The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time dela...The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.展开更多
【目的】比较3个杨树品种移栽后的生长特性,揭示一些杨树品种移栽造林后生长缓慢的原因。【方法】以欧美107杨(Populus×euramericana‘74/76’)、小美旱杨(Populus popularis Hsü(1-0))和毛白杨1316(Populus tomentosa‘1316...【目的】比较3个杨树品种移栽后的生长特性,揭示一些杨树品种移栽造林后生长缓慢的原因。【方法】以欧美107杨(Populus×euramericana‘74/76’)、小美旱杨(Populus popularis Hsü(1-0))和毛白杨1316(Populus tomentosa‘1316’)3个杨树品种为对象,2017年在观测全植株历经1个生长季后的地径、树高基础上,于2017-08-01和2017-09-14分别测定根、茎、叶生物量和叶面积,并于2017-08-30测定净光合速率和叶绿素含量(SPAD值),比较其相对生长速率(RGR)、净同化速率(NAR)、比叶面积(LSA)等指标。【结果】1)移栽1个生长季后,3个杨树品种地径、树高和生物量(包括茎、叶及植物整体)均表现为欧美107杨显著高于小美旱杨和毛白杨1316。2)欧美107杨相对生长速率显著高于小美旱杨和毛白杨1316,欧美107杨和毛白杨1316的平均叶面积均显著高于小美旱杨;三者净同化速率间差异显著,表现为小美旱杨>欧美107杨>毛白杨1316;小美旱杨和毛白杨1316的同化产物向茎的分配比例显著低于欧美107杨。3)欧美107杨和毛白杨1316的总叶面积、单叶面积和比叶面积均显著大于小美旱杨;三者叶片数量差异显著,表现为小美旱杨>欧美107杨>毛白杨1316;欧美107杨和小美旱杨的净光合速率和SPAD值均显著高于毛白杨1316。【结论】不同杨树品种生长特性取决于自身遗传特性,且移栽后生长缓慢的机制存在一定差别。展开更多
We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical;the other is the quantum revival time beyond w...We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical;the other is the quantum revival time beyond which the system is fully quantum. In between, the quantum system can be well approximated by classical ensemble distribution in phase space. These results can be summarized in a diagram which we call Ehrenfest diagram. We derive an analytical expression for Ehrenfest time, which is proportional to h-1/2. According to our formula, the Ehrenfest time for the solar-earth system is about 1026 times of the age of the solar system. We also find an analytical expression for the quantum revival time, which is proportional to h-1. Both time scales involve ω(I), the classical frequency as a function of classical action. Our results are numerically illustrated with two simple integrable models. In addition, we show that similar results exist for Bose gases, where 1/N serves as an effective Planck constant.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10865006)
文摘The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.
文摘【目的】比较3个杨树品种移栽后的生长特性,揭示一些杨树品种移栽造林后生长缓慢的原因。【方法】以欧美107杨(Populus×euramericana‘74/76’)、小美旱杨(Populus popularis Hsü(1-0))和毛白杨1316(Populus tomentosa‘1316’)3个杨树品种为对象,2017年在观测全植株历经1个生长季后的地径、树高基础上,于2017-08-01和2017-09-14分别测定根、茎、叶生物量和叶面积,并于2017-08-30测定净光合速率和叶绿素含量(SPAD值),比较其相对生长速率(RGR)、净同化速率(NAR)、比叶面积(LSA)等指标。【结果】1)移栽1个生长季后,3个杨树品种地径、树高和生物量(包括茎、叶及植物整体)均表现为欧美107杨显著高于小美旱杨和毛白杨1316。2)欧美107杨相对生长速率显著高于小美旱杨和毛白杨1316,欧美107杨和毛白杨1316的平均叶面积均显著高于小美旱杨;三者净同化速率间差异显著,表现为小美旱杨>欧美107杨>毛白杨1316;小美旱杨和毛白杨1316的同化产物向茎的分配比例显著低于欧美107杨。3)欧美107杨和毛白杨1316的总叶面积、单叶面积和比叶面积均显著大于小美旱杨;三者叶片数量差异显著,表现为小美旱杨>欧美107杨>毛白杨1316;欧美107杨和小美旱杨的净光合速率和SPAD值均显著高于毛白杨1316。【结论】不同杨树品种生长特性取决于自身遗传特性,且移栽后生长缓慢的机制存在一定差别。
基金supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0303302, and 2018YFA0305602)the National Natural Science Foundation of China (Grant Nos. 11334001, and 11429402)
文摘We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical;the other is the quantum revival time beyond which the system is fully quantum. In between, the quantum system can be well approximated by classical ensemble distribution in phase space. These results can be summarized in a diagram which we call Ehrenfest diagram. We derive an analytical expression for Ehrenfest time, which is proportional to h-1/2. According to our formula, the Ehrenfest time for the solar-earth system is about 1026 times of the age of the solar system. We also find an analytical expression for the quantum revival time, which is proportional to h-1. Both time scales involve ω(I), the classical frequency as a function of classical action. Our results are numerically illustrated with two simple integrable models. In addition, we show that similar results exist for Bose gases, where 1/N serves as an effective Planck constant.
