Open Quantum Physics and Environmental Heat Conversion into Usable Energy: Volume 2 E-Book
Eliade Stefanescu
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- Herausgeber: Bentham Science Publishers
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
Das E-Book können Sie in Legimi-Apps oder einer beliebigen App lesen, die das folgende Format unterstützen:
Seitenzahl: 199
Veröffentlichungsjahr: 2017
Ähnliche
Open Quantum Physics and
Environmental HeatConversion into Usable Energy
(Volume 2)
Authored by
Eliade Stefanescu
Center of Advanced Studies in Physics of the Romanian Academy,
BENTHAM SCIENCE PUBLISHERS LTD.
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PREFACE
A second volume seemed to be necessary for the integrity of this book. In this volume, we provide a self-consistent foundation for the description of the electron-field interaction, for the basic elements involved in our application, and for the dissipative couplings of the active elements, the quantum injection dot electrons and the coherent electromagnetic field, with the conduction electrons and the vibrations of the crystal lattice. These phenomena are specific to open quantum physics, a theoretical field lately describing the dissipative dynamics as a dynamic semigroup. However, in this study, we use a method of Ford, Lewis, and O’Connell, providing an analytic, microscopic description of the systems of interest. We consider the structural characteristics, as the electron wave functions, the dipole moments, the electron-field coupling coefficients, and the energy and polarization decay coefficients for the active electron couplings to the crystal lattice vibrations, and to the conduction electrons and holes. We calculate the operational characteristics of the devices, as the intensity of the electromagnetic field which propagates through a superradiant or an injection structure, and the injection currents in such a structure. These quantities depend on a large number of physical constants, and material properties, such as the effective masses of the electrons and holes, the mobilities of these particles in the semiconductor crystal, the atomic masses, the elasticity coefficients, the impurity concentrations, and the geometric parameters. For a better understanding of the physical models, I give a large number of explicit numerical calculations, with results which can be compared to well-known experimental data.
ACKNOWLEDGEMENTS
The author is grateful to Professor R. F. O’Connell from Louisiana State University, for providing a microscopic method for reducing the quantum dynamics to a quantum master equation, without altering the quantum-mechanical principles, and a Hamiltonian for the electron interaction with the angular momentum of the electromagnetic field.
CONFLICT OF INTEREST
The author declares that he has no affiliation with any organization or entity from financial point of view in the subject matter or materials discussed in this eBook.
Introduction
Eliade StefanescuAbstract
While in the first volume of this book we presented a set of methods for the description of the open systems, and applications to a superradiant semiconductor structure, in this volume we concentrate on the microscopic theory and a detailed investigation of the heat conversion into usable energy. Our study is essentially based on master equations with explicit microscopic coefficients, for the active electrons, superradiant field, and crystal lattice vibrations. The quantum dynamics of electrons and electromagnetic field is obtained in the framework of a unified relativistic quantum theory, from the description of a quantum particle as a vibration propagating in space, and a relativistic principle asserting a limitation of the wave function spectrum for a finite velocity c, which does not depend on the frame of reference. The electron dynamics is described in the periodic potential of a crystal lattice and an internal field induced by impurity doping, thermal vibrations, or the application of external fields. The dissipative processes are described as resonant phenomena, with energy conservation, of correlated transitions of particles in the systems of interest with other particles of the crystal. We investigate the operation characteristics for the two versions of the device, the longitudinal quantum heat converter, and the transversal one, and the corresponding structures for the conversion of electromagnetic energy into electric energy.
In the first volume of this book [1], we presented important physical and mathematical ideas of open quantum physics [2-9], issued for an adequate description of the realistic physical systems involved in the new technological developments, as the semiconductor optoelectronic nanostructures [10-13]. These ideas mainly refer to the atom-field interaction [14-16] and the couplings of the systems of interest to the dissipative neighboring systems [17-19], mainly contained in their physical support. The dynamics of a system of interest in a
dissipative environment is a multidisciplinary problem, including basic elements of classical and modern fields, which are still under investigation [20-25], such as quantum mechanics [26-32], electromagnetism [33-35], quantum optics [36-39], non-equilibrium thermodynamics [40-42], statistical mechanics [43-47], and stochastic physics [48-50].
