A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transf...A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.展开更多
It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ，r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and the...It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ，r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and there exists a sequence {tn}, 0<tn<1, /lim, tn =1, such that {(tnz)} is a Hamilton sequence. It is the precision of a theorem of Reich-Strebel in 1974, and gives a fairly satisfactory answer to a question of Reich in 1988.展开更多
文摘A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.
基金the National Natural Science Foundation of China!(No.19531060), the DoctoralProgram Fundation of the Ministry of Education o
文摘It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ，r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and there exists a sequence {tn}, 0<tn<1, /lim, tn =1, such that {(tnz)} is a Hamilton sequence. It is the precision of a theorem of Reich-Strebel in 1974, and gives a fairly satisfactory answer to a question of Reich in 1988.
