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
The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve ...The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve some results published recently.展开更多
By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from ...By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from the trivial vacuum solution.展开更多
In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo...In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.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The author is supported in part by NNSF of China and Monbusho Scholarship of Japan.
文摘The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve some results published recently.
基金Supported by the Outstanding Youth Foundationthe National Natural Science Foundation of Chinathe Doctoral Program of Higher Education.
文摘By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from the trivial vacuum solution.
文摘In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.
