通过数值求解Bogoliubov de Gennes方程,研究了具有自旋轨道耦合作用的一维费米晶格系统的性质.结果表明:在有限的自旋轨道耦合下和一定的磁场强度时,系统具有零能,此时的准粒子即为Majorana费米子.准无序效应研究表明,Majorana费米子...通过数值求解Bogoliubov de Gennes方程,研究了具有自旋轨道耦合作用的一维费米晶格系统的性质.结果表明:在有限的自旋轨道耦合下和一定的磁场强度时,系统具有零能,此时的准粒子即为Majorana费米子.准无序效应研究表明,Majorana费米子不会被弱准无序所破坏.展开更多
The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutatio...The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and seeond-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error （mutation） threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.展开更多
基金Supported in part by the National natural Science Foundation of China under Grant No.10675170Major State Basic Research Developing Program under Gant No.2007CB815003
文摘The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and seeond-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error （mutation） threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.
