Schwinger pair production rate and time for some space-dependent fields via worldline instantons formalism

Schwinger pair production rate and time in some space-dependent fields are studied analytically by using the worldline instantons formalism. The instanton path, action, production rate, vacuum-decay time and tunneling time are obtained, which depend on the Keldysh parameter significantly. It is found that under a given field the instanton paths with different Keldysh parameter are exactly in the same plane. Moreover, the normalized instanton actions are all bounded within the region from $$\pi$$ to $$2\pi$$. We also find the relationship between vacuum-decay time and tunneling time. Graphic abstract: Schwinger pair production rate and time in some space-dependent fields are studied analytically by using the worldline instantons formalism. The instanton path, action, production rate, vacuum-decay time and tunneling time are obtained, which depend on the Keldysh parameter significantly. It is found that under a given field the instanton paths with different Keldysh parameter are exactly in the same plane. Moreover, the normalized instanton actions are all bounded within the region from $$\pi$$ to $$2\pi$$. We also find the relationship between vacuum-decay time and tunneling time

Spatio-Temporal patterns of land use/cover changes over the past 20years in the middle reaches of the tarim river, Xinjiang, China

The interaction between land use/cover change and landscape pattern is pivotal in research concerning global environmental change. This study uses three different Landsat images of 1989, 1998 and 2009 to study the land use/cover and landscape pattern changes in the middle reaches of the Tarim River basin. envi®, erdas®, ArcGIS® and fragstats® software were used to analyse the land use/cover changes. The objectives of study were to map and study the changes in land use/cover and landscape pattern, and propose some possible factors in making the land use/cover changes from 1989 to 2009. Seven different types of land use/cover are analysed, and the results are listed in tables. From 1989 to 1998, the percentage of farmland, slight-moderate saline land, heavy saline land and water areas have increased; woodland, desert and the undeveloped land have decreased. From 1998 to 2009, farmland, heavy saline land and the undeveloped land have increased; the other types of land use/cover have decreased. The gravity centre of each land use/cover types has shifted. The farthest shifting of the gravity centre was heavy saline land, which occurred between 1989 and 1998. The transformation and changes of land use/covers and landscape occurred more frequently from 1989 to 2009. Other types of land use and land cover changes to saline land have increased, which implied that a serious salinization took place in the Tarim Basin. The results from this study would show the adverse environmental changes (e.g. salinization and desertification) and they can be used for future sustainable management of land resources