIG, Ti and Zr produced by given swift heavy ion irradiations are deduced and com- pared with experimental results. It is found that, from the fits to experimental results, the best λ values for SiO2, YIG, Ti and Zr are (6±1), (8±2), (6.1±1.0) and (9.6±1.0) nm, respectively. Moreover, the relationship between experimental damage and Qeff is discussed.
文摘For the Bariey model for correlated hopping in one dimension under open boundary conditions, the Bethe ansatz equations are analyzed for both a repulsive and an attractive interaction in several limiting cases, i.e., the ground state, the weak and strong coupling limits. The contributions of the boundary fields to both the magnetic susceptibility and the specific heat are obtained.
基金Supported by the National Natural Science Foundation of China (10075063) Major State Basic Research Development Program under Contract Number (G2000077400) and the Chinese Academy of Sciences.
文摘Thick gold targets were bombarded with 47 MeV/nucleon C ions and the radioactive isotopes of iridium 12 and platinum were produced through the multi-nucleon transfer reactions. The production cross-sections of iridium isotopes in the reactions have been determined by a combination of radiochemical separation and off-line γ-ray spec- troscopy technique. The obtained Ir isotope distribution was compared with those obtained in other experiment as well as calculated by the statistical model.
文摘We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenvalue of the free fermion Dirac operator as same as the result by [Hajime Aoki, Satoshi Iso, and Kelichi Nagao, Phys. Rev.D67 (2003) 065018]. Meanwhile, we also give the eigenvalue of Dirac operator with U(1) Dirac monopole background.
文摘For each of the Lie algebras gln and gl~n., we construct a family of integrable generalizations of the Toda chains characterized by two integers m+ and m-. The Lax matrices and the equations of motion are given explicitly, and the integrals of motion can be calculated in terms of the trace of powers of the Lax matrix L. For the case of m+ = m-,we find a symmetric reduction for each generalized Toda chain we found, and the solution to the initial value problems of the reduced systems is outlined. We also studied the spectral curves of the periodic (m+,m-)-Toda chains, which turns out to be very different for different pairs of m+ and m-. Finally we also obtain thenonabelian generalizations of the (m+, m-)-Toda chains in an explicit form.