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
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
In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exa...In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.展开更多
Integrator processes with long delay are difficult to control. Nonlinear characteristics of actuators make the control problem more challenging. A technique is proposed in this paper for global satisfactory control （...Integrator processes with long delay are difficult to control. Nonlinear characteristics of actuators make the control problem more challenging. A technique is proposed in this paper for global satisfactory control （GSC） of such processes with relay-type nonlinearity. An oscillatory control signal is injected into the nonlinear process; the amplitude and frequency of the oscillatory signal are designed to linearise the nonlinear process in the sense of harmonic analysis; and a state feedback controller is configured to implement GSC over the linearised process. An illustrative example is given to demonstrate the effectiveness of展开更多
The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space p...The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method. The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field are obtained.展开更多
The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damp...The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.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(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The project supported by National Natural Science Foundation of China under Grant No. 10675066 and K.C. Wong Magna Foundation in Ningbo University.
文摘In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.
文摘Integrator processes with long delay are difficult to control. Nonlinear characteristics of actuators make the control problem more challenging. A technique is proposed in this paper for global satisfactory control （GSC） of such processes with relay-type nonlinearity. An oscillatory control signal is injected into the nonlinear process; the amplitude and frequency of the oscillatory signal are designed to linearise the nonlinear process in the sense of harmonic analysis; and a state feedback controller is configured to implement GSC over the linearised process. An illustrative example is given to demonstrate the effectiveness of
文摘The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method. The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field are obtained.
文摘The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.
