Research on Sorting and Routing Method for Traffic Networks

Yuan, Huilin; Li, Juanjuan; Chao, Jinbo

doi:10.1166/jctn.2016.5168

Cited by 1 publication

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“…With such a state as the initial state for the TDSE, the real-time dynamics does not have much effect on our measures for decoherence (σ ) or thermalization (δ ). If we start with a non-equilibrium state, such as a product state of S and E, where S is in the ground state and E is in a canonical thermal state, the real-time dynamics play an important role in both the decoherence and the thermalization of S [39,41,60], as seen in Fig. 2.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Quantum decoherence and thermalization at finite temperature within the canonical-thermal-state ensemble

Novotny

Jin

Yuan³

et al. 2016

Phys. Rev. A

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We study measures of decoherence and thermalization of a quantum system S in the presence of a quantum environment (bath) E. The whole system is prepared in a canonical thermal state at a finite temperature. Applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider the uncoupled system to predict decoherence and thermalization measures of S. This decoupling allows closed form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of S and of E. Numerical results for both coupled and decoupled systems with up to 40 quantum spins validate these findings.PACS numbers: 03.65. Yz, 75.10.Jm, 75.10.Nr, 05.45.Pq Decoherence and thermalization are two basic concepts in quantum statistical physics [1]. Decoherence renders a quantum system classical due to the loss of phase coherence of the components of a system in a quantum superposition via interaction with an environment (or bath). Thermalization drives the system to a stationary state, the (micro) canonical ensemble via energy exchange with a thermal bath. As the evolution of a quantum system is governed by the time-dependent Schrödinger equation, it is natural to raise the question how classicality could emerge from a pure quantum state. This question is becoming more important technologically, for example in designing quantum computers [2] where decoherence effects are a major impediment in engineering implementations.Various theoretical and numerical studies have been performed, trying to answer this fundamental question, e.g., the microcanonical thermalization of an isolated quantum system [3][4][5][6], canonical thermalization of a system coupled to a (much) larger environment [3,[7][8][9][10][11][12][13][14][15][16][17], and of two identical quantum systems at different temperatures [18,19]. In our earlier work [20], we found that at infinite temperature the degree of decoherence of a system S scales with the dimension of the environment E if the state of the whole system S + E is randomly chosen from the Hilbert space of the whole system. We showed that in the thermodynamic limit, the system S decoheres thoroughly.In this Letter, we investigate for the first time quantitatively how classicality emerges from a pure quantum state when S + E is of a finite size and at a finite temperature. We assume that the whole system S + E is in a canonical thermal state, a pure state at finite inverse temperature β [21][22][23], and investigate measures of the decoherence and the thermalization of S. This canonical thermal state could be the result of a thermalization process of the whole system S + E coupled to a large heat bath, which we do not consider any further. The state of the system S is described by the reduced density matrix. The degree of decoherence of the system S is measured in terms of σ , defined below in terms of measures of the offdiagonal c...

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Section: Conclusion and Discussionmentioning

confidence: 99%