Current Search: Quantum theory (x)
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Pages
- Title
- Test spaces.
- Creator
- Broudo, Nissim., Florida Atlantic University, Schroeck, Franklin E., Foulis, D. J.
- Abstract/Description
-
A Test Space is a mathematical object which models the process of scientific inquiry. We examine the motivation of defining the Test Spaces and discuss connections between the Test Spaces and Metamathematics. A variant of Test Spaces called orthogonal partitions is introduced and we draw comparisons between the two. The combinatorial problems of counting finite Test Spaces and orthogonal partitions is highlighted. Some issues in manipulating infinite Test Spaces are discussed as well.
- Date Issued
- 1999
- PURL
- http://purl.flvc.org/fcla/dt/15751
- Subject Headings
- Quantum theory, Set theory
- Format
- Document (PDF)
- Title
- QUANTIZATION OF CONSTANTLY CURVED TETRAHEDRON.
- Creator
- Hsiao, Chen-Hung, Han, Muxin, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
- Abstract/Description
-
Quantum tetrahedron is a key building block in the theory of Loop Quantum Gravity (LQG) and plays a crucial role in the boundary states of the spinfoam amplitude of LQG. In LQG with vanishing cosmological constant, the physical Hilbert space of the quantum at tetrahedron is the 4-valent SU(2) intertwiner space labeled by irreducible representation, each assigned to a face of the quantum at tetrahedron. Furthermore, the space is the solution space of the quantum at closure condition. The area...
Show moreQuantum tetrahedron is a key building block in the theory of Loop Quantum Gravity (LQG) and plays a crucial role in the boundary states of the spinfoam amplitude of LQG. In LQG with vanishing cosmological constant, the physical Hilbert space of the quantum at tetrahedron is the 4-valent SU(2) intertwiner space labeled by irreducible representation, each assigned to a face of the quantum at tetrahedron. Furthermore, the space is the solution space of the quantum at closure condition. The area spectrum of each face of the quantum at tetrahedron is discrete and is characterized by a spin label. Classically, the correspondence between a set of solutions of at closure condition and at tetrahedron is guaranteed by the Minkowski theorem. This theorem has been generalized to the curved case, where a curved closure condition applies. The curved Minkowski theorem allows us to reconstruct homogeneously curved tetrahedra (spherical or hyperbolic tetrahedra) from a family of four SU(2) holonomies that satisfy the curved closure condition Although the quantization of the closure condition for a at tetrahedron has been extensively studied in LQG, the quantization of the curved closure condition and curved tetrahedron has not been explored yet. The homogeneously curved tetrahedron has played an important role in the recent construction of the spinfoam model with cosmological constant in 3+1 dimensional LQG. It is anticipated that the quantization of a curved tetrahedron should deFIne the building block for the boundary Hilbert space of the spinfoam model.
Show less - Date Issued
- 2024
- PURL
- http://purl.flvc.org/fau/fd/FA00014446
- Subject Headings
- Quantum physics, Quantum theory, Quantum gravity, Tetrahedra
- Format
- Document (PDF)
- Title
- ON THE ANALYSIS OF PARASTATISTICAL MODELS IN QUANTUM FIELD THEORY.
- Creator
- SHELLEY, JAMES DAVID., Florida Atlantic University
- Abstract/Description
-
Working with the creation and annihilation operators of the Cook formalism we develop methods to analyze the permutation symmetry of the (n-1)-particle system that results when the annihilation operator is applied to a system of n indistinguishable particles having a particular initial permutation symmetry. These methods are then applied to the Wigner supermultiplet model.
- Date Issued
- 1973
- PURL
- http://purl.flvc.org/fcla/dt/13543
- Subject Headings
- Quantum field theory
- Format
- Document (PDF)
- Title
- STOCHASTIC SPIN ENTROPY.
- Creator
- NESTOR, JOSEPH CARL, Florida Atlantic University
- Abstract/Description
-
The thesis first discusses the history and general properties of entropy, concentrating on the mathematical properties. It then introduces the formalism of stochastic quantum mechanics and the stochastic Boltzmann-Gibbs-Shannon entropy, emphasizing the advantages of the stochastic formalism. The relative entropy for the spin 1/2 system is constructed in the formalisms of usual quantum mechanics and stochastic quantum mechanics. The maximum spin entropy states are then found for the quantum...
