Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits...Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.展开更多
In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of...In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.展开更多
Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path...Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.展开更多
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wi...A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito' s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.展开更多
We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman ...We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schioberg potential. The obtained results are compared to those produced by other methods and are found to be consistent.展开更多
The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally average...The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.展开更多
We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point(i.e.,the origi...We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point(i.e.,the origin) to the forced point in the biopolymer,with arclength L_f.The second part consists of the segment counted from the forced point to the force-free end with arclength △L.We apply the path integral technique to find the relationship between these two parts.At finite temperature and without any constraint at the end,we show exactly that if we focus on the quantities related to the first part,then we can ignore the second part completely.Monte Carlo simulation confirms this conclusion.In contrast,the effect for the quantities related to the second part is dependent on what we want to observe.A force-free end has little effect on the relative extension,but it affects seriously the value of the end-to-end distance if △L is comparable to L_f.展开更多
Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangle...Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangled state representation is presented. Its advantages are explained.展开更多
As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon ...As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.展开更多
A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic ...A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites <em>n</em> when <em>β </em><em></em><span></span>→ 0.展开更多
We have investigated the effects of compression and quantization on atomic distribution in ice Ic and in its compressed states at 77 K and 10 K, using the path integral molecular dynamics (PIMD) simulations over wide ...We have investigated the effects of compression and quantization on atomic distribution in ice Ic and in its compressed states at 77 K and 10 K, using the path integral molecular dynamics (PIMD) simulations over wide range of volume. It has been found that the high density amorphous ice (HDA) is attained by compression but volume range to retain ice structure is wider at 10 K than 77 K. We have discovered that quantum dispersion of atoms in ice Ic at 10 K induces non-zero probability that hydrogen-bonded H<sub>2</sub>O molecular molecules are oriented nonlinearly in the crystal structure, which was believed to contain exclusively linear orientation of hydrogen-bonded molecular pairs in this ice. It has been found that for HDA there is each non-zero probability of orientational disorder of hydrogen-bonded H<sub>2</sub>O pairs, of such uniform distribution of H atoms as observed in supercritical fluids in general, and of H atoms located at the O-O midpoint. The present PIMD simulations have revealed that these observed anomalous characteristics of atomic distribution in HDA are caused by both quantization of atoms and compression of the system.展开更多
The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green func...The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.展开更多
Party construction aesthetics is a valuable aesthetic resource formed in the practical exploration of rural revitalization,and it has logical compatibility with ideological and political education in terms of concepts...Party construction aesthetics is a valuable aesthetic resource formed in the practical exploration of rural revitalization,and it has logical compatibility with ideological and political education in terms of concepts,goals,tasks,etc.At present,comprehensive deepening reform has entered a deep-water zone,and some erroneous value orientations such as utilitarianism,emptiness,and liberalization are common in colleges and universities,and ideological and political education is caught in a new round of difficulties.As the main position of ideological and political education,colleges and universities should further use party construction aesthetics to strengthen and improve ideological and political education,adhere to the carrier of aesthetic education,carry out diversified integrated education,broaden the ideological and political practical teaching system,build a long-term mechanism for collaborative education of ideological and political education and party construction aesthetics,and fully integrate party construction aesthetics into ideological and political education in colleges and universities.展开更多
This study focuses on the master of arts education in higher education institutions in Guangxi Zhuang Autonomous Region of China,explores the path of integrating Guangxi Zhuang’s intangible cultural heritage with the...This study focuses on the master of arts education in higher education institutions in Guangxi Zhuang Autonomous Region of China,explores the path of integrating Guangxi Zhuang’s intangible cultural heritage with the teaching of master of arts,and puts forward the teaching mode of“thinking guidance-autonomous judgement-program construction.”A theoretical model of innovative transformation of intangible cultural heritage is also summarized.Through the development of this study,it is expected to further enrich the practical teaching mechanism of master of arts education in Chinese universities and form a master of arts teaching model with strong local cultural characteristics.At the same time,the teaching reform based on the integration of Guangxi Zhuang’s intangible cultural heritage and master of arts education also has strong practical significance for promoting the inheritance and innovation of Chinese intangible cultural heritage,promoting the development of cultural and creative industries,and serving the economic and social development of Guangxi.展开更多
