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1.
Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation 下载免费PDF全文
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)~(1/2). 相似文献
2.
Kraus operator solutions to a fermionic master equation describing a thermal bath and their matrix representation 下载免费PDF全文
We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quantum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature. 相似文献
3.
For the first time, we obtain the entropy variation law in a laser process after finding the Kraus operator of the master equation describing the laser process with the use of the entangled state representation. The behavior of entropy is determined by the competition of the gain and damping in the laser process. The evolution formula for the number of photons is also obtained. 相似文献
4.
For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained. 相似文献
5.
Xiang-Guo Meng Ji-Suo Wang Hua-Chao Gao 《International Journal of Theoretical Physics》2016,55(8):3630-3636
Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M l, m is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ |β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping. 相似文献
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In order to describe quantum fluctuations a general method is developed, which also may be applied to nonstationary systems as well as to states far from thermodynamic equilibrium. After a concise derivation of the master equation quantum mechanically determined dissipation and fluctuation coefficients are introduced, for which several theorems and relations are given. By using these coefficients there is set up a general Fokker-Planck equation for the diffusion of the statistical operator due to quantum fluctuations. 相似文献
9.
C. van den Broeck 《Physics letters. A》1982,90(3):119-122
We derive the multivariate master equation describing reaction diffusion systems from a discrete form master equation in phase space, assuming that the elastic collisions of the chemically active substances with the inert carrier gas have relaxed. In this state of collisional equilibrium the stochastic operator modelling the displacement of the particles between spatial cells reduces to the random wall operator and the reactive collision term yields the usual birth and death operator. Correlation functions are derived and their validity is discussed. 相似文献
10.
Heng-Mei Li Shuai Wang Zhen Wang Xue-Fen Xu 《International Journal of Theoretical Physics》2014,53(3):830-836
According to operator-sum representation theory, we have identified infinite-dimensional Kraus operators for describing a thermal channel with self-Kerr interaction after directly solving the corresponding master equation by virtue of thermo entangled state. Then we also prove in detail that Kraus operators hold the normalization. As an example, we exactly calculate the evolving result of a chaotic field in the thermal environment with the Kerr medium and find that the chaotic field evolves into a new chaotic field unaffected by the coupling factor with the Kerr medium. 相似文献
11.
A semiclassical theory of a dissipative Henon—Heiles system is proposed. Based on -scaling of an equation for the evolution of the Wigner quasiprobability distribution function in the presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion, which is expressible in terms of a correlation of stochastic fluctuations of the curvature of the potential due to classical chaos, and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of a quantum operator master equation. 相似文献
12.
Quantum operations, are completely positive (CP) and trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of one-qubit open quantum system in layered environment which is a generalized spin star model. The Nakajima-Zwanzig and time-convolutionless projection operators technique are applied for deriving the master equations. Finally, a simple example will be studied to consider the relation between completely positive maps and initial quantum correlation and show that vanishing quantum discord is not necessary for CP maps. 相似文献
13.
Wei-Feng Wu 《International Journal of Theoretical Physics》2016,55(12):5062-5068
Using the thermo entangled state approach, we successfully solve the master equation of a damped harmonic oscillator affected by a linear resonance force in a squeezed heat reservoir, and obtain the analytical evolution formula for the density operator in the infinitive Kraus operator-sum representation. Interestingly, the Kraus operators Ml,m,n,r and \(\mathfrak {M}_{l,m,n,r}^{\dag }\) are not Hermite conjugate, but they are still trace-preserving quantum operations because of the normalization condition. We also investigate the evolution for an initial coherent state for damping in a squeezed heat reservoir, which shows that the initial coherent state decays to a complex mixed state as a result of damping and thermal noise. 相似文献
14.
Dr. Daniel F. Walls 《Zeitschrift für Physik A Hadrons and Nuclei》1970,234(3):231-241
The usual derivations of the master equation for coupled systems such as the laser make an assumption of weak coupling both for the coupling of the components to their heat baths and for the internal coupling between the components. It is this second condition that we wish to relax. In the usual derivation of the irreversible part of the master equation the approximation is made that the density operator for the coupled system factorizes into a product of the density operators for the two components. However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid. To illustrate how the irreversible part of the master equation may be derived without making the factorization ansatz we consider the case of two coupled boson fields. Our derivation leads to additional terms in the usual master equation arising from correlations between the heat baths introduced by the coupling. This modified master equation yields the correct stationary solution for the density operator of the coupled system, whereas the usual master equation leads to a stationary solution for the density operator correct for the free components only. 相似文献
15.
Microscopic Hamiltonian models of the composite system “open system + environment” typically do not provide the operator-sum Kraus form of the open system’s dynamical map. With the use of a recently developed method (Andersson et al. J. Mod. Opt. 54, 1695 2007), we derive the Kraus operators starting from the microscopic Hamiltonian model, i.e., from the proper master equation, of the one-qubit depolarizing channel. Those Kraus operators generalize the standard counterparts, which are widely used in the literature. Comparison of the standard and the here obtained Kraus operators is performed via investigating dynamical change of the Bloch sphere volume, entropy production, and the open system’s state trace distance. We compare the generalized with the standard Kraus operators for both single qubit and regarding the occurrence of the entanglement sudden death for a pair of initially correlated qubits. We find that the generalized Kraus operators describe the less deteriorating quantum channel than the standard ones. 相似文献
16.
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects.The completely positive reduced dynamical map can be constructed in the Kraus representation.Quantum entanglement decays more slowly in the non-Markovian environment.The decoherence time for quantum entanglement can be markedly increased with the change of the memory kernel.It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants. 相似文献
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R. Graham 《Zeitschrift für Physik A Hadrons and Nuclei》1968,210(4):319-336
We set up an effective Hamiltonian for an optical parametric oscillator. It contains the Bose operators of the three modes, signal, idler, and pump and their coupling to heat baths. This Hamiltonian is shown to be equivalent to a set of equations of motion, derived in a previous paper (I) from a microscopically exact Hamiltonian, provided that the heat baths are chosen in an adequate way. The comparison with the laser Hamiltonian makes clear the close analogy of the underlying elementary processes of spontaneous emission from atoms and spontaneous parametric emission from light modes in nonlinear media. The Hamiltonian is used to derive a master equation for the statistical operator of the three-mode system. In the coherent state representation this master equation transforms into an equivalentc-number Fokker-Planck equation without any approximation. The solution is obtained below threshold by linearization and above threshold by quasilinearization of the nonlinear dissipation coefficients. The results agree with those which were obtained by quantum mechanical Langevin methods in a previous paper (I). 相似文献
19.
New approach for obtaining the time-evolution law of a chaotic light field in a damping-gaining process 下载免费PDF全文
A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented.The new differential equation for determining the parameter of the density operator ρ(t) is derived and the solution of f ’ for the damping and gaining processes are studied separately.Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance. 相似文献
20.
FAN Hong-Yi 《理论物理通讯》2002,38(11)
We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom. 相似文献