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 this paper,we innovatively adopt the shadow radius to investigate the thermodynamics of an AdS black hole with non-commutative geometry terms.First,via geodesic analysis,we establish a quantitative relationship bet...In this paper,we innovatively adopt the shadow radius to investigate the thermodynamics of an AdS black hole with non-commutative geometry terms.First,via geodesic analysis,we establish a quantitative relationship between the shadow radius and the event horizon radius,and derive the shadow radius of the black hole as a function of the event horizon radius,which exhibits a positive correlation between the two quantities.Furthermore,within the shadow framework,we find that the stability and heat capacity of the black hole can be effectively represented through the shadow radius.Further analysis reveals that the results obtained using the shadow radius in revealing the black hole phase transition process are essentially consistent with those obtained using the event horizon.Based on this,we constructed the thermal profile for an AdS black hole incorporating non-commutative parameters.Within the framework of non-commutative geometry,for P<Pc,the temperature derived from the shadow radius exhibits a distinct N-shaped trend,which is in perfect agreement with that obtained from the event horizon radius.This result reveals that even in non-commutative spacetime,the phase transition process of AdS black holes can be effectively and intuitively characterized by the thermal profiles of their shadows.展开更多
In this paper, we study the thermodynamics of Schwarzschild-anti-de Sitter black holes within the framework of non-commutative geometry. By solving the Einstein equation, we derive the corrected Schwarzschild-AdS blac...In this paper, we study the thermodynamics of Schwarzschild-anti-de Sitter black holes within the framework of non-commutative geometry. By solving the Einstein equation, we derive the corrected Schwarzschild-AdS black hole with Lorentzian distribution and analyze the thermodynamics. Our results confirm that if the energy-momentum tensor outside the event horizon is related to the mass of the black hole, the conventional first law of thermodynamics will be violated. The study of criticality reveals that the black hole undergoes a small black hole-large black hole phase transition similar to that of the Van der Waals system, with a critical point and critical ratio slightly smaller than that of the Van der Waals fluid. As the non-commutative parameter increases, the phase transition process shortens, leading to a critical point, and ultimately to the disappearance of the phase transition. The violation of the conventional first law results in a discontinuity of the Gibbs free energy during the phase transition, indicating the occurrence of zeroth-order phase transition. Moreover, we investigate the Joule-Thomson expansion, obtaining the minimum inversion temperature and minimum inversion mass.展开更多
The shallow slip deficit(SSD)during strike-slip earthquakes raises a question of how the strain budget is accommodated over multiple cycles.However,the origin of variable SSD observed in different earthquakes is still...The shallow slip deficit(SSD)during strike-slip earthquakes raises a question of how the strain budget is accommodated over multiple cycles.However,the origin of variable SSD observed in different earthquakes is still under debate because each earthquake has its unique initial stress condition.Here,we derive the slip model of the 2021 M_(W) 7.4 Maduo earthquake in Qinghai,China,using multi-track radar images.Our results revealed that,in contrast to the large SSD on segments close to the epicenter,a much smaller SSD was observed at the west terminus of the rupture,where aftershock distribution indicates that the fault changes dip direction at 6 km depth.The 2021 Maduo earthquake thus represents an extraordinary case of significant along-strike SSD variation.After accounting for interseismic,postseismic,and diffuse off-fault deformation,we find that this variation is likely contributed by the along-dipping geometrical variation,implying that a multi-segment earthquake may leave heterogeneous stress condition on the fault with different amounts of SSD.展开更多
The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor...The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor(QGT),another important concept in the field of quantum geometry.The DWZC is Hermitian with respect to the two integer indices,just like the original Hermitian WZC.Based on the symmetric logarithmic derivative operator,we propose a mixed-state quantum geometric tensor.Using the symmetric properties of the DWZC,we find that the real part of the QGT is connected to the real part of the DWZC and the square of eigenvalue differences of the density matrix,whereas the imaginary part can be given in terms of the imaginary part of the DWZC and the cube of the eigenvalue differences.For density matrices with full rank or no full rank,the QGT can be given in terms of real and imaginary parts of the DWZC.展开更多
