By introducing thermo-entangled state representation Ⅰη〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using ＂dissipative interaction picture＂ ...By introducing thermo-entangled state representation Ⅰη〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using ＂dissipative interaction picture＂ we solve the master equation of Jaynes-Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state Ⅰ↑〉 and the cavity mode is in coherent state.展开更多
Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task.In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dyn...Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task.In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamicsof the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain thedensity operator of the system (field +atom). The coherence losses of the system and of the atom are investigated whentwo-photon process is involved. We also study the effect of different atomic initial states and the influence of the fieldamplitude on the atomic coherence loss.展开更多
F_1-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the centralγ-subunit rotates inside the α_3β_3 cylinder.A stochastic four-state mechanochemical coupling model of F_1-ATPase ...F_1-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the centralγ-subunit rotates inside the α_3β_3 cylinder.A stochastic four-state mechanochemical coupling model of F_1-ATPase isstudied with the aid of the master equation.In this model, the ATP hydrolysis and synthesis are dependent on ATP,ADP, and Pi concentrations.The effects of ATP concentration, ADP concentration, and the external torque on theoccupation probability of binding-state, the rotation rate and the diffusion coefficient of F_1-ATPase are investigated.Moreover, the results from this model are compared with experiments.The mechanochemical mechanism F_1-ATPase isqualitatively explained by the model.展开更多
The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degen...The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.展开更多
We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infec...We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infected ones (I), the cancer cells. From this model, we obtain a curve describing the tumour volume as a function of time, which can be compared to available experimental data.展开更多
Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be par...Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume （i.e., mesoscopic） in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation （CME）. Similar to the wavefnnction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved： multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand “complex behavior” and complexity theory, and from which important biological insight can be gained.展开更多
文摘By introducing thermo-entangled state representation Ⅰη〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using ＂dissipative interaction picture＂ we solve the master equation of Jaynes-Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state Ⅰ↑〉 and the cavity mode is in coherent state.
基金The project supported by National Natural Science Foundation of China under Grant No.10305002
文摘Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task.In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamicsof the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain thedensity operator of the system (field +atom). The coherence losses of the system and of the atom are investigated whentwo-photon process is involved. We also study the effect of different atomic initial states and the influence of the fieldamplitude on the atomic coherence loss.
基金Supported by the National Natural Science Foundation of China under Grant No.10847118the National Natural Science Foundation of the City of Tianjin under Grant No.08JCYBJC00900 the Science Research Program of Education office of Hebei Province under Grant No.2008427
文摘F_1-ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the centralγ-subunit rotates inside the α_3β_3 cylinder.A stochastic four-state mechanochemical coupling model of F_1-ATPase isstudied with the aid of the master equation.In this model, the ATP hydrolysis and synthesis are dependent on ATP,ADP, and Pi concentrations.The effects of ATP concentration, ADP concentration, and the external torque on theoccupation probability of binding-state, the rotation rate and the diffusion coefficient of F_1-ATPase are investigated.Moreover, the results from this model are compared with experiments.The mechanochemical mechanism F_1-ATPase isqualitatively explained by the model.
基金Project supported by the Key-Area Research and Development Program of GuangDong Province,China (Grant No. 2019B030330001)the National Natural Science Foundation of China (Grant Nos. 12025509, 11874434, and 11704420)+1 种基金the Science and Technology Program of Guangzhou (China)(Grant No. 201904020024)partially supported by the Guangzhou Science and Technology Projects (Grant No. 202002030459)
文摘The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.
文摘We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infected ones (I), the cancer cells. From this model, we obtain a curve describing the tumour volume as a function of time, which can be compared to available experimental data.
基金supported by US NIH under Grant Nos. GM079804, GM081682, GM086145, GM068610NSF of USA under GrantNos. DBI-0646035 and DMS-0800257‘985’ Phase II Grant of Shanghai Jiao Tong University under Grant No. T226208001
文摘Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume （i.e., mesoscopic） in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation （CME）. Similar to the wavefnnction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved： multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand “complex behavior” and complexity theory, and from which important biological insight can be gained.
