A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0...A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).展开更多
We analyze universal conditions where the l_1 norm and relative entropy of coherence are amplified and frozen under identical bit-flip channels;that is,using pre-measurements（quantum weak measurements or quantum meas...We analyze universal conditions where the l_1 norm and relative entropy of coherence are amplified and frozen under identical bit-flip channels;that is,using pre-measurements（quantum weak measurements or quantum measurement reversals） on the systems before undergoing local bit-flip channels.With the option of quantum weak measurements or quantum measurement reversals,the measurement strength and the success probability are all determined by the initial state of the quantum system.展开更多
基金Supported by the Tsinghua U niversity Science Fund
文摘A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11204156,61178012,11304179,and 11247240)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20133705110001)
文摘We analyze universal conditions where the l_1 norm and relative entropy of coherence are amplified and frozen under identical bit-flip channels;that is,using pre-measurements（quantum weak measurements or quantum measurement reversals） on the systems before undergoing local bit-flip channels.With the option of quantum weak measurements or quantum measurement reversals,the measurement strength and the success probability are all determined by the initial state of the quantum system.