We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D(D ≥ 1) dimensions. The coherent states, defined as the eigenstat...We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D(D ≥ 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.展开更多
We have developed a path integral formalism of the quantum mechanics in the rotating frame of reference, and proposed a path integral description of spin degrees of freedom, which is connected to the Schwinger bosons ...We have developed a path integral formalism of the quantum mechanics in the rotating frame of reference, and proposed a path integral description of spin degrees of freedom, which is connected to the Schwinger bosons realization of the angular momenta. We have also given several important examples for the applications in the rotating frames.展开更多
In this work,we study the dissipation mechanism and frictional force of a nanometer-sized tip scanning a metal surface via a path integral approach.The metal,with internal degrees of freedom(c,c^(†))and a tip with an ...In this work,we study the dissipation mechanism and frictional force of a nanometer-sized tip scanning a metal surface via a path integral approach.The metal,with internal degrees of freedom(c,c^(†))and a tip with an internal degree of freedom(d,d^(†))couple with one another by means of an exchanged potential,V.Having integrated out all internal degrees of freedom,we obtain the in-out amplitude.Moreover,we calculate the imaginary part of the in-out amplitude and the frictional force.We find the imaginary part of the in-out amplitude to be positive,and correlated to the sliding velocity in most cases.The frictional force is proportional to the sliding velocity for the case where v<0.01.However,for cases where v>0.01,the frictional force demonstrates nonlinear dependence on sliding velocity.展开更多
Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined.Coherent quantum dynamics is demonstrated with one dimensional test cases(qua...Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined.Coherent quantum dynamics is demonstrated with one dimensional test cases(quantum dot models)and performance of the Trotter kernel as compared with the exact kernels is tested.Also,a novel approach for finding the ground state and other stationary sates is presented.This is based on the incoherent propagation in real time.For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling.We asses the numerical prerequisites for all of the above.展开更多
Feynman’s path integral reformulates the quantum Schrödinger differential equation to be an integral equation.It has been being widely used to compute internuclear quantum-statistical effects on many-body molecu...Feynman’s path integral reformulates the quantum Schrödinger differential equation to be an integral equation.It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems.In this Review,the molecular Schrödinger equation will first be introduced,together with the BornOppenheimer approximation that decouples electronic and internuclear motions.Some effective semiclassical potentials,e.g.,centroid potential,which are all formulated in terms of Feynman’s path integral,will be discussed and compared.These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger’s energy eigenvalues.As a result,path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques.To complement these techniques,we will examine how Kleinert’s variational perturbation(KP)theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential.To enable the powerful KP theory to be practical for many-body molecular systems,we have proposed a new path-integral method:automated integrationfree path-integral(AIF-PI)method.Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method,we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions.The computational procedure of using our AIF-PI method,along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy(AMAZE),are also highlighted in this review.展开更多
A key strategy for raising students’humanistic aptitude is through music education.Culture is the soul of music and the source of innovation in music education.Under the current social education concept,it is advocat...A key strategy for raising students’humanistic aptitude is through music education.Culture is the soul of music and the source of innovation in music education.Under the current social education concept,it is advocated to carry forward excellent traditional and red culture in teaching,hence this paper further explores the path of integrating red culture into music education.The incorporation of the Taihang spirit,the most representative cultural resource in Shanxi,into music education in colleges and universities will promote the concept of Lide Shuren,further enhance students’training,and enable students to fulfill the dual education requirements.展开更多
文摘Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.
基金This work was supported by the Key International(Regional)Joint Research Program of the National Natural Science Foundation of China(No.12120101002).
文摘In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.
文摘Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.
文摘A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito' s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.
基金Project supported by CNEPRU(Grant No.D03920130021)
文摘We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schioberg potential. The obtained results are compared to those produced by other methods and are found to be consistent.
