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
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
By using the path integral approach, we investigate the problem of Hooke＇s atom （two electrons interacting with Coulomb potential in an external harmonic-oscillator potential） in an arbitrary time-dependent electri...By using the path integral approach, we investigate the problem of Hooke＇s atom （two electrons interacting with Coulomb potential in an external harmonic-oscillator potential） in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.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
Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy,but there is still no conclusion and consensus on it.We show it can be subsumed into the quantum the...Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy,but there is still no conclusion and consensus on it.We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths.According to this extended theory,we deduce not only the Klein-Gordon equation,but also the wave-function-collapse equation.It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the "potential noise" of the apparatus or environment and "inner correlation" of wave function respectively.Therefore,the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics.This work will give a new recognition for the measurement problem.展开更多
The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they...The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.展开更多
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more f...The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more features from full loop quantum gravity.The path integrals can be formulated in both timeless and deparameterized frameworks.It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other.Moreover,the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe,which coincide with those obtained in canonical theory.展开更多
Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of th...Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.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
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
The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,...The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,1） coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum.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
This article uses the phase space path integral method to find the propagator for a particle with a force quadratic in velocity. Two specific canonical transformations has been used for this purpose.
We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
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
Most path integral expressions for quantum open systems are formulated with diagonal systembath coupling,where the influence functional is a functional of scalar-valued trajectories.This formalism is enough if only a ...Most path integral expressions for quantum open systems are formulated with diagonal systembath coupling,where the influence functional is a functional of scalar-valued trajectories.This formalism is enough if only a single bath is under consideration.However,when multiple baths are present,non-diagonal system-bath couplings need to be taken into consideration.In such a situation,using an abstract Liouvillian method,the influence functional can be obtained as a functional of operator-valued trajectories.The value of the influence functional itself also becomes a superoperator rather than an ordinary scalar,whose meaning is ambiguous at first glance and its connection to the conventional understanding of the influence functional needs extra careful consideration.In this article,we present another concrete derivation of the superoperator-valued influence functional based on the straightforward Trotter-Suzuki splitting,which can provide a clear picture to interpret the superoperator-valued influence functional.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
We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making ...We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.展开更多
An efficient and accurate method for computing the equilibriurn reduced density matrix is presented for treating open quantum systems characterized by the systern-bath model. The method employs the rnultilayer nmltico...An efficient and accurate method for computing the equilibriurn reduced density matrix is presented for treating open quantum systems characterized by the systern-bath model. The method employs the rnultilayer nmlticonfiguration tirne-dependent Hartree theory for imag- inary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Harniltonian, which leads to ac- curate results in agreement with those produced by the rnulti-electronic-state path integral molecular dynamics method.展开更多
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.
基金Supported by the National Natural Science Foundation of China under Grant No.10805029ZheJiang NSF under Grant No.R6090717the K.C.Wong Magna Foundation of Ningbo University
文摘By using the path integral approach, we investigate the problem of Hooke＇s atom （two electrons interacting with Coulomb potential in an external harmonic-oscillator potential） in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.
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 Basic Research Program of China (973 Program) under Grant No. G2009CB929300the National Natural Science Foundation of China under Grant Nos. 10905016,10874013,60776061 and 60821061
文摘Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy,but there is still no conclusion and consensus on it.We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths.According to this extended theory,we deduce not only the Klein-Gordon equation,but also the wave-function-collapse equation.It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the "potential noise" of the apparatus or environment and "inner correlation" of wave function respectively.Therefore,the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics.This work will give a new recognition for the measurement problem.
基金supported by the National Natural Science Foundation of China(No.21961142017,No.22073009 and No.21421003)the Ministry of Science and Technology of China(No.2017YFA0204901)。
文摘The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.
基金Supported by National Natural Science Foundation of China under Grant No. 10975017the Fundamental Research Funds for the Central Universities
文摘The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more features from full loop quantum gravity.The path integrals can be formulated in both timeless and deparameterized frameworks.It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other.Moreover,the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe,which coincide with those obtained in canonical theory.
基金National Natural Science Foundation of China and the China Academy of Engineering Physics under Grant No.10676025(NSAF)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,the Ministry of Education
文摘Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.
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.
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The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,1） coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum.
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.
文摘This article uses the phase space path integral method to find the propagator for a particle with a force quadratic in velocity. Two specific canonical transformations has been used for this purpose.
文摘We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
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.
基金supported by the National Natural Science Foundation of China under Grant No.12104328the Sichuan Science and Technology Program under Grant No.2024NSFSC1388。
文摘Most path integral expressions for quantum open systems are formulated with diagonal systembath coupling,where the influence functional is a functional of scalar-valued trajectories.This formalism is enough if only a single bath is under consideration.However,when multiple baths are present,non-diagonal system-bath couplings need to be taken into consideration.In such a situation,using an abstract Liouvillian method,the influence functional can be obtained as a functional of operator-valued trajectories.The value of the influence functional itself also becomes a superoperator rather than an ordinary scalar,whose meaning is ambiguous at first glance and its connection to the conventional understanding of the influence functional needs extra careful consideration.In this article,we present another concrete derivation of the superoperator-valued influence functional based on the straightforward Trotter-Suzuki splitting,which can provide a clear picture to interpret the superoperator-valued influence functional.
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We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.
基金supported by the U.S.National Science Foundation CHE-1500285used resources from the National Energy Research Scientific Computing Center,which is supported by the Office of Science of the U.S.Department of Energy under Contract No.DE-AC02-05CH11231+2 种基金supported by the Ministry of Science and Technology of China(No.2017YFA0204901 and No.2016YFC0202803)the National Natural Science Foundation of China(No.21373018 and No.21573007)the Recruitment Program of Global Experts,and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund(the second phase) under grant No.U1501501
文摘An efficient and accurate method for computing the equilibriurn reduced density matrix is presented for treating open quantum systems characterized by the systern-bath model. The method employs the rnultilayer nmlticonfiguration tirne-dependent Hartree theory for imag- inary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Harniltonian, which leads to ac- curate results in agreement with those produced by the rnulti-electronic-state path integral molecular dynamics method.
