By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quant...By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.展开更多
Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,wh...Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,who considered the Einstein equation coupled with a nonlinear electromagnetic field.In this study,we investigate the gravitational perturbations,including the axial and polar sectors,of the Bardeen(Anti-)de Sitter black holes.We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes(QNMs)through numerical methods.For the Bardeen de Sitter black hole,we employ the 6thorder WKB approach.The numerical results reveal that the isospectrality is broken in this case.Conversely,the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.展开更多
The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation ...The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady- states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.展开更多
We theoretically study the quantum speed limit of a single atom trapped in a Fabry-Perot microresonator.The cavity mode will be squeezed when a driving laser is applied to the second-order nonlinear medium,and the eff...We theoretically study the quantum speed limit of a single atom trapped in a Fabry-Perot microresonator.The cavity mode will be squeezed when a driving laser is applied to the second-order nonlinear medium,and the effective Hamiltonian can be obtained under the Bogoliubov squeezing transformation.The analytical expression of the evolved atom state can be obtained by using the non-Hermitian Schr¨odinger equation for the initial excited state,and the quantum speed limit time coincides very well for both the analytical expression and the master equation method.From the perspective of quantum speed limit,it is more conducive to accelerate the evolution of the quantum state for the large detuning,strong driving,and coupling strength.For the case of the initial superposition state,the form of the initial state has more influence on the evolution speed.The quantum speed limit time is not only dependent on the system parameters but also determined by the initial state.展开更多
Single molecular shuttle-junction is one kind of nanoscale electromechanical tunneling system. In this junction, a molecular island oscillates depending on its charge occupation, and this charge dependent oscillation ...Single molecular shuttle-junction is one kind of nanoscale electromechanical tunneling system. In this junction, a molecular island oscillates depending on its charge occupation, and this charge dependent oscillation leads to modulation of electron tunneling through the molecular island. This paper reviews recent development on the study of current, shot noise and decoherence of electrons in the single molecular shuttle-junction. We will give detailed discussion on this topic using the typical system model, the theory of fully quantum master equation and the Aharonov-Bohm interferometer.展开更多
基金supported by President Foundation of Chinese Academy of Sciences and National Natural Science Foundation of China under Grant Nos. 10775097 and 10874174
文摘By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.
基金Supported by the the Natural Science Foundation of Hunan Province,China (2022J40262)the National Natural Science Foundation of China (12375046,12205254)。
文摘Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,who considered the Einstein equation coupled with a nonlinear electromagnetic field.In this study,we investigate the gravitational perturbations,including the axial and polar sectors,of the Bardeen(Anti-)de Sitter black holes.We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes(QNMs)through numerical methods.For the Bardeen de Sitter black hole,we employ the 6thorder WKB approach.The numerical results reveal that the isospectrality is broken in this case.Conversely,the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.
文摘The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady- states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.
基金Project supported by the National Natural Science Foundation of China(Grant No.12175029)the Fundamental Research Program of Shanxi Province,China(Grant No.20210302123063)。
文摘We theoretically study the quantum speed limit of a single atom trapped in a Fabry-Perot microresonator.The cavity mode will be squeezed when a driving laser is applied to the second-order nonlinear medium,and the effective Hamiltonian can be obtained under the Bogoliubov squeezing transformation.The analytical expression of the evolved atom state can be obtained by using the non-Hermitian Schr¨odinger equation for the initial excited state,and the quantum speed limit time coincides very well for both the analytical expression and the master equation method.From the perspective of quantum speed limit,it is more conducive to accelerate the evolution of the quantum state for the large detuning,strong driving,and coupling strength.For the case of the initial superposition state,the form of the initial state has more influence on the evolution speed.The quantum speed limit time is not only dependent on the system parameters but also determined by the initial state.
文摘Single molecular shuttle-junction is one kind of nanoscale electromechanical tunneling system. In this junction, a molecular island oscillates depending on its charge occupation, and this charge dependent oscillation leads to modulation of electron tunneling through the molecular island. This paper reviews recent development on the study of current, shot noise and decoherence of electrons in the single molecular shuttle-junction. We will give detailed discussion on this topic using the typical system model, the theory of fully quantum master equation and the Aharonov-Bohm interferometer.
