Quantum dots comprise a type of quantum impurity system. The entanglement and co- herence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipat...Quantum dots comprise a type of quantum impurity system. The entanglement and co- herence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-rnotion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.展开更多
The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Poin...The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Point Theorem in cones due to Krasnoselskii[1,6].展开更多
In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups...In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.展开更多
This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ? R^n, our boundary condition is given...This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ? R^n, our boundary condition is given by∫_?u(x)-u(y)/|x-y|^(n+2s)dy = 0 for x ∈ R^n\?.We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.展开更多
The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schrrdinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In ...The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schrrdinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states （unite vectors） and mixed states （density matrices, i.e., positive operators with trace one）. Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.展开更多
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. T...The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.展开更多
This paper studies coupled nonlinear diffusion equations with more general nonlinearities, subject to homogeneous Neumann boundary conditions. The necessary and sufficient conditions are obtained for the existence of ...This paper studies coupled nonlinear diffusion equations with more general nonlinearities, subject to homogeneous Neumann boundary conditions. The necessary and sufficient conditions are obtained for the existence of generalized solutions of the system, which extend the known results for nonlinear diffusion systems with more special nonlinearities.展开更多
基金supported by the Ministry of Science and Technology of China(No.2016YFA0400900 and No.2016YFA0200600)the National Natural Science Foundation of China(No.21573202 and No.21633006)the Fundamental Research Funds for the Central Universities(No.2340000074)
文摘Quantum dots comprise a type of quantum impurity system. The entanglement and co- herence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-rnotion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.
文摘The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Point Theorem in cones due to Krasnoselskii[1,6].
基金supported by the National Natural Science Foundation of China(No.11121101)the National Basic Research Program of China(No.2013CB834100)
文摘In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.
基金supported by National Natural Science Foundation of China (Grant No. 11401521)
文摘This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ? R^n, our boundary condition is given by∫_?u(x)-u(y)/|x-y|^(n+2s)dy = 0 for x ∈ R^n\?.We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.
基金supported by the National Natural Science Foundation of China(Grant Nos.11601300,and 11571213)the Fundamental Research Funds for the Central Universities(Grant No.GK201703093)
文摘The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schrrdinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states （unite vectors） and mixed states （density matrices, i.e., positive operators with trace one）. Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.
文摘The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
基金the National Natural Science Foundation of China (Nos.10471013 10771024)
文摘This paper studies coupled nonlinear diffusion equations with more general nonlinearities, subject to homogeneous Neumann boundary conditions. The necessary and sufficient conditions are obtained for the existence of generalized solutions of the system, which extend the known results for nonlinear diffusion systems with more special nonlinearities.
