Matching Items (3)
Filtering by
- All Subjects: Quantum Mechanics
- All Subjects: Dielectric constant
- Creators: Matyushov, Dmitry
- Resource Type: Text
- Status: Published
Description
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
ContributorsLanfear, Nathan A (Author) / Suslov, Sergei (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Platte, Rodrigo (Committee member) / Matyushov, Dmitry (Committee member) / Kuiper, Hendrik (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016
Description
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Temperature and polarizability effects on electron transfer in biology and artificial photosynthesis
Description
This study aims to address the deficiencies of the Marcus model of electron transfer
(ET) and then provide modifications to the model. A confirmation of the inverted energy
gap law, which is the cleanest verification so far, is presented for donor-acceptor complexes.
In addition to the macroscopic properties of the solvent, the physical properties of the solvent
are incorporated in the model via the microscopic solvation model. For the molecules
studied in this dissertation, the rate constant first increases with cooling, in contrast to the
prediction of the Arrhenius law, and then decreases at lower temperatures. Additionally,
the polarizability of solute, which was not considered in the original Marcus theory, is included
by the Q-model of ET. Through accounting for the polarizability of the reactants, the
Q-model offers an important design principle for achieving high performance solar energy
conversion materials. By means of the analytical Q-model of ET, it is shown that including
molecular polarizability of C60 affects the reorganization energy and the activation barrier
of ET reaction.
The theory and Electrochemistry of Ferredoxin and Cytochrome c are also investigated.
By providing a new formulation for reaction reorganization energy, a long-standing disconnect
between the results of atomistic simulations and cyclic voltametery experiments is
resolved. The significant role of polarizability of enzymes in reducing the activation energy
of ET is discussed. The binding/unbinding of waters to the active site of Ferredoxin leads
to non-Gaussian statistics of energy gap and result in a smaller activation energy of ET.
Furthermore, the dielectric constant of water at the interface of neutral and charged
C60 is studied. The dielectric constant is found to be in the range of 10 to 22 which is
remarkably smaller compared to bulk water( 80). Moreover, the interfacial structural
crossover and hydration thermodynamic of charged C60 in water is studied. Increasing the
charge of the C60 molecule result in a dramatic structural transition in the hydration shell,
which lead to increase in the population of dangling O-H bonds at the interface.
(ET) and then provide modifications to the model. A confirmation of the inverted energy
gap law, which is the cleanest verification so far, is presented for donor-acceptor complexes.
In addition to the macroscopic properties of the solvent, the physical properties of the solvent
are incorporated in the model via the microscopic solvation model. For the molecules
studied in this dissertation, the rate constant first increases with cooling, in contrast to the
prediction of the Arrhenius law, and then decreases at lower temperatures. Additionally,
the polarizability of solute, which was not considered in the original Marcus theory, is included
by the Q-model of ET. Through accounting for the polarizability of the reactants, the
Q-model offers an important design principle for achieving high performance solar energy
conversion materials. By means of the analytical Q-model of ET, it is shown that including
molecular polarizability of C60 affects the reorganization energy and the activation barrier
of ET reaction.
The theory and Electrochemistry of Ferredoxin and Cytochrome c are also investigated.
By providing a new formulation for reaction reorganization energy, a long-standing disconnect
between the results of atomistic simulations and cyclic voltametery experiments is
resolved. The significant role of polarizability of enzymes in reducing the activation energy
of ET is discussed. The binding/unbinding of waters to the active site of Ferredoxin leads
to non-Gaussian statistics of energy gap and result in a smaller activation energy of ET.
Furthermore, the dielectric constant of water at the interface of neutral and charged
C60 is studied. The dielectric constant is found to be in the range of 10 to 22 which is
remarkably smaller compared to bulk water( 80). Moreover, the interfacial structural
crossover and hydration thermodynamic of charged C60 in water is studied. Increasing the
charge of the C60 molecule result in a dramatic structural transition in the hydration shell,
which lead to increase in the population of dangling O-H bonds at the interface.
ContributorsWaskasi, Morteza M (Author) / Matyushov, Dmitry (Thesis advisor) / Richert, Ranko (Committee member) / Heyden, Matthias (Committee member) / Beckstein, Oliver (Committee member) / Arizona State University (Publisher)
Created2019