In this study,we comprehensively investigated charged AdS black holes surrounded by a distinct form of dark matter.In particular,we focused on key elements including the Hawking temperature,quasi-normal modes(QNMs),em...In this study,we comprehensively investigated charged AdS black holes surrounded by a distinct form of dark matter.In particular,we focused on key elements including the Hawking temperature,quasi-normal modes(QNMs),emission rate,and shadow.We first calculated the Hawking temperature,thereby identifying critical values such as the critical radius and maximum temperature of the black hole,essential for determining its phase transition.Further analysis focused on the QNMs of charged AdS black holes immersed in perfect fluid dark matter(PFDM)within the massless scalar field paradigm.Employing the Wentzel-Kramers-Brillouin(WKB)method,we accurately derived the frequencies of these QNMs.Additionally,we conducted a meticulous assessment of how the intensity of the PFDM parameterαinfluences the partial absorption cross sections of the black hole,along with a detailed study of the frequency variation of the energy emission rate.The pivotal role of geodesics in understanding astrophysical black hole characteristics is highlighted.Specifically,we examined the influence of the dark matter parameter on photon evolution by computing the shadow radius of the black hole.Our findings distinctly demonstrate the significant impact of the PFDM parameterαon the boundaries of this shadow,providing crucial insights into its features and interactions.We also provide profound insights into the intricate dynamics between a charged AdS black hole,novel dark matter,and various physical phenomena,elucidating their interplay and contributing valuable knowledge to the understanding of these cosmic entities.展开更多
Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated...Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated using the operator form of Taylor＇s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e.l＇ ≠ k＇ and m＇≠ n＇ .Their selection rules are a/so given. We also verify the correctness of those integral formulas numerically.展开更多
The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the pha...The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.展开更多
Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independen...Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.展开更多
The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hype...The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.展开更多
A Fermi resonance-algebraic model is proposed for molecular vibrations, where aU(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into ...A Fermi resonance-algebraic model is proposed for molecular vibrations, where aU(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent moleculeXY 2 and a moleculeXY 3 is successfully applied to fitting the recently obsenred vibrational spectrum of the water molecule and arsine (AsH3), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations.展开更多
The bound state solutions of the Klein-Gordon equation with the rotating Deng-Fan molecular potential are presented by using a proper approximation to the centrifugal term within the framework of equal scalar and vect...The bound state solutions of the Klein-Gordon equation with the rotating Deng-Fan molecular potential are presented by using a proper approximation to the centrifugal term within the framework of equal scalar and vector Deng-Fan potentials. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.展开更多
The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a n...The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[（p）], It is interesting to see that the [~ （p）[ is symmetric with respect to the axis p = 0 and the number of wave crest of [ （p）[ is equal to n ＋ 1. We also study the variation of ]k（p）l with respect to . The arnplitude of ｜ψ（p）] first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments.展开更多
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂L...Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂Landau＂ potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.展开更多
A U(2)algebraic model is used to explain the stretching and bending vibrational spectrum of methane,where the interactions between the stretching and the bending modes are taken into account.This model provides good f...A U(2)algebraic model is used to explain the stretching and bending vibrational spectrum of methane,where the interactions between the stretching and the bending modes are taken into account.This model provides good fits to the experimental vibrational eigenvalues with the smaller standard deviations of 9.57 and 9.08 cm^(-1) than those in other published algebraic models.展开更多
We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. ...We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.展开更多
Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acc...Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π_(4) and geometric average Π_(4) is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter γ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S_(ABCDI), S_(ABCIDI), S_(ABICIDI) and S_(AIBICIDI) always decrease with the controllable angle θ, while the entropies S_(3-3 non), S_(3-2 non), S_(3-1 non) and S_(3-0 non) first increase with the angle θ and then decrease with it.展开更多
We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation in...We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.展开更多
In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be c...In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).展开更多
基金Supported by the Doctoral Foundation of Zunyi Normal University of China(BS[2022]07,QJJ-[2022]-314)the National Natural Science Foundation of China(12265007)+1 种基金supported by 20230316 and 20240220-SIP-IPN,Mexico,and began this work with permission from IPN for a research stay in Chinapartially supported by the Long-Term Conceptual Development of a University of Hradec Kralove for 2023,issued by the Ministry of Education,Youth,and Sports of the Czech Republic。
文摘In this study,we comprehensively investigated charged AdS black holes surrounded by a distinct form of dark matter.In particular,we focused on key elements including the Hawking temperature,quasi-normal modes(QNMs),emission rate,and shadow.We first calculated the Hawking temperature,thereby identifying critical values such as the critical radius and maximum temperature of the black hole,essential for determining its phase transition.Further analysis focused on the QNMs of charged AdS black holes immersed in perfect fluid dark matter(PFDM)within the massless scalar field paradigm.Employing the Wentzel-Kramers-Brillouin(WKB)method,we accurately derived the frequencies of these QNMs.Additionally,we conducted a meticulous assessment of how the intensity of the PFDM parameterαinfluences the partial absorption cross sections of the black hole,along with a detailed study of the frequency variation of the energy emission rate.The pivotal role of geodesics in understanding astrophysical black hole characteristics is highlighted.Specifically,we examined the influence of the dark matter parameter on photon evolution by computing the shadow radius of the black hole.Our findings distinctly demonstrate the significant impact of the PFDM parameterαon the boundaries of this shadow,providing crucial insights into its features and interactions.We also provide profound insights into the intricate dynamics between a charged AdS black hole,novel dark matter,and various physical phenomena,elucidating their interplay and contributing valuable knowledge to the understanding of these cosmic entities.
