By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topologi...By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.展开更多
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mo...Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.展开更多
We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined t...We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.展开更多
The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, w...The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.展开更多
In this study,we construct a non-commtative gauge theory of the modified structure of the gravitational field using the Seiberg-Witten map and the general tetrad fields of Schwarzschild space-time to show that the non...In this study,we construct a non-commtative gauge theory of the modified structure of the gravitational field using the Seiberg-Witten map and the general tetrad fields of Schwarzschild space-time to show that the noncommutative geometry removes the singularity at the origin of the black hole,thus obtaining a non-singular Schwarzschild black hole.The geodetic structure of this black hole presents new types of motion next to the event horizon within stable orbits that are not allowed by the ordinary Schwarzschild spacetime.The noncommutative periastron advance of the Mercury orbit is obtained,and with the available experimental data,we find a parameter of non-commutativity on the order of 10^(-25)s·kg^(-1).This result shows that the new fundamental length,√h■,is on the order of 10^(-31)m.展开更多
Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determin...Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.展开更多
The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the mod...The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.展开更多
We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in b...We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces.By considering the Rashba interaction,we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space.We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling.Finally,we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.展开更多
First a description of 2＋1 dimensional non-commutative（NC） phase space is presented,and then we find that in this formulation the generalized Bopp＇s shift has a symmetric representation and one can easily and stra...First a description of 2＋1 dimensional non-commutative（NC） phase space is presented,and then we find that in this formulation the generalized Bopp＇s shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10575026, 10465004, 10665001 and 10447005)
文摘By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.
基金the President Foundation of the Chinese Academy of Sciencesthe Specialized Research Fund for the Doctoral Program of Higher Education
文摘Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.
文摘We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.
文摘The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.
基金Supported by PRFU Research Project(B00L02UN050120190001)Univ.Batna 1,Algeria。
文摘In this study,we construct a non-commtative gauge theory of the modified structure of the gravitational field using the Seiberg-Witten map and the general tetrad fields of Schwarzschild space-time to show that the noncommutative geometry removes the singularity at the origin of the black hole,thus obtaining a non-singular Schwarzschild black hole.The geodetic structure of this black hole presents new types of motion next to the event horizon within stable orbits that are not allowed by the ordinary Schwarzschild spacetime.The noncommutative periastron advance of the Mercury orbit is obtained,and with the available experimental data,we find a parameter of non-commutativity on the order of 10^(-25)s·kg^(-1).This result shows that the new fundamental length,√h■,is on the order of 10^(-31)m.
基金the Shanghai Science and Technology Commission, No. 01ZA14003.
文摘Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
基金Supported by the China Scholarship Councilthe Hanjiang Scholar Project of Shaanxi University of Technology
文摘The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.
基金the National Elites Foundation(INEF),Iran for financial support under research project No.15/6072。
文摘We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces.By considering the Rashba interaction,we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space.We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling.Finally,we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.
基金Supported by National Natural Science Foundation of China( 10875035,10965006)Natural Science Foundation of Zhejiang Provence (Y607437)
文摘First a description of 2＋1 dimensional non-commutative（NC） phase space is presented,and then we find that in this formulation the generalized Bopp＇s shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space.
基金Open Topic of State Key Laboratory for Superlattices and Microstructures(CHJG200902)Scientific Research Project in Shaanxi Province(2009K01-54)Foundation of Shanxi University of Technology(SLGKY10-02)~~