基金supported by the National Natural Science Foundation of China(Grant Nos.11474207 and 11374217)
文摘The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.
文摘We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point(i.e.,the origin) to the forced point in the biopolymer,with arclength L_f.The second part consists of the segment counted from the forced point to the force-free end with arclength △L.We apply the path integral technique to find the relationship between these two parts.At finite temperature and without any constraint at the end,we show exactly that if we focus on the quantities related to the first part,then we can ignore the second part completely.Monte Carlo simulation confirms this conclusion.In contrast,the effect for the quantities related to the second part is dependent on what we want to observe.A force-free end has little effect on the relative extension,but it affects seriously the value of the end-to-end distance if △L is comparable to L_f.
文摘Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangled state representation is presented. Its advantages are explained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374360,11405266,and 11505285)the National Basic Research Program of China(Grant No.2013CBA01504)
文摘As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.
文摘A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites <em>n</em> when <em>β </em><em></em><span></span>→ 0.
文摘We have investigated the effects of compression and quantization on atomic distribution in ice Ic and in its compressed states at 77 K and 10 K, using the path integral molecular dynamics (PIMD) simulations over wide range of volume. It has been found that the high density amorphous ice (HDA) is attained by compression but volume range to retain ice structure is wider at 10 K than 77 K. We have discovered that quantum dispersion of atoms in ice Ic at 10 K induces non-zero probability that hydrogen-bonded H<sub>2</sub>O molecular molecules are oriented nonlinearly in the crystal structure, which was believed to contain exclusively linear orientation of hydrogen-bonded molecular pairs in this ice. It has been found that for HDA there is each non-zero probability of orientational disorder of hydrogen-bonded H<sub>2</sub>O pairs, of such uniform distribution of H atoms as observed in supercritical fluids in general, and of H atoms located at the O-O midpoint. The present PIMD simulations have revealed that these observed anomalous characteristics of atomic distribution in HDA are caused by both quantization of atoms and compression of the system.
文摘The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.
基金supported by the National Social Science Foundation of China under the General Program“Study on the Mechanism and Path of Creative Transformation of China’s Traditional Aesthetic Education Ideas in the New Development Stage”,Project No.21BKS083Key Project of 2022 Research on Higher Education Reform and Development of Nanjing University of Finance and Economics,“Thoughts and Paths on Empowering High-level University Construction with Party Building Aesthetics”,Project No.GJGF202203.
文摘Party construction aesthetics is a valuable aesthetic resource formed in the practical exploration of rural revitalization,and it has logical compatibility with ideological and political education in terms of concepts,goals,tasks,etc.At present,comprehensive deepening reform has entered a deep-water zone,and some erroneous value orientations such as utilitarianism,emptiness,and liberalization are common in colleges and universities,and ideological and political education is caught in a new round of difficulties.As the main position of ideological and political education,colleges and universities should further use party construction aesthetics to strengthen and improve ideological and political education,adhere to the carrier of aesthetic education,carry out diversified integrated education,broaden the ideological and political practical teaching system,build a long-term mechanism for collaborative education of ideological and political education and party construction aesthetics,and fully integrate party construction aesthetics into ideological and political education in colleges and universities.
基金2023 Innovation Project of Guangxi Graduate Education“Innovation Transformation·Integration of Industry and Education-Research on the Integration Path of Zhuang Intangible Cultural Heritage and Master of Arts Course Teaching”(Project number:JGY2023052)2023 Special Project of Guangxi 14th Five-Year Plan for Educational Science“Revitalisation of Non-Heritage-Integration of Industry and Education-Research on the Service of Regional Economic Development of Design Professional Innovation and Entrepreneurship Education in Guangxi Colleges and Universities”(Project number:2023ZJY1836)。
文摘This study focuses on the master of arts education in higher education institutions in Guangxi Zhuang Autonomous Region of China,explores the path of integrating Guangxi Zhuang’s intangible cultural heritage with the teaching of master of arts,and puts forward the teaching mode of“thinking guidance-autonomous judgement-program construction.”A theoretical model of innovative transformation of intangible cultural heritage is also summarized.Through the development of this study,it is expected to further enrich the practical teaching mechanism of master of arts education in Chinese universities and form a master of arts teaching model with strong local cultural characteristics.At the same time,the teaching reform based on the integration of Guangxi Zhuang’s intangible cultural heritage and master of arts education also has strong practical significance for promoting the inheritance and innovation of Chinese intangible cultural heritage,promoting the development of cultural and creative industries,and serving the economic and social development of Guangxi.
