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
Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate...Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values Fn（t） for all t are always on the circle centered at 1 with radius 1; （2） If a quantum system S with a time-dependent Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values F,（t） for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.展开更多
Seed vigor is an index of seed quality that is used to describe the rapid and uniform germination and the establish- ment of strong seedlings in any environmental conditions. Strong seed vigor in low-temperature germi...Seed vigor is an index of seed quality that is used to describe the rapid and uniform germination and the establish- ment of strong seedlings in any environmental conditions. Strong seed vigor in low-temperature germination conditions is particularly important in direct-sowing rice production systems. However, seed vigor has not been selected as an important breeding trait in traditional breeding programs due to its quantitative inherence. In this study, we identified and mapped eight quantitative trait loci （QTLs） for seed vigor by using a recombinant inbred population from a cross between rice （Oryza sativa L. ssp. indica） cultivars ZS97 and MH63. Conditional QTL analysis identified qSV-1, qSV-Sb, qSV-6a, qSV- 6b, and qSV-11 influenced seedling establishment and that qSV- 5a, qSV-Sc, and qSV-8 influenced only germination. Of these, qSV-1, qSV-Sb, qSV-6a, qSV-6b, and qSV-8 were low-tempera- ture-specific QTLs. Two major-effective QTLs, qSV-1, and qSV-5cwere narrowed down to 1.13-Mbp and 4oo-kbp genomic regions, respectively. The results provide tightly linked DNA markers for the marker-assistant pyramiding of multiple positive alleles for increased low-temperature germination seed vigor in both normal and environments.展开更多
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.
基金supported by the National Natural Science Foundation of China(Grant No. 11171197)the IFGP of Shaanxi Normal University(Grant No. 2011CXB004)the FRF for the Central Universities(Grant No. GK201002006)
文摘Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values Fn（t） for all t are always on the circle centered at 1 with radius 1; （2） If a quantum system S with a time-dependent Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values F,（t） for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.
基金supported in part by the National High Technology Research and Development Program of China (2012AA10A304)
文摘Seed vigor is an index of seed quality that is used to describe the rapid and uniform germination and the establish- ment of strong seedlings in any environmental conditions. Strong seed vigor in low-temperature germination conditions is particularly important in direct-sowing rice production systems. However, seed vigor has not been selected as an important breeding trait in traditional breeding programs due to its quantitative inherence. In this study, we identified and mapped eight quantitative trait loci （QTLs） for seed vigor by using a recombinant inbred population from a cross between rice （Oryza sativa L. ssp. indica） cultivars ZS97 and MH63. Conditional QTL analysis identified qSV-1, qSV-Sb, qSV-6a, qSV- 6b, and qSV-11 influenced seedling establishment and that qSV- 5a, qSV-Sc, and qSV-8 influenced only germination. Of these, qSV-1, qSV-Sb, qSV-6a, qSV-6b, and qSV-8 were low-tempera- ture-specific QTLs. Two major-effective QTLs, qSV-1, and qSV-5cwere narrowed down to 1.13-Mbp and 4oo-kbp genomic regions, respectively. The results provide tightly linked DNA markers for the marker-assistant pyramiding of multiple positive alleles for increased low-temperature germination seed vigor in both normal and environments.
