Charged Particles in Near-Earth Space

In this chapter we discuss the concepts that govern the motion of charged particles in the geomagnetic field and the principles how they stay trapped in the radiation belts. The basic particle orbit theory can be found in most plasma physics textbooks. We partly follow the presentation in Koskinen (Physics of space storms, from solar surface to the earth. Springer-Praxis, Heidelberg, 2011). A more detailed discussion can be found in Roederer and Zhang (Dynamics of magnetically trapped particles. Springer, Heidelberg, 2014). A classic treatment of adiabatic motion of charged particles is Northrop (The adiabatic motion of charged particles. Interscience Publishers, Wiley, New York, 1963).

Analysis of pairing phase transition in Sn-isotopes within semiclassical approach

We demonstrate that pairing phase transition (superfluid to normal) can be described quite generally in terms of the thermodynamical properties after verifying the obtained level densities with the available experimental data for [Formula: see text]- isotopes. Periodic-orbit theory conveniently connects the oscillatory part of level density to the underlying classical periodic orbits and hence, leads to the shell effects in the single-particle level density. Such methods incorporated with pairing effects can be used effectively to study the phase transitions in [Formula: see text]-isotopes. In addition to this, an interplay between pairing correlations and the shell effects has been understood by analyzing the results obtained for the critical temperatures and shell structure energies for [Formula: see text] isotopes. A relation between variation in critical temperatures caused by shell effects and the shell structure energies determined with and without pairing effects has been established. Furthermore, the systematics of the heat capacity (giving a clear signature of pairing phase transition) as function of temperature for these nuclei are investigated as well.

Quantum chaos and quantum graphs

This article examines the origins of the universality of the spectral statistics of quantum chaotic systems in the context of periodic orbit theory. It also considers interesting analogies between periodic orbit theory and the sigma model, along with related work on quantum graphs. The article first reviews some facts and definitions for classically chaotic systems in order to elucidate their quantum behaviour, focusing on systems with two degrees of freedom: one characterized by ergodicity and another by hyperbolicity. It then describes two semiclassical approximation techniques — Gutzwiller’s periodic orbit theory and a refined approach incorporating the unitarity of the quantum evolution — and highlights their importance in understanding universal spectral statistics, and how they are related to the sigma model. This is followed by an analysis of parallel developments for quantum graphs, which are relevant to quantum chaos.