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1.
We discuss the Lindblad equation for the density matrix where the dissipation is linear in the position operator. We consider a potential which is a bounded perturbation of the harmonic oscillator. We show that the perturbation of the potential leads to an analytic perturbation of the Wigner distribution. Then the Wigner distribution of the quantum dissipative system tends (uniformly in time) to the classical phase space distribution of the classical dissipative system (if the initial distribution converges when 0).  相似文献
2.
The ergodicity principle in quantum theory is employed for elaboration of a new quantum trajectory technique which is used for numerical simulation of quantum dissipative systems. With this purpose the density matrix of a quantum system is represented as a sum over an ensemble of quantum states in time intervals. The method is employed for computations of a quantum anharmonic oscillator. Original Russian Text ? H.H. Adamyan, T.V. Gevorgyan, G.Yu. Kryuchkyan, 2007, published in Izvestiya NAN Armenii, Fizika, 2007, Vol. 42, No. 1, pp. 3–8.  相似文献
3.
A Markovian master equation with time-dependent generator is constructed that respects basic constraints of quantum mechanics, in particular the von Neumann conditions. For the case of a two-level system, Bloch equations with time-dependent parameters are obtained. Necessary conditions on the latter are formulated. By employing a time-local counterpart of the Nakajima–Zwanzig equation, we establish a relation with unitary dynamics. We also discuss the relation with the weak-coupling limit. On the basis of a uniqueness theorem, a standard form for the generator of time-local master equations is proposed. The Jaynes–Cummings model with atomic damping is solved. The solution explicitly demonstrates that reduced dynamics can be described by time-local master equations only on a finite time interval. This limitation is caused by divergencies in the generator. A limit of maximum entropy is presented that corroborates the foregoing statements. A second limiting case demonstrates that divergencies may even occur for small perturbations of the weak-coupling regime.  相似文献
4.
We discuss the Lindblad equation for the density matrix where the dissipation is linear in the position operator. We consider a potential which is a bounded perturbation of the harmonic oscillator. We show that the perturbation of the potential leads to an analytic perturbation of the Wigner distribution. Then the Wigner distribution of the quantum dissipative system tends (uniformly in time) to the classical phase space distribution of the classical dissipative system (if the initial distribution converges when 0).  相似文献
5.
Adopting the standard mathematical framework for describing reduced dynamics, we derive two formal identities for the density operator of an open quantum system. Each of these is equivalent to the old Nakajima-Zwanzig equation. The first identity is local in time. It contains the inverse of the dynamical map which govern the evolution of the density operator. We indicate a time interval on which this inverse exists. The second identity constitutes a suitable starting point for going beyond the Markov approximation in a controlled way. On the basis of the Bloch equations we argue once more that in studying quantum dissipation one has to pay attention to the von Neumann conditions. In the Nakajima-Zwanzig equation we make the first Born approximation. The ensuing master equation possesses the correct weak-coupling limit. While proving this rather obvious but at the same time important statement, we elucidate the mathematical methods which underlie the weak-coupling limit. Moving to a two-dimensional Hilbert space, we find that both for short and for long times our approximate master equation respects the von Neumann conditions. Assuming exponential decay for correlation functions, we propose a physical limit in which the solutions for the density operator become Markovian in character. We confirm the well-known statement that, as seen from a macroscopic standpoint, the system starts from an effective initial condition. The approach to equilibrium is exponential. The accessory relaxation constants can differ from the usual Bloch parameters and by more than 50%.  相似文献
6.
The dynamic properties of a biased two-level system in contact with a dissipative bath are studied in the weak coupling limit using a resolvent expansion method. The theory yields consistent results at low temperatures, a regime in which the widely used dilute bounce gas approximation (DBGA) to an underlying functional integral expression breaks down. The present results are however equivalent to a recently adapted functional integral technique that goes beyond the DBGA. The calculated expressions are relevant for analyzing the neutron scattering data on tunneling of light interstitials, e.g., hydrogen, in metals, at very low temperatures.  相似文献
7.
The problem of a quantum oscillator coupled to an independent-oscillator model of a heat bath is discussed. The transformation to normal coordinates is explicitly constructed using the method of Ullersma. With this transformation an alternative derivation of an exact formula for the oscillator free energy is constructed. The various contributions to the oscillator energy are calculated, with the aim of further understanding this formula. Finally, the limitations of linear coupling models, such as that used by Ullersma, are discussed in the form of some critical remarks.  相似文献
8.
应用最近发展的量子耗散理论 ,研究了耗散对简单三能级体系的受激拉曼绝热转移过程的影响 ,并与pump dump过程比较 .计算结果表明 ,受激拉曼绝热转移的机制能很好地抑制中间态的弛豫与涨落的影响 .数值结果也表明了新的量子耗散理论可以正确地描述场与耗散相互耦合的动力学问题  相似文献
9.
10.
The dissipative harmonic oscillator has two representations. In the first representation the central oscillator couples with its position to an oscillator bath. In the second one it couples with its momentum to the bath. Both representations are related by a unitary transformation. If the central oscillator couples with its position and momentum to two independent baths, no such unitary transformation exists. We discuss two possible models of this type and their physical relevance.  相似文献
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