文摘Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated using the operator form of Taylor＇s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e.l＇ ≠ k＇ and m＇≠ n＇ .Their selection rules are a/so given. We also verify the correctness of those integral formulas numerically.
基金Project supported by the National Natural Science Foundation of China(Grant No.11275165)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010291)partly by Secretaria de Investigacio'ny Posgrado de Instituto Polite'cnico Nacional,Mexico(Grant No.20131150-SIP-IPN)
文摘The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.
基金Supported in part by Project 20150964-SIP-IPN,COFAA-IPN,Mexico
文摘Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.
基金Supported Partly by Projects 20120876-SIP-IPN and COFAA-IPN,Mexico
文摘The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19377103)the Chinese Academy of Sciences
文摘A Fermi resonance-algebraic model is proposed for molecular vibrations, where aU(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent moleculeXY 2 and a moleculeXY 3 is successfully applied to fitting the recently obsenred vibrational spectrum of the water molecule and arsine (AsH3), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations.
基金Supported partly by Projects 20110491-SIP-IPN and COFAA-IPN,Mexico
文摘The bound state solutions of the Klein-Gordon equation with the rotating Deng-Fan molecular potential are presented by using a proper approximation to the centrifugal term within the framework of equal scalar and vector Deng-Fan potentials. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.
基金Supported partially by 20120876-SIP-IPN, COFAA-IPN, Mexico
文摘The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[（p）], It is interesting to see that the [~ （p）[ is symmetric with respect to the axis p = 0 and the number of wave crest of [ （p）[ is equal to n ＋ 1. We also study the variation of ]k（p）l with respect to . The arnplitude of ｜ψ（p）] first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments.
基金Project supported by the National Natural Science Foundation of China(Grant No.11375005)partially by 20150964-SIP-IPN,Mexico
文摘Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂Landau＂ potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.
基金Supported by the Climbing Program(8507)of Chinese National Commission of Science and Technologythe Grant No.LWTZ-1298 of the Chinese Academy of Sciences.
文摘A U(2)algebraic model is used to explain the stretching and bending vibrational spectrum of methane,where the interactions between the stretching and the bending modes are taken into account.This model provides good fits to the experimental vibrational eigenvalues with the smaller standard deviations of 9.57 and 9.08 cm^(-1) than those in other published algebraic models.
基金Supported by the National Natural Science Foundation of China under Grant No.11275165partly by 20140772-SIP-IPN,Mexico
文摘We study the mathematical characteristics of the super-universal associated-Legendre polynomials arising from a kind of double ring-shaped potentials and obtain their polar angular wave functions with certain parity. We find that there exists the even or odd parity for the polar angular wave functions when the parameter η is taken to be positive integer, while there exist both even and odd parities when η is taken as positive non-integer real values. The relations among the super-universal associated-Legendre polynomials, the hypergeometric polynomials, and the Jacobi polynomials are also established.
基金partially supported by the 20210414-SIPIPN, Mexico。
文摘Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π_(4) and geometric average Π_(4) is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter γ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S_(ABCDI), S_(ABCIDI), S_(ABICIDI) and S_(AIBICIDI) always decrease with the controllable angle θ, while the entropies S_(3-3 non), S_(3-2 non), S_(3-1 non) and S_(3-0 non) first increase with the angle θ and then decrease with it.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975196)partially by SIP,Instituto Politecnico Nacional(IPN),Mexico(Grant No.20210414)。
文摘We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.
基金Supported by the project under Grant No.20180677-SIP-IPN,COFAA-IPN,Mexicopartially by the CONACYT project under Grant No.288856-CB-2016
文摘In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).
