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
Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying effects produced by statistica...Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying effects produced by statistical operator or statistical matrix. Thus, respective representation-varied equilibrium statistical matrixes have been found. Specific mean value equations have been found and their equilibrium solutions have been obtained.展开更多
Russula vinosa Lindblad(R.vinosa Lindblad)is a nutrient-rich wild edible fungus,abundant in car-bohydrates.In this study,two polysaccharides(Russula polysaccharides extracted from 1%KOH(RP-1)and Russula polysaccharide...Russula vinosa Lindblad(R.vinosa Lindblad)is a nutrient-rich wild edible fungus,abundant in car-bohydrates.In this study,two polysaccharides(Russula polysaccharides extracted from 1%KOH(RP-1)and Russula polysaccharides extracted from 5%KOH(RP-5))were extracted from Russula fruit bodies using KOH-graded extraction technology.The molecular weights of RP-1 and RP-5 were 187000 and 97300 u,respectively.Their glycosyl compositions(galactose꞉glucose꞉xylose꞉mannose,i.e.,Gal꞉Glu꞉Xyl꞉Man)were 0.27:1.00:0.01:0.16 for RP-1 and 0.12:1.00:0.03:0.19 for RP-5.Nuclear magnetic resonance(NMR)analysis revealed that the main structural component of RP-1 was→3,6)-β-d-Glu p-(1→,with a→6)-β-d-Glu p-(1→residue linked at sites 1 and 6,and a→3)-β-d-Glu p-(1→residue linked at sites 3.The RP-5 shared this structure with an additional→4)-β-d-Man p-(1→residue attached to the→3)-β-d-Glu p-(1→.Phagocytosis assay demonstrated that RP-5,with a lower molecular weight,lower galactose content,and higher xylose and man-nose content,enhanced RAW 264.7 cell phagocytic activity by 121.04%,outperforming RP-1,which showed a 42.15%increase at the same concentration of 600𝜇g/mL.Furthermore,both RP-1 and RP-5 reduced the release of inflammatory factors and induced the nuclear translocation of the nuclear transcription factor-𝜅B(NF-𝜅B)pathway in RAW 264.7 cells.This study provided insights into the structural characteristics and immunomodulatory properties of Russula polysac-charides,offering potential for further applications in bioactive compound development.展开更多
We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation.Adopting a minimal lattice model of a handful of interacting fermions with single-particle ...We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation.Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation,we show that the non-Hermitian effective Hamiltonian of the master equation gives rise to two-body scattering states with state-and interaction-dependent parity-time transition.The resulting two-body exceptional points can be extracted from the trace-preserving density-matrix dynamics of the same dissipative system with three atoms.Our results not only demonstrate the interplay of parity-time symmetry and interaction on the exact few-body level,but also serve as a minimal illustration on how key features of non-Hermitian few-body physics can be probed in an open dissipative many-body system.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
Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. ...Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.展开更多
In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. Gene...In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. General fundamental conditions that should follow our quantum mechanical diffusion coefficients appearing in the master equation are kindly derived. From the master equation, the expressions of density operator, the Wigner distribution function, the expectation and variance with respect to coordinates and momenta are obtained. Based on these quantities, the total energy of the system is evaluated and simulations show its dependency to phase-space structure and its improvement due to noncommutativity effects and the environmental temperature as well. In addition, we also evaluate the decoherence time scale and show that it increases with noncommutativity phase-space effects as compared to the commutative case. It turns out from simulations that this time scale is significantly improved under magnetic field effects.展开更多
Google Page Rank is a prevalent algorithm for ranking the significance of nodes or websites in a network,and a recent quantum counterpart for Page Rank algorithm has been raised to suggest a higher accuracy of ranking...Google Page Rank is a prevalent algorithm for ranking the significance of nodes or websites in a network,and a recent quantum counterpart for Page Rank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google Page Rank.The quantum Page Rank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation,which,however,needs to solve the Kronecker products of an O(N^(4))dimension and requires severely large memory and time when the number of nodes N in a network increases above 150.Here,we present an efficient solver for quantum Page Rank by using the Runge-Kutta method to reduce the matrix dimension to O(N^(2))and employing Tensor Flow to conduct GPU parallel computing.We demonstrate its performance in solving quantum stochastic walks on Erdos-Rényi graphs using an RTX 2060 GPU.The test on the graph of 6000 nodes requires a memory of 5.5 GB and time of 223 s,and that on the graph of 1000 nodes requires 226 MB and 3.6 s.Compared with QSWalk,a currently prevalent Mathematica solver,our solver for the same graph of 1000 nodes reduces the required memory and time to only 0.2%and 0.05%.We apply the solver to quantum Page Rank for the USA major airline network with up to 922 nodes,and to quantum stochastic walk on a glued tree of 2186 nodes.This efficient solver for large-scale quantum Page Rank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.展开更多
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.
