A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems.We demonstrate that it is the unraveling of the tilted quantum master equation.The latter is widely used in the analy...A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems.We demonstrate that it is the unraveling of the tilted quantum master equation.The latter is widely used in the analysis and calculations of stochastic thermodynamic quantities in quantum stochastic thermodynamics.展开更多
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
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
The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utiliz...The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.展开更多
We consider the population and decay of a qubit under the electromagnetic environment. Employing the time- convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding...We consider the population and decay of a qubit under the electromagnetic environment. Employing the time- convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper.展开更多
The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of op...The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.展开更多
In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using...In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.展开更多
The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly...The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.展开更多
In this paper,we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems.The coefficients...In this paper,we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems.The coefficients of the equations are re-evaluated according to the scheme in[(2019),Phys.Rev.A 99,022118].They are complex numbers rather than the real numbers obtained from traditional simplified methods.The dynamics of two models(one is an open threelevel quantum system model,and the other is the model of phycoerythrin 545(PE545)in a photosynthesis system)are studied.It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments,but a large distortion of the dynamics in others.These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.展开更多
This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f （N） aρ （1/f （N - 1））a^＋ -a^＋aρ- ρa^＋a], where f（N） is an operator-valued function of N = a^＋a, for describing amplitude d...This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f （N） aρ （1/f （N - 1））a^＋ -a^＋aρ- ρa^＋a], where f（N） is an operator-valued function of N = a^＋a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field （a mixed state） when f （N） = 1√N ＋ 1.展开更多
We construct a number（n）-resolved master equation （ME） approach under self-consistent Born approxi- mation （SCBA） for noise spectrum calculation. The formulation is essentially non-Markovian and incorporates pro...We construct a number（n）-resolved master equation （ME） approach under self-consistent Born approxi- mation （SCBA） for noise spectrum calculation. The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations. We apply this approach to the chall1enging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum. The proposed n-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach, in the sense of being applicable to the shot noise of transport under small bias voltage, in non-Markovian regime, and with strong Coulomb correlations as favorably demonstrated in the nonequilibrium Kondo system.展开更多
In this paper we investigate an environmental effects to Josephson charge qubit (JCQ) when the environmentis taken as the Ohmic bath.At first,we derive the master equation from a JCQ-bath model.Then we investigate the...In this paper we investigate an environmental effects to Josephson charge qubit (JCQ) when the environmentis taken as the Ohmic bath.At first,we derive the master equation from a JCQ-bath model.Then we investigate thecoefficients of the equations that describe the shift in frequency,diffusive,decoherence,and so on.It is shown that ourresult on decoherence agrees with experimental one very well as the time is short enough.展开更多
We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution...We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.展开更多
By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective....By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.展开更多
We develop a master equation approach to describe the dynamics of distant resonators coupled through a one-dimensional waveguide. Our method takes into account the back-actions of the reservoirs, and enables us to cal...We develop a master equation approach to describe the dynamics of distant resonators coupled through a one-dimensional waveguide. Our method takes into account the back-actions of the reservoirs, and enables us to calculate the exact dynamics of the complete system at all times. We show that such system can cause nonexponential and long-lived photon decay due to the existence of a relaxation effect. The physical origin of non-Markovianity in our model system is the finite propagation speed resulting in time delays in communication between the nodes, and strong decay rate of the emitters into the waveguide. When the distance satisfies the standing wave condition, we find that when the time delay is increased, the dark modes formation is no longer perfect, and the average photon number of dark mode decreases in steady time limit.展开更多
We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dyn...We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite being widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.展开更多
We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantu...We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.展开更多
By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quant...By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .展开更多
We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation(Hong-Yi Fan and Jun-Hua Chen,J.Phys.A35(2002)6873)to two-mode case.In this appro...We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation(Hong-Yi Fan and Jun-Hua Chen,J.Phys.A35(2002)6873)to two-mode case.In this approach the two-photon master equations can be directly and conveniently converted into c-number partial differential equations.As an example,we solve the typical master equation for two-photon process in some limiting cases.展开更多
The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈...The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.展开更多
基金supported by the National Science Foundation of China under Grant No.11174025 and No.11575016.
文摘A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems.We demonstrate that it is the unraveling of the tilted quantum master equation.The latter is widely used in the analysis and calculations of stochastic thermodynamic quantities in quantum stochastic thermodynamics.
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.
