The modeling of physical processes is an integral part of scientific and technical research. In this area, the Extendible C++ Application in Quantum Technologies (ECAQT) package provides the numerical simulations and ...The modeling of physical processes is an integral part of scientific and technical research. In this area, the Extendible C++ Application in Quantum Technologies (ECAQT) package provides the numerical simulations and modeling of complex quantum systems in the presence of decoherence with wide applications in photonics. It allows creating models of interacting complex systems and simulates their time evolution with a number of available time-evolution drivers. Physical simulations require massive amounts of calculations are often executed on distributed computing infrastructures. It is often difficult for non expert users to use such computational infrastructures or even to use advanced libraries over the infrastructures, because they often require being familiar with middleware and tools, parallel programming techniques and packages. The Parallel Grid Run-time and Application Development Environment (P-RADE) Grid Portal is a Grid portal solution that allows users to manage the whole life-cycle for executing a parallel application on the computing Grid infrastructures. The article describes the functionality and the structure of the web portal based on ECAQT package.展开更多
本文主要研究了在非马尔可夫环境下在时变磁场中具有各种参数的交互作用非常丰富的两个比特的海森堡XYZ模型的量子稠密编码的性质。通过量子态扩散方法Quantum State Diffusion Method(QSD)模拟了信道容量χ随时间的演化关系。经过数值...本文主要研究了在非马尔可夫环境下在时变磁场中具有各种参数的交互作用非常丰富的两个比特的海森堡XYZ模型的量子稠密编码的性质。通过量子态扩散方法Quantum State Diffusion Method(QSD)模拟了信道容量χ随时间的演化关系。经过数值模拟显示:量子稠密编码对环境关联系数γ、耦合系数J和Jz以及余弦磁场的强度B都有依赖。当环境关联系数γ变小时也就是非马尔科夫特性增加时,量子稠密编码的信道容量χ明显呈现上升趋势。在这里值得提出的是较小的耦合系数Jz、较大的耦合系数J、和较强的时变磁场强度B对于在本系统下进行有效的量子稠密编码是非常有用的,其中在非马尔科夫情形下非常明显,这对能够有效地进行信息传输非常的重要。展开更多
In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expans...In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10325523the National Fundamental Research Program of China under Grant No.2001CB309310
文摘The modeling of physical processes is an integral part of scientific and technical research. In this area, the Extendible C++ Application in Quantum Technologies (ECAQT) package provides the numerical simulations and modeling of complex quantum systems in the presence of decoherence with wide applications in photonics. It allows creating models of interacting complex systems and simulates their time evolution with a number of available time-evolution drivers. Physical simulations require massive amounts of calculations are often executed on distributed computing infrastructures. It is often difficult for non expert users to use such computational infrastructures or even to use advanced libraries over the infrastructures, because they often require being familiar with middleware and tools, parallel programming techniques and packages. The Parallel Grid Run-time and Application Development Environment (P-RADE) Grid Portal is a Grid portal solution that allows users to manage the whole life-cycle for executing a parallel application on the computing Grid infrastructures. The article describes the functionality and the structure of the web portal based on ECAQT package.
文摘本文主要研究了在非马尔可夫环境下在时变磁场中具有各种参数的交互作用非常丰富的两个比特的海森堡XYZ模型的量子稠密编码的性质。通过量子态扩散方法Quantum State Diffusion Method(QSD)模拟了信道容量χ随时间的演化关系。经过数值模拟显示:量子稠密编码对环境关联系数γ、耦合系数J和Jz以及余弦磁场的强度B都有依赖。当环境关联系数γ变小时也就是非马尔科夫特性增加时,量子稠密编码的信道容量χ明显呈现上升趋势。在这里值得提出的是较小的耦合系数Jz、较大的耦合系数J、和较强的时变磁场强度B对于在本系统下进行有效的量子稠密编码是非常有用的,其中在非马尔科夫情形下非常明显,这对能够有效地进行信息传输非常的重要。
基金supported by National Natural Science Foundation of China(Grant No. 10971253)
文摘In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.
