Einstein–Podolsky–Rosen(EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world.The directivity(or asymmetry) is a fascinating trait of EPR steering,and it is diff...Einstein–Podolsky–Rosen(EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world.The directivity(or asymmetry) is a fascinating trait of EPR steering,and it is different from other quantum nonlocalities.Here,we consider the strategy in which two atoms compose a two-qubit X state,and the two atoms are owned by Alice and Bob,respectively.The atom of Alice suffers from a reservoir,and the atom of Bob couples with a bit flip channel.The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation.The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits.The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime.In the weak coupling regime,the EPR steering monotonously decreases as t increases when coupling auxiliary qubits.The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob(or from Bob to Alice) can be more effectively revealed.Notably,the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.12175001)the Key Project of Natural Science Research of West Anhui University(Grant No.WXZR202311)+7 种基金the Natural Science Research Key Project of Education Department of Anhui Province of China(Grant Nos.KJ2021A0943,2022AH051681,and 2023AH052648)the Open Fund of Anhui Undergrowth Crop Intelligent Equipment Engineering Research Center(Grant No.AUCIEERC-2022-01)Anhui Undergrowth Crop Intelligent Equipment Engineering Research Center(Grant No.2022AH010091)the University Synergy Innovation Program of Anhui Province(Grant No.GXXT-2021-026)the Anhui Provincial Natural Science Foundation(Grant Nos.2108085MA18 and 2008085MA20)Key Project of Program for Excellent Young Talents of Anhui Universities(Grant No.gxyq ZD2019042)the open project of the Key Laboratory of Functional Materials and Devices for Informatics of Anhui Higher Education Institutes(Grant No.FMDI202106)the research start-up funding project of High Level Talent of West Anhui University(Grant No.WGKQ2021048)。
文摘Einstein–Podolsky–Rosen(EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world.The directivity(or asymmetry) is a fascinating trait of EPR steering,and it is different from other quantum nonlocalities.Here,we consider the strategy in which two atoms compose a two-qubit X state,and the two atoms are owned by Alice and Bob,respectively.The atom of Alice suffers from a reservoir,and the atom of Bob couples with a bit flip channel.The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation.The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits.The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime.In the weak coupling regime,the EPR steering monotonously decreases as t increases when coupling auxiliary qubits.The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob(or from Bob to Alice) can be more effectively revealed.Notably,the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