Show moreThe thesis first discusses the history and general properties of entropy, concentrating on the mathematical properties. It then introduces the formalism of stochastic quantum mechanics and the stochastic Boltzmann-Gibbs-Shannon entropy, emphasizing the advantages of the stochastic formalism. The relative entropy for the spin 1/2 system is constructed in the formalisms of usual quantum mechanics and stochastic quantum mechanics. The maximum spin entropy states are then found for the quantum mechanical relative spin entropy and the stochastic classical relative spin entropy. The latter is shown to be an acceptable candidate for a new relative spin entropy for the spin 1/2 system.
Show less - Date Issued
- 1983
- PURL
- http://purl.flvc.org/fcla/dt/14182
- Subject Headings
- Entropy, Quantum theory
- Format
- Document (PDF)
- Title
- Measurements of output factors for small photon fields up to 10 cm x 10 cm.
- Creator
- Bacala, Angelina, Pella, Silvia, Charles E. Schmidt College of Science, Department of Physics
- Abstract/Description
-
Field output factors (OF) for photon beams from a 6 MV medical accelerator were measured using five different detectors in a scanning water phantom. The measurements were taken for square field sizes of integral widths ranging from 1 cm to 10 cm for two reference source-to-surface distances (SSD) and depths in water. For the diode detectors, square field widths as small as 2.5 mm were also studied. The photon beams were collimated by using either the jaws or the multileaf collimators....
Show moreField output factors (OF) for photon beams from a 6 MV medical accelerator were measured using five different detectors in a scanning water phantom. The measurements were taken for square field sizes of integral widths ranging from 1 cm to 10 cm for two reference source-to-surface distances (SSD) and depths in water. For the diode detectors, square field widths as small as 2.5 mm were also studied. The photon beams were collimated by using either the jaws or the multileaf collimators. Measured OFs are found to depend upon the field size, SSD, depth and also upon the type of beam collimation, size and type of detector used. For field sizes larger than 3 cm x 3 cm, the OF measurements agree to within 1% or less. The largest variation in OF occurs for jawsshaped field of size 1 cm x 1cm, where a difference of more than 18% is observed.
Show less - Date Issued
- 2013
- PURL
- http://purl.flvc.org/fau/fd/FA0004003
- Subject Headings
- Integrated circuits, Photonics, Quantum electrodynamics, Quantum theory
- Format
- Document (PDF)
- Title
- ON THE PARAXIAL APPROXIMATION IN QUANTUM OPTICS.
- Creator
- Jongewaard, Maria Fernanda de Boer, Beetle, Christopher, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
- Abstract/Description
-
We examine how best to associate quantum states of a single particle to modes of a narrowly collimated beam of classical radiation modeled in the paraxial approximation, both for scalar particles and for photons. Our analysis stresses the importance of the relationship between the inner product used to define orthogonal modes of the paraxial beam, on the one hand, and the inner product underlying the statistical interpretation of the quantum theory, on the other. While several candidates for...
Show moreWe examine how best to associate quantum states of a single particle to modes of a narrowly collimated beam of classical radiation modeled in the paraxial approximation, both for scalar particles and for photons. Our analysis stresses the importance of the relationship between the inner product used to define orthogonal modes of the paraxial beam, on the one hand, and the inner product underlying the statistical interpretation of the quantum theory, on the other. While several candidates for such an association have been proposed in the literature, we argue that one of them is uniquely well suited to the task. Specifically, the mapping from beam modes to ”henochromatic” fields on spacetime is unique within a large class of similar mappings in that it is unitary in a mathematically precise sense. We also show that the single-particle quantum states associated to the orthogonal modes of a classical beam in the henochromatic approach are not only orthogonal, but also complete in the quantum Hilbert space.
Show less - Date Issued
- 2023
- PURL
- http://purl.flvc.org/fau/fd/FA00014212
- Subject Headings
- Quantum optics, Hilbert space, Quantum theory
- Format
- Document (PDF)
- Title
- COMPUTATIONAL ASPECTS OF QUANTUM GRAVITY: NUMERICAL METHODS IN SPINFOAM MODELS.
- Creator
- Qu, Dongxue, Han, Muxin, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
- Abstract/Description
-
Quantum Gravity attempts to unify general relativity (GR) and quantum theory, and is one of the challenging research areas in theoretical physics. LQG is a background-independent and non-perturbative approach towards the theory of quantum gravity. The spinfoam formulation gives the covariant path integral formulation of LQG. The spinfoam amplitude plays a crucial role in the spinfoam formulation by defining the transition amplitude of covariant LQG. It is particularly interesting for testing...
