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This chapter focuses on collective motion of isoscalar nature parameterized by shape variables. The equations of motion are derived from energy conservation as implied by self-consistency. A basic ingredient is the variation of the total static energy with deformation, which at finite thermal excitations has to be calculated for constant entropy. Linear response theory is exploited for the dynamics, especially for separating reactive and dissipative forces. Response functions for intrinsic, nucleonic motion are distinguished from those for collective dynamics. The origin of irreversible behavior due to the decay of simple to more complicated nucleonic configurations is described in detail. In practical applications, dressed single particle states are used in their dependence on temperature. The variation of the transport coefficients for inertia and friction with T obtained this way is confronted with that given in various other models, like in the diabatic one, in common RPA, in the random matrix model, or in the liquid drop model and for wall friction. Implications on rotational motion are discussed.

This chapter develops the basic equations that will be used to analyse the Fermi-Dirac and Bose-Einstein gases. The representation of many-particle states in terms of products of single-particle states is presented. The reasons for using the quantum grand canonical ensemble are given, and a general expression for the grand canonical partition function is derived. The essential equations for fermions, bosons, and distinguishable particles are developed, and the basic strategy for using them to solve problems is given.

As a preliminary to discussing the properties of Bose–Einstein and Fermi–Dirac gases, this chapter presents the basic quantum equations that underlie both. The process of building N-body states from single-particle states is described, along with notation necessary to simplify the problem. The average number of particles in a given energy state and chemical potential is derived for fermions and bosons. Although all atoms are either bosons or fermions, and therefore indistinguishable, there are nevertheless real systems that are composed of distinguishable particles. Although all atoms are either bosons or fermions, and therefore indistinguishable, there are nevertheless real systems that are composed of distinguishable particles.

In certain cases, the electron involved in the scattering process may begin in a well-defined initial state and end up in an equally well-defined final state. Scattering is assumed to conserve energy and crystal momentum and occurs at a rate given by Fermi's Golden Rule. Because the dynamic state of each particle cannot be determined precisely, the concepts of statistical physics must be taken into account in order to describe the observable properties of the system. Thus, both quantum and statistical concepts must be incorporated into the description of semiconductor physics via the concept of the density matrix. This chapter focuses on quantum transport in semiconductors by considering systems that can be reasonably well described in terms of single-particle states. It first looks at the density matrix and uses it to derive the Lindhard dielectric function before turning to screening effects and two-level systems. It then looks at Fermi's Golden Rule as well as Wannier-Stark states, the intracollisional field effect, and the semi-classical approximation.

This chapter describes the mechanism of Bose–Einstein condensation in the simplest ideal Bose gas case. An explicit expression for the critical temperature is derived in the analytically soluble case of a gas confined in a box. Various thermodynamic quantities are calculated above and below the critical temperature. Emphasis is given to the isothermal compressibility which diverges below the critical temperature. The behaviour of the off-diagonal one-body density matrix is discussed. Results for the fluctuations of the single-particle occupation numbers are derived in both the canonical and grand canonical ensembles.