Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing

We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in its ciritical region. By studying the spectral statistics, we show that the bandwidth distribution and level spacing distribution in the critical region follow inverse power laws, which however break down in the extended and localized regions. By performing a finite-size scaling analysis, we can obtain some critical exponents of the system and find these exponents fulfilling a hyperscaling law in the whole critical region. We also carry out a multifractal analysis on system's wavefuntions by using a box-counting method and unveil the wavefuntions displaying different behaviors in the critical, extended and localized regions.Comment: 9 pages, 8 figure

GLONASS

The Global’naya Navigatsionnaya Sputnikova Sistema (GLONASS) is a global navigation satellite system developed by the Russian Federation. Similar to its US counterpart, the NAVSTAR global positioning system (GPS), GLONASS provides dualfrequency L-band navigation signals for civil and military navigation. Initiated in the 1980s, the system first achieved its full operational capability in 1995. Following a temporary degradation, the nominal constellation of 24 satellites was ultimately reestablished in 2011 and the system has been in continued service since then. This chapter describes the architecture and operations of GLONASS and discusses its current performance. In addition, the planned evolution of the space and ground segment are outlined