Show moreQuantum Gravity attempts to unify general relativity (GR) and quantum theory, and is one of the challenging research areas in theoretical physics. LQG is a background-independent and non-perturbative approach towards the theory of quantum gravity. The spinfoam formulation gives the covariant path integral formulation of LQG. The spinfoam amplitude plays a crucial role in the spinfoam formulation by defining the transition amplitude of covariant LQG. It is particularly interesting for testing the semiclassical consistency of LQG, because of the connection between the semiclassical approximation of path integral and the stationary phase approximation. The recent semiclassical analysis reveals the interesting relation between spinfoam amplitudes and the Regge calculus, which discretizes GR on triangulations. This relation makes the semiclassical consistency of covariant LQG promising. The spinfoam formulation also provides ways to study the n-point functions of quantum-geometry operators in LQG. Despite the novel and crucial analytic results in the spinfoam formulation, the computational complexity has been obstructed further explorations in spinfoam models. Nevertheless, numerical approaches to spinfoams open new windows to circumvent this obstruction. There has been enlightening progress on numerical computation of the spinfoam amplitudes and the two-point function. The numerical technology should expand the toolbox to investigate LQG.
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FA00013878
- Subject Headings
- Quantum gravity, Quantum theory, Quantum gravity--Mathematics, Theoretical physics
- Format
- Document (PDF)
- Title
- One Dimensional Three Body Problems with Delta Function Potentials.
- Creator
- Rhodes, C. E., McGuire, James B., Florida Atlantic University
- Abstract/Description
-
Solutions and partial solutions of some three body, one dimensional, quantum mechanical problems are presented in this thesis. The particles are assumed to interact with one another through delta function potentials. The three body mathematical problems are transformed into an equivalent problem which can be interpreted as one particle moving in a two dimensional space. Some special cases are then considered which can be worked or partially worked.
- Date Issued
- 1968
- PURL
- http://purl.flvc.org/fau/fd/FA00000819
- Subject Headings
- Three-body problem, Quantum theory
- Format
- Document (PDF)
- Title
- Non-equilibrium transport phenomena in low-dimensional quantum systems.
- Creator
- Valtchinov, Vladimir Ivanov., Florida Atlantic University, Wille, Luc T.
- Abstract/Description
-
In this thesis we have introduced and extensively studied a model for describing some essential non-equilibrium transport properties of a quantum system with reduced dimensionality. The problem of finding some of the kinetic characteristics of such a model system is formulated as that of finding a solution of a tunneling Hamiltonian with a Hubbard term. To solve this Hamiltonian we first make use of the path integral formalism, generalized for systems far from equilibrium, to perform the...
Show moreIn this thesis we have introduced and extensively studied a model for describing some essential non-equilibrium transport properties of a quantum system with reduced dimensionality. The problem of finding some of the kinetic characteristics of such a model system is formulated as that of finding a solution of a tunneling Hamiltonian with a Hubbard term. To solve this Hamiltonian we first make use of the path integral formalism, generalized for systems far from equilibrium, to perform the quantum-statistical average. The spectral function for the electrons in the well is calculated for different relevant sets of parameters. The possible presence of a Kondo peak in the interacting density of states is discussed. We calculate the frequency-driven conductance and energy losses in the linear response approximation. Numerical simulations of the general expressions show that for a given set of parameters consistent with the particular physical situation of interest, a resonant behavior is obtained for both the conductance and energy absorption for external frequencies equal to the Coulomb repulsion energy E(C).
Show less - Date Issued
- 1993
- PURL
- http://purl.flvc.org/fcla/dt/14938
- Subject Headings
- Statistical mechanics, Quantum theory, Green's functions, Equilibrium
- Format
- Document (PDF)
- Title
- The jj-coupling scheme by tensor operators and a thorough interpretation of the spectra of some nickel(II) complexes.
- Creator
- Alves, Gelio., Florida Atlantic University, Perumareddi, Jayarama R.
- Abstract/Description
-
The ligand field theory of complexes has been completely developed and the energy matrix elements for complexes in various geometries in different coupling schemes have been worked in considerable detail. However for many coupling schemes the computing of energy matrix elements is a tedious and laborious process. In the first part of my thesis we present a solution to the Weak-Field II problem using ladder operators and tensor operators. We used the Weak-Field II as an example to stress the...