The starting point of our research was Lindblad’s axiomatic theory of the dissipative coupling [51], and the method of Sandulescu and Scutaru for reducing Lindblad’s description of the dissipative dynamics by semigroups, to the well-known phenomenological processes of quantum friction and diffusion [52]. This is a description of the quantum dynamics, obtained from Lindblad’s master equation of a system with the density matrix ρ(t) and the Hamiltonian H,
(1.1)which includes a dissipation term with the openness operators
(1.2)These operators are linear combinations of the system operators An with unspecified complex coefficients anm. This form of the dissipation term, valid for the most cases of practical interest of the weak dissipative coupling, guarantees the positivity of the density matrix during the whole evolution of the system. Our first objective was to investigate the physical effects of the dissipation terms on two basic quantum phenomena: (1) quantum tunneling, and (2) the atom-field interaction. In this way, we found two interesting effects: (1) tunneling enhancement, due to the additional transitions stimulated by environment [53-60], and (2) coupling through environment of the atomic operators, leading to a possible absorption of the environmental energy by a coherent electromagnetic field propagating through this environment [61].
Although Lindblad’s master equation (1.1) is in agreement with the quantum principles, and provides interesting informations about the dissipative dynamics, this equation is still unsatisfactory, including a number of unspecified parameters anm. The difficulties encountered in the application of this equation to a harmonic oscillator by considering the openness with the two operators x and p of this system have been subjects of contradictory discussions [62-68]. In principle, from physical point of view, the openness of a harmonic oscillator with x and p is not understandable, since, as one can see from subsection 2.1.8 in [1], x and p of a harmonic oscillator represent the same operator at two different moments of time, for a phase difference π/2 in the Heisenberg representation. This phase difference is not significant in this problem where the dissipative processes, as damping and diffusion, are described as slow processes in comparison with the Hamiltonian oscillations of this system. For an openness with x and p, from equation (1.1) for a harmonic oscillator with the Hamiltonian H, the mass M, and a resonance frequency ω0, at a temperature T, one can obtain the quantum master equation [69]:
(1.3)We obtain equations for the diagonal elements,
(1.4)which are physically comprehensible, being in agreement with the Pauli master equation (subsection 3.2.1 in [1]) and detailed balance relations:
(1.5)However, equations for the non-diagonal elements are
(1.6)Besides the Hamiltonian and the decay terms, two coupling terms of the transitions m↔n are included with the transitions m+1↔n+1 and m−1↔n−1, which are not understandable from the physical point of view. As it is shown in subsection 7.1.1 in [1], we understand a quantum dissipation process as a correlated transition of a particle of interest with a particle of the environment, with energy conservation: a decay of a particle of interest with an energy ħωnm is correlated to an excitation of an environment particle with an energy ħωαβ ≈ ħωnm, while the spontaneous excitation of a particle of interest with an energy ħωnm is correlated to a decay of an environment particle with an energy ħωαβ ≈ ħωnm (Fig. 1).
In agreement with the basic knowledge of the atomic dynamics, in the framework of this model we notice that although the two couplings are equal, the decay rates are much higher than the excitation rates, since, at a certain temperature T, the populations of the lower environment levels are larger than the populations of the higher environment levels.
