We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Marko...We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.展开更多
Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where ...Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.展开更多
基金Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 09JJ6011)the Natural Science Foundation of the Education Department of Hunan Province of China (Grant Nos. 06C652 and 07C528)
文摘We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171027, 11101339） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20120003110003）.
文摘Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.