基金Project supported by the National Natural Science Foundation of China (Grant No 60261004) and Yunnan Province Science Foundation (Grant No 2002E0008M).
文摘We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D(D ≥ 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.
基金Supported by National Natural Science Foundation of China (10875129, 10525522)
文摘We have developed a path integral formalism of the quantum mechanics in the rotating frame of reference, and proposed a path integral description of spin degrees of freedom, which is connected to the Schwinger bosons realization of the angular momenta. We have also given several important examples for the applications in the rotating frames.
文摘In this work,we study the dissipation mechanism and frictional force of a nanometer-sized tip scanning a metal surface via a path integral approach.The metal,with internal degrees of freedom(c,c^(†))and a tip with an internal degree of freedom(d,d^(†))couple with one another by means of an exchanged potential,V.Having integrated out all internal degrees of freedom,we obtain the in-out amplitude.Moreover,we calculate the imaginary part of the in-out amplitude and the frictional force.We find the imaginary part of the in-out amplitude to be positive,and correlated to the sliding velocity in most cases.The frictional force is proportional to the sliding velocity for the case where v<0.01.However,for cases where v>0.01,the frictional force demonstrates nonlinear dependence on sliding velocity.
文摘Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined.Coherent quantum dynamics is demonstrated with one dimensional test cases(quantum dot models)and performance of the Trotter kernel as compared with the exact kernels is tested.Also,a novel approach for finding the ground state and other stationary sates is presented.This is based on the incoherent propagation in real time.For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling.We asses the numerical prerequisites for all of the above.
基金supported by HK RGC(ECS-209813)NSF of China(NSFC-21303151)+2 种基金HKBU FRG(FRG2/12-13/037)startup funds(38-40-088 and 40-49-495)to K.-Y.WongThe computing resources for our work summarized in this Review were supported in part by Minnesota Supercomputing Institute,and High Performance Cluster Computing Centre and Office of Information Technology at HKBU(sciblade&jiraiya).
文摘Feynman’s path integral reformulates the quantum Schrödinger differential equation to be an integral equation.It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems.In this Review,the molecular Schrödinger equation will first be introduced,together with the BornOppenheimer approximation that decouples electronic and internuclear motions.Some effective semiclassical potentials,e.g.,centroid potential,which are all formulated in terms of Feynman’s path integral,will be discussed and compared.These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger’s energy eigenvalues.As a result,path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques.To complement these techniques,we will examine how Kleinert’s variational perturbation(KP)theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential.To enable the powerful KP theory to be practical for many-body molecular systems,we have proposed a new path-integral method:automated integrationfree path-integral(AIF-PI)method.Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method,we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions.The computational procedure of using our AIF-PI method,along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy(AMAZE),are also highlighted in this review.
基金Achievements of“Continuing the Red Bloodline and Inheriting the Spirit of Taihang”by Shanxi Province’s characteristic cultural education brand.
文摘A key strategy for raising students’humanistic aptitude is through music education.Culture is the soul of music and the source of innovation in music education.Under the current social education concept,it is advocated to carry forward excellent traditional and red culture in teaching,hence this paper further explores the path of integrating red culture into music education.The incorporation of the Taihang spirit,the most representative cultural resource in Shanxi,into music education in colleges and universities will promote the concept of Lide Shuren,further enhance students’training,and enable students to fulfill the dual education requirements.