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 study the propagator for an electron moving in a two-dimensional （2D） quadratic saddle-point potential, in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is de...We study the propagator for an electron moving in a two-dimensional （2D） quadratic saddle-point potential, in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.展开更多
In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrar...In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter, the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the field of magnetic effects in nano-structures and quantum optics. The presented solution, after minor extensions, can also be used for motion in three dimensions, and in fact it has been used for years in such cases. Also it can be used as a good exercise of a Feynman Path Integral that can be calculated easily with just the help of the Classical Action.展开更多
The solution of Dirac particles confined in a one-dimensional finite square well potential is solved by using the path-integral formalism for Dirac equation. The propagator of the Dirac equation in case of the bounded...The solution of Dirac particles confined in a one-dimensional finite square well potential is solved by using the path-integral formalism for Dirac equation. The propagator of the Dirac equation in case of the bounded Dirac particles is obtained by evaluating an appropriate path integral, directly constructed from the Dirac equation. The limit of integration techniques for evaluating path integral is only valid for the piecewise constant potential. Finally, the Dirac propagator is expressed in terms of standard special functions.展开更多
In this paper, by means of the maximum circle tensile stress on curve of constant ω and stress intensity factors by a path independent contour integral method, trajectories of maxed mode crack propagation are simulat...In this paper, by means of the maximum circle tensile stress on curve of constant ω and stress intensity factors by a path independent contour integral method, trajectories of maxed mode crack propagation are simulated through numerical manifold method. The crack propagation is traced dynamically by modifying the neighboring connection between the crack-top and nodes within elements in the calculating process. This method has the advantages such as less modified area, easiness of programming, high realizability and so on. Then a single sharp nicked specimen is used to verified the numerical result. It is shown that the provided method is reasonable and effective.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
常规非线性反演方法虽然对初始模型的依赖大为减弱,但局部收敛现象和计算速度慢仍然是瓶颈.本文提出了一种新的反演方法——量子路径积分算法(Quantum Path Integral Algorithm,简称QPIA).该方法引入量子力学的横向场、传播子等概念,并...常规非线性反演方法虽然对初始模型的依赖大为减弱,但局部收敛现象和计算速度慢仍然是瓶颈.本文提出了一种新的反演方法——量子路径积分算法(Quantum Path Integral Algorithm,简称QPIA).该方法引入量子力学的横向场、传播子等概念,并充分利用量子隧穿效应,大大提高反演的效率,具体是通过对反演目标函数的构建,并以Feynman的传播子来构成模型的接收概率来实现.在对一维大地电磁模型和实际数据进行试验后,表明该方法比常规反演方法更能够精确、稳定和快速地逼近真实模型.展开更多
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 the National Natural Science Foundation of China under Grant No.10805029ZheJiang NSF under Grant No.R6090717the K.C.Wong Magna Foundation of Ningbo University
基金supported by the National Natural Science Foundation of China (Grant No. 10805029)the Zhejiang Natural Science Foundation,China (Grant No. R6090717)the K.C. Wong Magna Foundation of Ningbo University,China
文摘We study the propagator for an electron moving in a two-dimensional （2D） quadratic saddle-point potential, in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.
文摘In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter, the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the field of magnetic effects in nano-structures and quantum optics. The presented solution, after minor extensions, can also be used for motion in three dimensions, and in fact it has been used for years in such cases. Also it can be used as a good exercise of a Feynman Path Integral that can be calculated easily with just the help of the Classical Action.
文摘The solution of Dirac particles confined in a one-dimensional finite square well potential is solved by using the path-integral formalism for Dirac equation. The propagator of the Dirac equation in case of the bounded Dirac particles is obtained by evaluating an appropriate path integral, directly constructed from the Dirac equation. The limit of integration techniques for evaluating path integral is only valid for the piecewise constant potential. Finally, the Dirac propagator is expressed in terms of standard special functions.
基金Funded by the National Natural Science Foundation of China (No. 10272033) and Guangdong Provincial Natural Science Foundation(Nos.04105386,5300090 and 05001844).
文摘In this paper, by means of the maximum circle tensile stress on curve of constant ω and stress intensity factors by a path independent contour integral method, trajectories of maxed mode crack propagation are simulated through numerical manifold method. The crack propagation is traced dynamically by modifying the neighboring connection between the crack-top and nodes within elements in the calculating process. This method has the advantages such as less modified area, easiness of programming, high realizability and so on. Then a single sharp nicked specimen is used to verified the numerical result. It is shown that the provided method is reasonable and effective.
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.
文摘常规非线性反演方法虽然对初始模型的依赖大为减弱,但局部收敛现象和计算速度慢仍然是瓶颈.本文提出了一种新的反演方法——量子路径积分算法(Quantum Path Integral Algorithm,简称QPIA).该方法引入量子力学的横向场、传播子等概念,并充分利用量子隧穿效应,大大提高反演的效率,具体是通过对反演目标函数的构建,并以Feynman的传播子来构成模型的接收概率来实现.在对一维大地电磁模型和实际数据进行试验后,表明该方法比常规反演方法更能够精确、稳定和快速地逼近真实模型.
