In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spec...In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spectrum of the condensate, it indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter 8. The gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.展开更多
In this paper,using Hamiltonian formalism,we obtain solutions for constant-roll inflation according to the noncommutativity and the non-minimal coupling field of the Lagrangian.We consider three different types of cou...In this paper,using Hamiltonian formalism,we obtain solutions for constant-roll inflation according to the noncommutativity and the non-minimal coupling field of the Lagrangian.We consider three different types of couplings:power-law,exponential,and logarithmic.Subsequently,by plotting some figures,we study the effects of these coupling in constant-roll inflation with noncommutative parameters.We identify and specify the permissible regions of each case of the swampland conjecture and determine the best model.We find that the exponential,logarithmic,and power-law couplings with agree with the dS swampland conjecture.These couplings provide similar results in both cases,some of which are compatible and some incompatible with the dS swampland conjectures.Moreover,is more compatible than,and the consistency value in the second boundary condition is much higher than in the first.The order of better compatibility of couplings with the swampland conjecture is ranked as follows:exponential non-minimal coupling,logarithmic non-minimal coupling,and power-law non-minimal coupling.For each type of coupling,we calculate the values of the scalar spectral index and the tensor-to-scalar ratio r for two different potentials and compare them with the observational data from Planck 2018.We also determine the range of the free parameters of the further refining de Sitter swampland conjecture(FRDSSC)that make the model consistent with the conjecture.We find that the model satisfies the FRDSSC for all types of couplings and both potentials,with some constraints on the parameters.展开更多
For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct ...For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.展开更多
We discuss how to generate a dynamical Dp-brane with a topology of R^(p-2)×S^(2) from N D(p-2)-branes with R^(p-2) topology with or without the presence of a constant RR(p+2)-form flux.This extends the previous w...We discuss how to generate a dynamical Dp-brane with a topology of R^(p-2)×S^(2) from N D(p-2)-branes with R^(p-2) topology with or without the presence of a constant RR(p+2)-form flux.This extends the previous work(Chen and Lu 2004 arXiv:hep-th/0405265)of generating a dynamical spherical D2 brane from N DO branes in a constant RR four-form flux to a general p.In particular,dynamically generating a higher dimensional brane from lower dimensional ones does not necessarily need the presence of a relevant RR background flux but needs excess energy,lending support to the spacetime uncertainty principle.The time evolution of the dynamical p-brane for a general p remains the same as for the p=2 case,however there is a class of spatial dependent Dp configurations when p≥3.Some of these spatial-dependent Dp brane configurations and their properties have been discussed previously which can also be obtained from the time-dependent one by euclideanizing the time.Properties of the spatial-dependent solutions and their relations to the corresponding brane-anti brane system are discussed.展开更多
Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity.The m...Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity.The models include the bosonized chiral Schwinger model,the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation.We establish the Lagrangian theories of the models,and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion,and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach.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
Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M...Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.展开更多
Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSding...Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.展开更多
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
Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp...Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.展开更多
In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe ...In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.展开更多
We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizont...We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.展开更多
By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As a...By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.展开更多
In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusio...In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.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 H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm...Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.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
Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on...Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.展开更多
Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some ...Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.展开更多
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10174086. Luo greatly appreciates Prof. J.Z. Zhang for valuable discussions.
文摘In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spectrum of the condensate, it indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter 8. The gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.
文摘In this paper,using Hamiltonian formalism,we obtain solutions for constant-roll inflation according to the noncommutativity and the non-minimal coupling field of the Lagrangian.We consider three different types of couplings:power-law,exponential,and logarithmic.Subsequently,by plotting some figures,we study the effects of these coupling in constant-roll inflation with noncommutative parameters.We identify and specify the permissible regions of each case of the swampland conjecture and determine the best model.We find that the exponential,logarithmic,and power-law couplings with agree with the dS swampland conjecture.These couplings provide similar results in both cases,some of which are compatible and some incompatible with the dS swampland conjectures.Moreover,is more compatible than,and the consistency value in the second boundary condition is much higher than in the first.The order of better compatibility of couplings with the swampland conjecture is ranked as follows:exponential non-minimal coupling,logarithmic non-minimal coupling,and power-law non-minimal coupling.For each type of coupling,we calculate the values of the scalar spectral index and the tensor-to-scalar ratio r for two different potentials and compare them with the observational data from Planck 2018.We also determine the range of the free parameters of the further refining de Sitter swampland conjecture(FRDSSC)that make the model consistent with the conjecture.We find that the model satisfies the FRDSSC for all types of couplings and both potentials,with some constraints on the parameters.
基金supported by the National Natural Science Foundation of China under Grant No.12071237KC Wong Magna Fund in Ningbo University。
文摘For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.
基金The author would like to thank J X Lu for fruitful discussion and acknowledge support by a grant from the NNSF of China with Grant No:11775212.
文摘We discuss how to generate a dynamical Dp-brane with a topology of R^(p-2)×S^(2) from N D(p-2)-branes with R^(p-2) topology with or without the presence of a constant RR(p+2)-form flux.This extends the previous work(Chen and Lu 2004 arXiv:hep-th/0405265)of generating a dynamical spherical D2 brane from N DO branes in a constant RR four-form flux to a general p.In particular,dynamically generating a higher dimensional brane from lower dimensional ones does not necessarily need the presence of a relevant RR background flux but needs excess energy,lending support to the spacetime uncertainty principle.The time evolution of the dynamical p-brane for a general p remains the same as for the p=2 case,however there is a class of spatial dependent Dp configurations when p≥3.Some of these spatial-dependent Dp brane configurations and their properties have been discussed previously which can also be obtained from the time-dependent one by euclideanizing the time.Properties of the spatial-dependent solutions and their relations to the corresponding brane-anti brane system are discussed.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11175090the Fundamental Research Funds for the Central Universities under Grant No.65030021the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences under Grant No.KJCX2.YW.W10
文摘Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity.The models include the bosonized chiral Schwinger model,the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation.We establish the Lagrangian theories of the models,and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion,and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach.
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 (11071190)
文摘Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.
基金The project supported by Tianyuan Foundation for Mathematics under Grant No. 10626016 of National Natural Science Foundation of China, China Postdoctoral Science Foundation, Beijing Jiao-Wei Key Project under Grant No. KZ 200310028010, and National Natural Science Foundation of China under Grant No. 10375038
文摘Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
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.
文摘Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.
基金Supported by National Natural Science Foundation of China under Grant No.10801027Fok Ying Tong Education Foundation under Grant No.121003
文摘In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.
基金The project supported by National Natural Science Foundation of China under Grant No.10626016China Postdoctor Science Foundation of Henan University under Grant No.05YBZR014
文摘We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.
基金Supported by the China Pcetdoctoral Science Foundation by a grant from Henan University(05YBZR014)Supported by the Tianyuan Foundation for Mathematics of National Natural Science Foundation of China(10626016)
文摘By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.
文摘In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.
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partly supported by Natural Science Foundation of the Xinjiang Uygur Autonomous Region(2013211A001)
文摘Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.
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.
基金This work is partially supported by NNSF of China(10671124)the Specialized Research Fund for the Doctoral Program of Higher Education(20040247024).
文摘Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.
基金Supported by the National Natural Science Foundation of China under Grant No.11071157Shanghai Leading Academic Discipline Project under Grant No.J50101Beijing Natural Science Foundation under Grant No.1101024 and PHR(IHLB)
文摘Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.