文摘Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying effects produced by statistical operator or statistical matrix. Thus, respective representation-varied equilibrium statistical matrixes have been found. Specific mean value equations have been found and their equilibrium solutions have been obtained.
基金supported by the National Key Research and Development Program of China(No.2022YFD2200804).
文摘Russula vinosa Lindblad(R.vinosa Lindblad)is a nutrient-rich wild edible fungus,abundant in car-bohydrates.In this study,two polysaccharides(Russula polysaccharides extracted from 1%KOH(RP-1)and Russula polysaccharides extracted from 5%KOH(RP-5))were extracted from Russula fruit bodies using KOH-graded extraction technology.The molecular weights of RP-1 and RP-5 were 187000 and 97300 u,respectively.Their glycosyl compositions(galactose꞉glucose꞉xylose꞉mannose,i.e.,Gal꞉Glu꞉Xyl꞉Man)were 0.27:1.00:0.01:0.16 for RP-1 and 0.12:1.00:0.03:0.19 for RP-5.Nuclear magnetic resonance(NMR)analysis revealed that the main structural component of RP-1 was→3,6)-β-d-Glu p-(1→,with a→6)-β-d-Glu p-(1→residue linked at sites 1 and 6,and a→3)-β-d-Glu p-(1→residue linked at sites 3.The RP-5 shared this structure with an additional→4)-β-d-Man p-(1→residue attached to the→3)-β-d-Glu p-(1→.Phagocytosis assay demonstrated that RP-5,with a lower molecular weight,lower galactose content,and higher xylose and man-nose content,enhanced RAW 264.7 cell phagocytic activity by 121.04%,outperforming RP-1,which showed a 42.15%increase at the same concentration of 600𝜇g/mL.Furthermore,both RP-1 and RP-5 reduced the release of inflammatory factors and induced the nuclear translocation of the nuclear transcription factor-𝜅B(NF-𝜅B)pathway in RAW 264.7 cells.This study provided insights into the structural characteristics and immunomodulatory properties of Russula polysac-charides,offering potential for further applications in bioactive compound development.
基金the National Natural Science Foundation of China(Grant No.11974331)the National Key R&D Program of China(Grant Nos.2016YFA0301700 and 2017YFA0304100).
文摘We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation.Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation,we show that the non-Hermitian effective Hamiltonian of the master equation gives rise to two-body scattering states with state-and interaction-dependent parity-time transition.The resulting two-body exceptional points can be extracted from the trace-preserving density-matrix dynamics of the same dissipative system with three atoms.Our results not only demonstrate the interplay of parity-time symmetry and interaction on the exact few-body level,but also serve as a minimal illustration on how key features of non-Hermitian few-body physics can be probed in an open dissipative many-body system.
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Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.
文摘In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. General fundamental conditions that should follow our quantum mechanical diffusion coefficients appearing in the master equation are kindly derived. From the master equation, the expressions of density operator, the Wigner distribution function, the expectation and variance with respect to coordinates and momenta are obtained. Based on these quantities, the total energy of the system is evaluated and simulations show its dependency to phase-space structure and its improvement due to noncommutativity effects and the environmental temperature as well. In addition, we also evaluate the decoherence time scale and show that it increases with noncommutativity phase-space effects as compared to the commutative case. It turns out from simulations that this time scale is significantly improved under magnetic field effects.
基金supported by the National Key R&D Program of China(2019YFA0308700,and 2017YFA0303700)the National Natural Science Foundation of China(61734005,11761141014,11690033)+3 种基金the Science and Technology Commission of Shanghai Municipality(STCSM)(17JC1400403)the Shanghai Municipal Education Commission(SMEC)(2019SHZDZX01,2017-01-07-0002-E00049)supported by the National Natural Science Foundation of China(11904229)China Postdoctoral Science Foundation(2019T120334)。
文摘Google Page Rank is a prevalent algorithm for ranking the significance of nodes or websites in a network,and a recent quantum counterpart for Page Rank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google Page Rank.The quantum Page Rank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation,which,however,needs to solve the Kronecker products of an O(N^(4))dimension and requires severely large memory and time when the number of nodes N in a network increases above 150.Here,we present an efficient solver for quantum Page Rank by using the Runge-Kutta method to reduce the matrix dimension to O(N^(2))and employing Tensor Flow to conduct GPU parallel computing.We demonstrate its performance in solving quantum stochastic walks on Erdos-Rényi graphs using an RTX 2060 GPU.The test on the graph of 6000 nodes requires a memory of 5.5 GB and time of 223 s,and that on the graph of 1000 nodes requires 226 MB and 3.6 s.Compared with QSWalk,a currently prevalent Mathematica solver,our solver for the same graph of 1000 nodes reduces the required memory and time to only 0.2%and 0.05%.We apply the solver to quantum Page Rank for the USA major airline network with up to 922 nodes,and to quantum stochastic walk on a glued tree of 2186 nodes.This efficient solver for large-scale quantum Page Rank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.
