The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potenti...The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V1 (x) = (ix)(2n+1)/m and general polynomial potential V2(x) = x2M + ib1x2M-1 + b2x2M-2 +... + ib2M-1x. The level spacing distribution of V1 has two forms. When 2n + 1 - 2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n + 1 - 2m is negative.The PT symmetry of this system is spontaneously broken as 2n + 1 - 2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V2 assumes an increasing power function when order of the polynomial is greater than two.展开更多
In the statistical standard literature the stationarity of a time dependent process generally is defined by the invariance in time of the distribution of the variable, like a SPL （sound pressure level） fluctuating i...In the statistical standard literature the stationarity of a time dependent process generally is defined by the invariance in time of the distribution of the variable, like a SPL （sound pressure level） fluctuating in time. However in reality there cannot exist constant distribution, respectively characteristics, in time in the strict mathematical sense because the time intervals of observation only can be finite due to practical reasons. Hence on every distribution and characteristics based on it a certain, but evaluable uncertainty is imposed. For monitoring these uncertainties the online-measurement technique, i.e. primarily appropriate software, is already available, also for customers. According to this state of the art the following expanded definition of the stationarity is proposed： Stationarity during a quality controlled measurement process becomes established, when the upper confidence limit of the interesting specific characteristic has no positive slope in time and correspondingly the lower confidence limit of the specific characteristic no negative slope and, as a third, a common condition, the interesting specific characteristic has adjusted itself to a constant position in time. From this a systematic criteria scheme is established and in examples applied on different in- and outdoor situations of sound impact.展开更多
As the most import fault of the Late Pleistocene in the Lhasa area,the Nalinlaka fault is a left-lateral thrust fault,striking NWW,dipping SSW with a high dip angle,and extending over 33km.According to studies on the ...As the most import fault of the Late Pleistocene in the Lhasa area,the Nalinlaka fault is a left-lateral thrust fault,striking NWW,dipping SSW with a high dip angle,and extending over 33km.According to studies on the latest strata on the Nalinlaka fault zone,this fault zone has been obviously active since the Late Pleistocene and the movement left behind some geomorphologic phenomena on the earth's surface,especially at the sites of the gully west of Cijiaolin and around Xiecun village.For example,some rivers,ridges and terraces are displaced,forming beheaded gullies and fault escarps.The horizontal displacements since the Late Pleistocene at the above two places are 54m ～ 87m,20m ～ 67m,respectively.Based on studies on the 4 trenches along the fault using the progressive constraining method,we conclude that there might have been 5 paleoearthquake events along the Nalinlaka fault since 70ka B.P.,the ages of each paleoearthquake are 68.53,54.40,< 41.23,21.96,9.86ka B.P.,and the average recurrence interval is 14.67ka.Because of the limits of trenches and earthquake events exposed by each trench,no single trench completely revealed all 5 events.There may therefore be some errors in determining the upper and lower limits of some events in this article.展开更多
文摘The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V1 (x) = (ix)(2n+1)/m and general polynomial potential V2(x) = x2M + ib1x2M-1 + b2x2M-2 +... + ib2M-1x. The level spacing distribution of V1 has two forms. When 2n + 1 - 2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n + 1 - 2m is negative.The PT symmetry of this system is spontaneously broken as 2n + 1 - 2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V2 assumes an increasing power function when order of the polynomial is greater than two.
文摘In the statistical standard literature the stationarity of a time dependent process generally is defined by the invariance in time of the distribution of the variable, like a SPL （sound pressure level） fluctuating in time. However in reality there cannot exist constant distribution, respectively characteristics, in time in the strict mathematical sense because the time intervals of observation only can be finite due to practical reasons. Hence on every distribution and characteristics based on it a certain, but evaluable uncertainty is imposed. For monitoring these uncertainties the online-measurement technique, i.e. primarily appropriate software, is already available, also for customers. According to this state of the art the following expanded definition of the stationarity is proposed： Stationarity during a quality controlled measurement process becomes established, when the upper confidence limit of the interesting specific characteristic has no positive slope in time and correspondingly the lower confidence limit of the specific characteristic no negative slope and, as a third, a common condition, the interesting specific characteristic has adjusted itself to a constant position in time. From this a systematic criteria scheme is established and in examples applied on different in- and outdoor situations of sound impact.
基金sponsored by the Specialized Project of Earthquake Profession(201008007),CEA
文摘As the most import fault of the Late Pleistocene in the Lhasa area,the Nalinlaka fault is a left-lateral thrust fault,striking NWW,dipping SSW with a high dip angle,and extending over 33km.According to studies on the latest strata on the Nalinlaka fault zone,this fault zone has been obviously active since the Late Pleistocene and the movement left behind some geomorphologic phenomena on the earth's surface,especially at the sites of the gully west of Cijiaolin and around Xiecun village.For example,some rivers,ridges and terraces are displaced,forming beheaded gullies and fault escarps.The horizontal displacements since the Late Pleistocene at the above two places are 54m ～ 87m,20m ～ 67m,respectively.Based on studies on the 4 trenches along the fault using the progressive constraining method,we conclude that there might have been 5 paleoearthquake events along the Nalinlaka fault since 70ka B.P.,the ages of each paleoearthquake are 68.53,54.40,< 41.23,21.96,9.86ka B.P.,and the average recurrence interval is 14.67ka.Because of the limits of trenches and earthquake events exposed by each trench,no single trench completely revealed all 5 events.There may therefore be some errors in determining the upper and lower limits of some events in this article.
