The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutativ...The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.展开更多
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
In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presen...In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric function. It is shown that in the non-commutative space, the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.展开更多
The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as th...The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further, we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures, the occurrence of the magnetization in a zero magnetic field and zero temperature limit, and so on.展开更多
This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole...This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.展开更多
In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the b...In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.展开更多
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equ...We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.展开更多
This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived...This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.展开更多
This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1...This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1] [2]. The paper describes how these non-associative and non commutative properties can be established by using the Cayley table on which a binary operation is defined to act on the 123-avoiding and 132-avoiding patterns of Aunu permutations using a pairing scheme. Our results have generated larger matrices from permutations of points of the Aunu patterns of prime cardinality. It follows that the generated symbols can be used in further studies and analysis in cryptography and game theory thereby providing an interdisciplinary approach and applications of these important permutation patterns.展开更多
In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum...In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation （Phys. Rev. D, 2005, 72： 025010）. The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.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
Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storag...Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storage and access,our proposed work designs a Novel Quantum Key Distribution(QKD)relying upon a non-commutative encryption framework.It makes use of a Novel Quantum Key Distribution approach,which guarantees high level secured data transmission.Along with this,a shared secret is generated using Diffie Hellman(DH)to certify secured key generation at reduced time complexity.Moreover,a non-commutative approach is used,which effectively allows the users to store and access the encrypted data into the cloud server.Also,to prevent data loss or corruption caused by the insiders in the cloud,Optimized Genetic Algorithm(OGA)is utilized,which effectively recovers the data and retrieve it if the missed data without loss.It is then followed with the decryption process as if requested by the user.Thus our proposed framework ensures authentication and paves way for secure data access,with enhanced performance and reduced complexities experienced with the prior works.展开更多
Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commutin...Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90303003 and 10575026） and the Natural Science Foundation of Zhejiang Province, China （Grant No M103042）.
文摘The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
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National Natural Science Foundation of China(10347003,60666001)Planned Training Excellent Scientific and Technological Youth Foundation of Guizhou Province,China(2002,2013)Science Foundation of Guizhou Province,China,and Creativity Foundation for Graduate Guizhou University,China(2006031)
文摘In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric function. It is shown that in the non-commutative space, the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.
基金supported by the National Natural Science Foundation of China (Grant Nos 10575026 and 10875035)the Natural Science Foundation of Zhejiang Province,China (Grant No Y607437)
文摘The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further, we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures, the occurrence of the magnetization in a zero magnetic field and zero temperature limit, and so on.
基金DST,New Delhi,India,for its financial support for research facilities under DSTFIST-2019。
文摘This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.
基金the National Natural Science Foundation of China (Grant No. 10375008) the National Basic Research Program of China (Grant No. 2003CB716300)
文摘In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.
基金Supported by National Natural Science Foundation of China(Grant No.10971206)
文摘We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.
文摘This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.
文摘This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1] [2]. The paper describes how these non-associative and non commutative properties can be established by using the Cayley table on which a binary operation is defined to act on the 123-avoiding and 132-avoiding patterns of Aunu permutations using a pairing scheme. Our results have generated larger matrices from permutations of points of the Aunu patterns of prime cardinality. It follows that the generated symbols can be used in further studies and analysis in cryptography and game theory thereby providing an interdisciplinary approach and applications of these important permutation patterns.
基金National Natural Science Foundation of China(10347003,60666001)Planned Training Excellent Scientific Technological Youth Foundation of Guizhou Province,China(2002,2013)Science Foundation of Guizhou Province,China Creativity Foundation for Graduate Guizhou University,China(2006031)
文摘In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation （Phys. Rev. D, 2005, 72： 025010）. The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.
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Nowadays,succeeding safe communication and protection-sensitive data from unauthorized access above public networks are the main worries in cloud servers.Hence,to secure both data and keys ensuring secured data storage and access,our proposed work designs a Novel Quantum Key Distribution(QKD)relying upon a non-commutative encryption framework.It makes use of a Novel Quantum Key Distribution approach,which guarantees high level secured data transmission.Along with this,a shared secret is generated using Diffie Hellman(DH)to certify secured key generation at reduced time complexity.Moreover,a non-commutative approach is used,which effectively allows the users to store and access the encrypted data into the cloud server.Also,to prevent data loss or corruption caused by the insiders in the cloud,Optimized Genetic Algorithm(OGA)is utilized,which effectively recovers the data and retrieve it if the missed data without loss.It is then followed with the decryption process as if requested by the user.Thus our proposed framework ensures authentication and paves way for secure data access,with enhanced performance and reduced complexities experienced with the prior works.
基金The NSF(11301150,11371124)of Chinathe NSF(142300410134)of Henan ProvincePlan for Scientific Innovation Talent(11CXRC19)of Henan University of Technology
文摘Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If ｜X｜ ≥ ｜Y｜ for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.