The calculation of viewing and solar geometry angles is a critical first step in retrieving atmospheric and surface variables from geostationary satellite observations.Whereas the viewing angles for geostationary sate...The calculation of viewing and solar geometry angles is a critical first step in retrieving atmospheric and surface variables from geostationary satellite observations.Whereas the viewing angles for geostationary satellites are not timevarying,a primary source of inaccuracy in solar positioning is the use of a single timestamp.Since pixel scanning times can differ significantly across the field-of-view disk(e.g.,by approximately 13 min for Fengyun-4B),this practice leads to errors of up to±2°in solar zenith angle,which translates to±50 W m^(−2) in extraterrestrial irradiance;the errors in solar azimuth angle can exceed±100°.Beyond scanning time,this work also quantifies the impact of other inputs—including altitude,surface pressure,air temperature,difference between Terrestrial Time and Universal Time,and atmospheric refraction—on the resulting angles.A comparison of our precise calculations with the official National Satellite Meteorological Center L1_GEO product shows an accuracy within 0.1°,confirming its utility for most retrieval tasks.To facilitate higher precision when required,this work releases the corresponding satellite and solar positioning codes in both R and Python.展开更多
This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New ...This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.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
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
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 effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a...The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains aterm corresponding to a Wess-Zumino-Witten-like term.展开更多
Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geomet...Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.展开更多
A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the resu...A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of ω/ωe and certain algebra realization （SU（2）and SU（1,1））, and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.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
In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time...In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.展开更多
This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings,denoted ΓI（R）.ΓI（R） is a directed graph.The properties and possible structures of the graph is studied.
For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld inva...For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.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
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
The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fed...The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.展开更多
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Sichuan Province Science and Education Joint Key Project(Project No.:25LHJJ0097)。
文摘In this paper,we innovatively adopt the shadow radius to investigate the thermodynamics of an AdS black hole with non-commutative geometry terms.First,via geodesic analysis,we establish a quantitative relationship between the shadow radius and the event horizon radius,and derive the shadow radius of the black hole as a function of the event horizon radius,which exhibits a positive correlation between the two quantities.Furthermore,within the shadow framework,we find that the stability and heat capacity of the black hole can be effectively represented through the shadow radius.Further analysis reveals that the results obtained using the shadow radius in revealing the black hole phase transition process are essentially consistent with those obtained using the event horizon.Based on this,we constructed the thermal profile for an AdS black hole incorporating non-commutative parameters.Within the framework of non-commutative geometry,for P<Pc,the temperature derived from the shadow radius exhibits a distinct N-shaped trend,which is in perfect agreement with that obtained from the event horizon radius.This result reveals that even in non-commutative spacetime,the phase transition process of AdS black holes can be effectively and intuitively characterized by the thermal profiles of their shadows.
文摘In this paper, we study the thermodynamics of Schwarzschild-anti-de Sitter black holes within the framework of non-commutative geometry. By solving the Einstein equation, we derive the corrected Schwarzschild-AdS black hole with Lorentzian distribution and analyze the thermodynamics. Our results confirm that if the energy-momentum tensor outside the event horizon is related to the mass of the black hole, the conventional first law of thermodynamics will be violated. The study of criticality reveals that the black hole undergoes a small black hole-large black hole phase transition similar to that of the Van der Waals system, with a critical point and critical ratio slightly smaller than that of the Van der Waals fluid. As the non-commutative parameter increases, the phase transition process shortens, leading to a critical point, and ultimately to the disappearance of the phase transition. The violation of the conventional first law results in a discontinuity of the Gibbs free energy during the phase transition, indicating the occurrence of zeroth-order phase transition. Moreover, we investigate the Joule-Thomson expansion, obtaining the minimum inversion temperature and minimum inversion mass.
