Download Open Quantum Physics and Environmental Heat Conversion into Usable Energy Brochure

Brochure
More information from http://www.researchandmarkets.com/reports/3169444/
Open Quantum Physics and Environmental Heat Conversion into Usable
Energy
Description:
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 of 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 queantum systems
- Entropy dynamics in a matter field system
Contents:
Foreword
Preface
Acknowledgements
1 Introduction
2 Quantum dynamics
2.1 Quantum particles
2.1.1 Wavefunctions
2.1.2 Schr¨odinger equation
2.1.3 Quantum states and operators
2.1.4 Representations
2.1.5 Density matrix
2.1.6 Fermions (Pauli exclusion principle)
2.1.7 Bosons (coherent states)
2.1.8 Quantum harmonic oscillator
2.1.9 Single-particle states in a Z-Fermion system (Hartree-Fock)
2.1.10 Single-particle states and operators
2.2 Quantum electromagnetic field
2.2.1 Equations of propagation in a dissipative environment
2.2.2 Density and flow of electromagnetic energy
2.2.3 Electron-field interaction
2.2.4 Quantization of electromagnetic field
2.2.5 Quantum matter-field system
2.3 Statistics of quantum particles
2.3.1 Coupling to a thermostat
(Fermi-Dirac and Bose-Einstein distributions)
2.3.2 Densities of states and occupation probabilities
(Fermi-Dirac integrals)
2.3.3 Spin-statistics relation
3 Dissipative dynamics
3.1 Brownian motion
3.1.1 Heavy particle in a molecular environment
(Einstein-Smoluchowski)
3.1.2 Electron mobility and diffusion
3.1.3 Di?usion equation and Einstein’s relation
3.2 Stochastic equations
3.2.1 Pauli’s classical master equation and entropy
3.2.2 Boltzmann’s equation and electron transport in semiconductors
(Marshak and van Vliet)
3.2.3 Fokker-Planck equation
3.2.4 Particle distribution in a nonuniform structure (Kramers-Moyal)
3.2.5 Characteristic function with cumulants
3.2.6 Markov process in a multidimensional system
3.3 Open harmonic oscillator
3.3.1 Damping and quality factor
3.3.2 Forced harmonic oscillator and the shape of the spectral line
3.3.3 Langevin equation, correlation, autocorrelation, and memory
3.3.4 Stability, bifurcation, self-organization, and chaos
3.4 Quantum dynamic equations with dissipative terms
3.4.1 Optical potential and Breit-Wigner formula
3.4.2 Gisin equation
3.4.3 Kostin (Schr¨odinger-Langevin) equation
3.5 Method of projection operators
3.5.1 Coupled Schr¨odinger equations of a dissipative system
3.5.2 Master equation with projection operators
4 Axiomatic open quantum physics
4.1 Lindblad’s master equation
4.1.1 Lindblad’s master equation as a generator of a dynamic semigroup
4.1.2 Lindblad’s master equation as generator of a dynamic map with
linear openness operators (Alicki and Lendi)
4.1.3 Lindblad’s master equation as dynamics of an open system with
bilinear dissipative potential
4.1.4 Positivity conservation of a dissipative map
4.2 Sandulescu-Scutaru description of dissipative dynamics
4.2.1 Open harmonic oscillator
4.2.2 Schr¨odinger equation for an open system
5 Quantum tunneling with dissipative coupling
5.1 Quantum tunneling and states
5.1.1 Tunneling operator
5.1.2 Fermi’s golden rule
5.1.3 Gamow’s formula
5.1.4 Energy levels in neighboring wells
5.1.5 Tunneling from a ground state (Brink)
5.2 Tunneling dynamics
5.2.1 Dissipative tunneling (Caldera and Leggett)
5.2.2 Tunneling spectrum
6 Atom-field interaction with dissipative coupling
6.1 Maxwell-Bloch equations (Feynman, Vernon, and Hellwarth)
6.1.1 Quantum atom-?eld system
6.1.2 Carmichael’s polarization amplitudes
6.1.3 Absorption spectrum
6.2 Field propagation in a Fabry-Perot cavity
6.2.1 McCall coe?cients
6.2.2 Optical bistability in the mean-?eld approximation
(Bonifacio’s cooperativity)
6.3 Open atom-?eld systems
6.3.1 Optical equations for an open atom-?eld system
6.3.2 Optical bistability of an open atom-?eld system
7 Microscopic open quantum physics
7.1 Dissipative dynamics of Fermions
7.1.1 Reduced quantum dynamics (Ford, Lewis, and O’Connell)
7.1.2 Quantum master equation for a system of Fermions
7.2 Dissipative dynamics of an electromagnetic field
7.2.1 Field propagation in a crystal (refractive index)
7.2.2 Field interaction with electrons and phonons
7.2.3 Quantum master equations for an electromagnetic field
and the crystal lattice vibration induced by this field
7.2.4 Equations for slowly varying amplitudes
8 Open hydrogen atom
8.1 Hydrogen atom
8.1.1 Schr¨odinger equation and operators
8.1.2 Angular momentum in spherical coordinates
8.1.3 Radial eigenfunctions and energy eigenvalues
8.1.4 Angular eigenfunctions
8.2 Hydrogen atom in free electromagnetic field
8.2.1 Master equation for an open hydrogen atom
8.2.2 Decay in free electromagnetic field
9 Quantum heat converter
9.1 Superradiant transistor
9.2 Field interaction with crystal lattice vibrations
9.2.1 Field generation as a Raman component
9.2.2 Field propagation in a superradiant semiconductor structure
9.3 Quantum injection and principle 2 of thermodynamics
A Integrals
A.1 Fourier integral
A.2 Dirac’s function as an integral
A.3 Gauss integral
A.4 Fermi-Dirac integrals
A.5 Euler integrals
A.6 Integrals with asymptotic representations and Stirling’s formula
B Inequalities
B.1 Schwarz’s inequality
B.2 Uncertainty relations
C Openness with pseudo-spin of an atom-field system
D Dipole moments
D.1 Dipole moments of a hydrogen atom
D.2 Dipole moments of a dissipative cluster
E Field absorption in an electron-phonon environment
Bibliography
Index
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