The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum f...The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.展开更多
Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
In this paper,we study the time-dependent Aharonov-Casher effect and its corrections due to spatial noncommutativity.Given that the charge of the infinite line in the Aharonov-Casher effect can adiabatically vary with...In this paper,we study the time-dependent Aharonov-Casher effect and its corrections due to spatial noncommutativity.Given that the charge of the infinite line in the Aharonov-Casher effect can adiabatically vary with time,we show that the original Aharonov-Casher phase receives an adiabatic correction,which is characterized by the time-dependent charge density.Based on Seiberg-Witten map,we show that noncommutative corrections to the time-dependent Aharonov-Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.展开更多
The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The expli...The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.展开更多
In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the ...In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.展开更多
We study the Dirac oscillator problem in the presence of the Aharonov-Bohm effect with the harmonic potential in commutative and noncommutative spaces in S-= V and S =-V symmetry limits. We calculate exact energy leve...We study the Dirac oscillator problem in the presence of the Aharonov-Bohm effect with the harmonic potential in commutative and noncommutative spaces in S-= V and S =-V symmetry limits. We calculate exact energy levels and the corresponding eigenfunctions by the Nikiforov-Uvarov （NU） method and report the impact of the spin and the magnetic flux on the problem. Helpful numerical data is included.展开更多
We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in t...We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.展开更多
In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix paramet...In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix parameter β_(ij)=∈_(ij)~kβ_k,is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS).Imposing some constraints on this particular transformation,we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations,and secondly that the two parameters are equivalent but with opposite sign,up to a dimension factor depending on the physical system under study.This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS.Within our framework,we treat some physical systems on NCQPS:free particle,harmonic oscillator,system of two-charged particles,Hydrogen atom.Among the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,representing the same particle in presence of a magnetic field=q~(-1).For the other examples,additional correction terms depending on β appear in the expression of the energy spectrum.Finally,in the two-particle system case,we emphasize the fact that for two opposite charges noncornmutativity is effectively feeled with opposite sign.展开更多
Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated...Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.展开更多
All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as ...All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.展开更多
The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphat...The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative(NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.展开更多
First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmoment...First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).展开更多
A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed;in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommu...A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed;in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommutative phase-space are investigated and the Schrödinger-Pauli equation is found, knowing that the used methods for extracting the full phase-space noncommutative Dirac equation are, the Bopp-shift linear translation method, and the Moyal-Weyl product (*-product).展开更多
We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state repres...We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.展开更多
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously inclu...The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of deformed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.展开更多
基金Supported by the Natural Science Foundation of Sichuan Education Committee under Grant No.08ZA038
文摘The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
基金supported by the Innovation Capability Support Program of Shaanxi Province(Program No.2021KJXX-47)
文摘In this paper,we study the time-dependent Aharonov-Casher effect and its corrections due to spatial noncommutativity.Given that the charge of the infinite line in the Aharonov-Casher effect can adiabatically vary with time,we show that the original Aharonov-Casher phase receives an adiabatic correction,which is characterized by the time-dependent charge density.Based on Seiberg-Witten map,we show that noncommutative corrections to the time-dependent Aharonov-Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11465006 and 11565009)the Project of Research Foundation for Graduate Students in Guizhou Province,China(Grant No.(2017)11108)
文摘The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.
文摘In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.
文摘We study the Dirac oscillator problem in the presence of the Aharonov-Bohm effect with the harmonic potential in commutative and noncommutative spaces in S-= V and S =-V symmetry limits. We calculate exact energy levels and the corresponding eigenfunctions by the Nikiforov-Uvarov （NU） method and report the impact of the spin and the magnetic flux on the problem. Helpful numerical data is included.
文摘We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.
文摘In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix parameter β_(ij)=∈_(ij)~kβ_k,is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS).Imposing some constraints on this particular transformation,we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations,and secondly that the two parameters are equivalent but with opposite sign,up to a dimension factor depending on the physical system under study.This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS.Within our framework,we treat some physical systems on NCQPS:free particle,harmonic oscillator,system of two-charged particles,Hydrogen atom.Among the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,representing the same particle in presence of a magnetic field=q~(-1).For the other examples,additional correction terms depending on β appear in the expression of the energy spectrum.Finally,in the two-particle system case,we emphasize the fact that for two opposite charges noncornmutativity is effectively feeled with opposite sign.
基金supported by National Natural Science Foundation of China(Grant No.11371233)the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)
文摘Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.
基金The author was supported by grant No. 1999-2-102-001-3 from the interdis- ciplinary research program year of the KOSEF.
文摘All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11465006 and 11565009
文摘The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative(NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10965006 and 10875035
文摘First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).
文摘A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed;in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommutative phase-space are investigated and the Schrödinger-Pauli equation is found, knowing that the used methods for extracting the full phase-space noncommutative Dirac equation are, the Bopp-shift linear translation method, and the Moyal-Weyl product (*-product).
基金Supported by the National Natural Science Foundation of China under Grant Nos 11405060 and 11571119
文摘We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.
基金The project Supported by National Natural Science Foundation of China under Grant Nos. 10375056 and 90203002
文摘The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of deformed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.
