Open Quantum Physics and Environmental Heat Conversion into Usable Energy: Volume 2

Eliade Stefanescu

• Publisher: Bentham Science Publishers
• Year: 2017
• ISBN:
  9781681084190
• Topic: Physical Sciences
• Subtopic: Quantum Theory

A Quantum system can be viewed as a larger closed system comprising of two components: an open quantum system and its surrounding environment. These two components interact with each other, and in the realm of theoretical physics, this interaction cannot be neglected. This eBook explains mathematical and statistical concepts essential for describing a realistic quantum system by presenting recent contributions in this field. The book commences by explaining the basics of quantum mechanics, statistical physics, and physics of open quantum systems. Detailed methods of deriving theoretical equations with explicit analytical coefficients with respect to open quantum systems are also explained. The book concludes with the study of a quantum heat converter in the framework of an all-microscopic theory involving fermions, photons, and phonons.
Readers of this book will gain a better understanding on the following topics:
· Quantum mechanics including the Boson and Fermion states, Fermi-Dirac and Bose-Einstein statistics, spin-statistics relation, many-body systems of Bosons and Fermions, the Fermi-Dirac integrals of the Fermion state densities, and transport phenomena in semiconductors.
· Dissipative dynamics and quantum systems such as friction, diffusion, friction-diffusion relation, mobility, occupation probability dynamics, damping, spectral width, correlation and autocorrelation, memory, stability, bifurcation, self-organization, and chaos.
· Lindblad's theory of open quantum systems through the work of Alicki and Lendi.
· Quantum tunneling as an interaction with a system.
· Optical bistability, including the fundamental contributions of Carmichael, McCall, and Bonifacio.
· Master equations based on the microscopic theory of Ford, Lewis, and O'Connell.
· Field propagation in a semiconductor structure.
· Coherent light propagation in the framework of a microscopic model including the refractive index and the Raman frequency shift.
· Heat conversion in the framework of an all-microscopic model of open quantum systems.
· Entropy dynamics in a matter field system.

Quantum Systems of Electrons in a Semiconductor Crystal

Eliade Stefanescu

St.Petersburg, Russia

Abstract

In this chapter, we describe steady states and dynamical characteristics of the electrons in the periodic potential of a crystal, and the application of three semiconductor elements: the rectifying junction, the bipolar transistor, and the superradiant junction. While for an arbitrary potential the electron momentum does not commute with the Hamiltonian, in the periodic potential of a crystal lattice we find a quasi-momentum, which commutes with this Hamiltonian. We obtain the quasi-momentum eigenvalues as eigenvectors of the reciprocal lattice. In this way, we find quasi-momentum eigenstates, called Bloch states, the energy as a function of this quasi-momentum, and equilibrium eigenstates in the quasi-momentum space. From the energy variation with the quasi-momentum in the equilibrium states, we find the tensor of the effective mass of the electron in a crystal lattice. We find that for an internal potential of interaction oriented with the gradient perpendicular to the equilibrium quasi-momentum, the electron dynamics in the semiconductor structure is simply described by the Schrödinger equation of this potential, while the periodic potential of the crystal lattice does not play any role. For N electrons in a quantization volume V, we derive the density of Bloch states as a function of the crystal lattice characteristics. We find the velocity and the acceleration of an electron under the action of...

Table of contents

• Welcome
• Table of Contents
• Title Page
• BENTHAM SCIENCE PUBLISHERS LTD.
• PREFACE
• ACKNOWLEDGEMENTS
• Introduction
• Unitary Relativistic Quantum Dynamics and Electromagnetic Field
• Quantum Systems of Electrons in a Semiconductor Crystal
• Superradiant Structure and Heat Conversion into Usable Energy
• Appendix A
• Appendix B
• REFERENCES