For an arbitrary system of Fermions, we obtained a quantum master equation with a dissipation term depending on the transition operator cn+cm of the system [69],
(1.7)From this master equation, for the non-diagonal matrix elements, we obtain the following equations:
(1.8)which do not include couplings between the transitions elements, but describes dissipative transitions with specific coefficients for the couplings with the environment particles. From this perspective, the dynamics of both operators, the coordinate x and momentum p, depends on the dynamics of the transitions cm+cn, according to the expressions of these operators (subsection 2.1.6 in [1]),
(1.9)(1.10)Fig. (1)) Resonant dissipation, ħωαβ ≈ ħωnm: A spontaneous decay of a system particle is correlated with a resonant excitation of an environment particle, while a spontaneous excitation of a system particle is correlated with a resonant decay of an environment particle.Difficulties encountered in analyzing the openness with x and p have been resolved in [70]. More than that, in this framework, we obtain explicit microscopic dissipation coefficients, depending on the matrix elements of the dissipative potential, the densities of the environmental states, and the occupation probabilities of these states at a given temperature. For instance, for a harmonic oscillator in the free electromagnetic field at temperature T, we obtain the quantum master equation [69]:
(1.11)which describes transitions between successive states, with transition rates depending on the energies of these states. Compared to the master equation (1.3), this equation of the form (1.7) does not describe any couplings between the non-diagonal matrix elements, and does not include any unspecified coefficient. In this way, we generalized the detailed balance principle, as a ’dynamical detailed balance principle’, based on the condition that, in the evolution of a quantum system, dissipation yields only damping, without any couplings between the quantum transitions, which, in the general case, have different transition energies [69]. However, a dissipative environment may also generate a coupling between the transitions and the populations of a Fermion system, as any field does. It is interesting that, by this coupling, a dissipative environment may cease a part of its energy to a coherent electromagnetic field propagating through this environment [61].
In this book, we develop a microscopic theory [71-74], and with the application of a semiconductor device we propose the conversion of environmental heat into usable energy [75-80]. While in the first volume we equally presented various other approaches of open systems, proposed by famous authors, in this volume we concentrate only on the microscopic theory. Taking into account a correlation between the wave function of a quantum particle and the Hamilton equations as group velocities of this particle in the two conjugated spaces, of the coordinate and momentum, in chapter 2 of this volume we obtain the relativistic dynamics and the electromagnetic equations as a consequence of the wavy nature of the quantum particles [81]. In this way, quantum mechanics, relativity, and electromagnetism arise as parts of a unified physical theory. In this way, the spin Dirac’s theory is considered as pure quantum theory, without including any aspects outside of this theory, and so does the spin-statistic relation derived in the subsection (2.3.3) of the first volume. In chapter 3, we present the quantum system of a semiconductor crystal. We obtain the Bloch wave functions, the energy of an electron in the crystal lattice, the effective mass tensor, the quasi-momentum of an equilibrium state, the density of states, and the charge flow density induced by an internal field of the crystal. We find an interesting condition of the orientation of an internal potential for the electron energy maximization in this potential. We describe the electron dynamics in such a crystal, and three basic elements we believe fundamental for the heat conversion into usable energy: semiconductor junction, bipolar transistor, and superradiant transistor. For superradiant transitions, we calculate the coupling coefficients as functions of physical parameters. In chapter 4, we describe the dissipative dynamics of a superradiant system and basic phenomena in devices converting environmental heat into usable energy. We calculate the dissipative couplings for the superradiant transitions, the superradiant field and the optical vibrations induced by this field, in the dissipative environment of other vibrations and electrons of the crystal. We compare two possible structures of the device, the longitudinal structure with the field propagating in the direction of the injected current, i.e. perpendicularly to the semiconductor chip, and the transversal one, with the field propagating in a perpendicular direction to the injected current, i.e. in the plane of the semiconductor chip. The transversal structure, with a higher dissipation of the superradiant field propagating on the chip length, has the advantage of two mirrors with total reflection, as simpler injection electrodes. At the same time, a longitudinal structure, with a much weaker dissipation of the superradiant field, but a well-controlled transmission coefficient of the output mirror, which, at the same time, plays the role of current injection electrode, seems to be more appropriate for coupling to a compatible structure converting the superradiant energy into electric energy, and to other electronic structures as well which could be cooled down, due to the absorption of the heat generated by dissipation in this structures, through surface thermal contacts of the semiconductor chips.
Unitary Relativistic Quantum Dynamics and Electromagnetic Field
Eliade StefanescuAbstract
In this chapter we consider a quantum particle wave function with a bound spectrum of velocity c
