Following Jaynes-Cummings model,the evolution of the field entropy in the system of a two-level atom interacting with the single mode coherent field is investigated under rotating-wave approximation.The typical case &...Following Jaynes-Cummings model,the evolution of the field entropy in the system of a two-level atom interacting with the single mode coherent field is investigated under rotating-wave approximation.The typical case "the field frequency variance with time in the form of sine ω=ω0+usin(wt) has been considered.The influences of the amplitude and angle frequency of the field frequency variance on entropy evolution of the field are discussed by numerical calculations.Calculation results indicate that the field frequency variance influences violently the behavior of field entropy evolution;the larger the amplitude of the field frequency variance is,the stronger the influence of the field frequency variance on the time evolution of field entropy is.展开更多
The decoherence process is analyzed for an open quantum system that is classically chaotic,with a classicallinear frequency entropy developed to measure the stability of classical motion,Investigation shows that the d...The decoherence process is analyzed for an open quantum system that is classically chaotic,with a classicallinear frequency entropy developed to measure the stability of classical motion,Investigation shows that the decoherencemeasured by the rate of quantum linear entropy production varies significantly with both the underlying classical orbitsand the classical linear frequency entropy.Such correspondence is also supported by the further investigation on theLoschmidt Echo.展开更多
This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of ent...This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem （CRTBP） are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator （OFLI）. The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.展开更多
基金Natural Science Foundation of Fujian Province under Grant(No.2008J0217)
文摘Following Jaynes-Cummings model,the evolution of the field entropy in the system of a two-level atom interacting with the single mode coherent field is investigated under rotating-wave approximation.The typical case "the field frequency variance with time in the form of sine ω=ω0+usin(wt) has been considered.The influences of the amplitude and angle frequency of the field frequency variance on entropy evolution of the field are discussed by numerical calculations.Calculation results indicate that the field frequency variance influences violently the behavior of field entropy evolution;the larger the amplitude of the field frequency variance is,the stronger the influence of the field frequency variance on the time evolution of field entropy is.
基金Supported by National Natural Science Foundation of China under Grant Nos.10375042 and 10875087
文摘The decoherence process is analyzed for an open quantum system that is classically chaotic,with a classicallinear frequency entropy developed to measure the stability of classical motion,Investigation shows that the decoherencemeasured by the rate of quantum linear entropy production varies significantly with both the underlying classical orbitsand the classical linear frequency entropy.Such correspondence is also supported by the further investigation on theLoschmidt Echo.
基金supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11525208)the National Natural Science Foundation of China(Grant No.11572166)
文摘This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem （CRTBP） are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator （OFLI）. The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.