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Project supported by the National Basic Research Program of China(Grant No.2012CB922103)the National Natural Science Foundation of China(GrantNos.11175113 and 11274104)the Natural Science Foundation of Hubei Province of China(Grant No.2011CDA021)
文摘The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.
基金Project supported by the National Natural Science Foundation of China(Grant No.11074072)
文摘We consider the population and decay of a qubit under the electromagnetic environment. Employing the time- convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper.
基金support from NYU Shanghai,the National Natural Science Foundation of China(No.21903054)the Hefei National Laboratory for Physical Sciences at the Microscale(No.KF2020008)+1 种基金the Shanghai Sailing Program(No.19YF1435600)the Program for Eastern Young Scholar at Shanghai Institutions of Higher Learning。
文摘The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.
文摘In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675119,11575125,and 11105097
文摘The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.
文摘In this paper,we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems.The coefficients of the equations are re-evaluated according to the scheme in[(2019),Phys.Rev.A 99,022118].They are complex numbers rather than the real numbers obtained from traditional simplified methods.The dynamics of two models(one is an open threelevel quantum system model,and the other is the model of phycoerythrin 545(PE545)in a photosynthesis system)are studied.It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments,but a large distortion of the dynamics in others.These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097)
文摘This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f （N） aρ （1/f （N - 1））a^＋ -a^＋aρ- ρa^＋a], where f（N） is an operator-valued function of N = a^＋a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field （a mixed state） when f （N） = 1√N ＋ 1.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11274085 and 11304031the Major State Basic Research Project of China under Grant Nos.2011CB808502,and 2012CB932704+1 种基金the Fundamental Research Funds for the Central Universities of Chinathe Program for Excellent Young Teachers in Hangzhou Normal University
文摘We construct a number（n）-resolved master equation （ME） approach under self-consistent Born approxi- mation （SCBA） for noise spectrum calculation. The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations. We apply this approach to the chall1enging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum. The proposed n-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach, in the sense of being applicable to the shot noise of transport under small bias voltage, in non-Markovian regime, and with strong Coulomb correlations as favorably demonstrated in the nonequilibrium Kondo system.
基金National Natural Science Foundation of China under Grant No.10675066K.C.Wong Magna Foundation in Ningbo University
文摘In this paper we investigate an environmental effects to Josephson charge qubit (JCQ) when the environmentis taken as the Ohmic bath.At first,we derive the master equation from a JCQ-bath model.Then we investigate thecoefficients of the equations that describe the shift in frequency,diffusive,decoherence,and so on.It is shown that ourresult on decoherence agrees with experimental one very well as the time is short enough.
基金supported by the National Science Foundation of China under Grants No. 11 174 025 and No. 11 575 016the support of the CAS Interdisciplinary Innovation Team, No. 2060 299。
文摘We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.
基金supported by the Natural Science Foundation of Heze University of Shandong Province,China (Grant No XY07WL01)the University Experimental Technology Foundation of Shandong Province,China (Grant No S04W138)
文摘By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11574041,11475037,and 11704026
文摘We develop a master equation approach to describe the dynamics of distant resonators coupled through a one-dimensional waveguide. Our method takes into account the back-actions of the reservoirs, and enables us to calculate the exact dynamics of the complete system at all times. We show that such system can cause nonexponential and long-lived photon decay due to the existence of a relaxation effect. The physical origin of non-Markovianity in our model system is the finite propagation speed resulting in time delays in communication between the nodes, and strong decay rate of the emitters into the waveguide. When the distance satisfies the standing wave condition, we find that when the time delay is increased, the dark modes formation is no longer perfect, and the average photon number of dark mode decreases in steady time limit.
基金Project supported by the National Basic Research Program of China (Grant Nos. 2009CB929300 and 2006CB921205)the National Natural Science Foundation of China (Grant Nos. 10534060 and 0625416)the Research Grant Council of Hong Kong SAR project (Grant No. 500908)
文摘We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite being widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105133)
文摘We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.
基金This research work is supported by the National Natural Science Foundation of China.
文摘By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .
基金The project supported by National Natural Science Foundation of China under Grant No.10175057the President Foundation of the Chinese Academy of Sciences
文摘We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation(Hong-Yi Fan and Jun-Hua Chen,J.Phys.A35(2002)6873)to two-mode case.In this approach the two-photon master equations can be directly and conveniently converted into c-number partial differential equations.As an example,we solve the typical master equation for two-photon process in some limiting cases.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605003 and 11547231
文摘The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.