基金the Deep Earth Probe and Mineral Resources Exploration-National Science and Technology Major Project under Grant 2024ZD1000500。
文摘The shallow slip deficit(SSD)during strike-slip earthquakes raises a question of how the strain budget is accommodated over multiple cycles.However,the origin of variable SSD observed in different earthquakes is still under debate because each earthquake has its unique initial stress condition.Here,we derive the slip model of the 2021 M_(W) 7.4 Maduo earthquake in Qinghai,China,using multi-track radar images.Our results revealed that,in contrast to the large SSD on segments close to the epicenter,a much smaller SSD was observed at the west terminus of the rupture,where aftershock distribution indicates that the fault changes dip direction at 6 km depth.The 2021 Maduo earthquake thus represents an extraordinary case of significant along-strike SSD variation.After accounting for interseismic,postseismic,and diffuse off-fault deformation,we find that this variation is likely contributed by the along-dipping geometrical variation,implying that a multi-segment earthquake may leave heterogeneous stress condition on the fault with different amounts of SSD.
基金Project supported by Quantum Science and Technology–National Science and Technology Major Project(Grant No.2024ZD0301000)the National Natural Science Foundation of China(Grant No.12305031)+1 种基金the Hangzhou Joint Fund of the Natural Science Foundation of Zhejiang Province,China(Grant No.LHZSD24A050001)the Science Foundation of Zhejiang Sci-Tech University(Grant Nos.23062088Y and 23062153-Y)。
文摘The Wilczek–Zee connection(WZC)is a key concept in the study of topology of quantum systems.Here,we introduce the double Wilczek–Zee connection(DWZC)which naturally appears in the pure-state quantum geometric tensor(QGT),another important concept in the field of quantum geometry.The DWZC is Hermitian with respect to the two integer indices,just like the original Hermitian WZC.Based on the symmetric logarithmic derivative operator,we propose a mixed-state quantum geometric tensor.Using the symmetric properties of the DWZC,we find that the real part of the QGT is connected to the real part of the DWZC and the square of eigenvalue differences of the density matrix,whereas the imaginary part can be given in terms of the imaginary part of the DWZC and the cube of the eigenvalue differences.For density matrices with full rank or no full rank,the QGT can be given in terms of real and imaginary parts of the DWZC.
基金supported by the National Natural Science Foundation of China(Grant No.42375192).
文摘The calculation of viewing and solar geometry angles is a critical first step in retrieving atmospheric and surface variables from geostationary satellite observations.Whereas the viewing angles for geostationary satellites are not timevarying,a primary source of inaccuracy in solar positioning is the use of a single timestamp.Since pixel scanning times can differ significantly across the field-of-view disk(e.g.,by approximately 13 min for Fengyun-4B),this practice leads to errors of up to±2°in solar zenith angle,which translates to±50 W m^(−2) in extraterrestrial irradiance;the errors in solar azimuth angle can exceed±100°.Beyond scanning time,this work also quantifies the impact of other inputs—including altitude,surface pressure,air temperature,difference between Terrestrial Time and Universal Time,and atmospheric refraction—on the resulting angles.A comparison of our precise calculations with the official National Satellite Meteorological Center L1_GEO product shows an accuracy within 0.1°,confirming its utility for most retrieval tasks.To facilitate higher precision when required,this work releases the corresponding satellite and solar positioning codes in both R and Python.
文摘This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.
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.
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.
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 effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by usingpath integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains aterm corresponding to a Wess-Zumino-Witten-like term.
文摘Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.
基金Supported by the National Natural Science Foundation of China under Grant No 10575026, and the Natural Science Foundation of Zhejiang Provence under Grant No Y607437.
文摘A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of ω/ωe and certain algebra realization （SU（2）and SU（1,1））, and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.
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.
文摘In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.
基金Supported by Guangxi Natural Sciences Foundation(0575052,0640070)Supported byInnovation Project of Guangxi Graduate Education(2006106030701M05)Supported Scientific Research Foun-dation of Guangxi Educational Committee
文摘This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings,denoted ΓI（R）.ΓI（R） is a directed graph.The properties and possible structures of the graph is studied.
文摘For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.
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 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.
文摘The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.