Show moreThe ligand field theory of complexes has been completely developed and the energy matrix elements for complexes in various geometries in different coupling schemes have been worked in considerable detail. However for many coupling schemes the computing of energy matrix elements is a tedious and laborious process. In the first part of my thesis we present a solution to the Weak-Field II problem using ladder operators and tensor operators. We used the Weak-Field II as an example to stress the complexity of computing energy matrix elements using ladder operators versus the simplicity of calculating matrix elements with tensor operators. Also the Weak-Field II was used as a model example hoping to be able to accomplish the same with the jj-II coupling scheme. In the last part of my thesis we present a derivation of simplifying expressions for the energy matrix elements for the d 2 complex in the jj-II coupling scheme. It is worth mentioning that the expressions derived can be applied to complexes other than octahedral and further they can be generalized for complexes with n-electrons in the valence shell. Finally, we present a thorough analysis of the electronic spectra of some Nickel(II) complexes.
Show less - Date Issued
- 2005
- PURL
- http://purl.flvc.org/fcla/dt/13256
- Subject Headings
- Ligand field theory, Quantum chemistry, Stereochemistry
- Format
- Document (PDF)
- Title
- Three impenetrable particles on a ring and the quantum billiard in a triangle.
- Creator
- Dirk, Charlotte Joan, Florida Atlantic University, McGuire, James B.
- Abstract/Description
-
Remarkable similarities are found in the problem of three impenetrable quantum mechanical particles on a ring and the problem of the quantum billiard in a triangle. If the energy contributed by the motion of the center of mass in the ring problem is subtracted from the total energy, the energy eigenvalues of the particles on the ring are proportional to the energy eigenvalues of the wave function in the corresponding triangle. The eigenvalues derived from the ring solution are unique to that...
Show moreRemarkable similarities are found in the problem of three impenetrable quantum mechanical particles on a ring and the problem of the quantum billiard in a triangle. If the energy contributed by the motion of the center of mass in the ring problem is subtracted from the total energy, the energy eigenvalues of the particles on the ring are proportional to the energy eigenvalues of the wave function in the corresponding triangle. The eigenvalues derived from the ring solution are unique to that triangle and that energy level. A mathematical relationship is derived, which connects the masses of the particles on the ring to the angles of the triangle. There are three quantum billiard triangles that have previously been solved by the method of separation of variables. The three quantum particles on a ring problem, however, has now been solved for many cases. By correlating the three known triangle solutions to the masses on the ring problem we derive and verify a relationship between the two problems. For the three known triangle solutions, the eigenvalues found in the ring problem are proportional to those found in the triangle. The correlation between the masses on the ring and the triangle is then used to find solutions to other triangles, which do not yield to solution by separation of variables.
Show less - Date Issued
- 2002
- PURL
- http://purl.flvc.org/fau/fd/FADT12005
- Subject Headings
- Quantum theory, Wave mechanics, Statistical mechanics
- Format
- Document (PDF)
- Title
- QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA.
- Creator
- Dias, Rafael Guolo, Engle, Jonathan S., Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
- Abstract/Description
-
We propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the...
Show moreWe propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the number of terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature, with special attention to a most recent case. In addition, we discuss a lapse commonly chosen to decouple the evolution of the two degrees of freedom of the model, yielding exact solubility of the model, and we show that such choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, but must include an infinite number of shift operators. Also, we show the reasons why we call the classical limit “naïve”, and point this out as a reason for one limitation of some present prescriptions.
Show less - Date Issued
- 2024
- PURL
- http://purl.flvc.org/fau/fd/FA00014546
- Subject Headings
- Black holes (Astronomy), Quantum theory, Diffeomorphisms, Gravity
- Format
- Document (PDF)
- Title
- Power dependent van der Waals interaction and cold atom reflection.
- Creator
- Estrada, Gerardo, Guzmán , Angela M., Graduate College
- Date Issued
- 2011-04-08
- PURL
- http://purl.flvc.org/fcla/dt/3164525
- Subject Headings
- Van der Waals forces, Quantum field theory, Force and energy
- Format
- Document (PDF)
- Title
- Charge Regulation of a Surface Immersed in an Electrolyte Solution.
- Creator
- Acharya, Pramod, Lau, Andy W. C., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
- Abstract/Description
-
In this thesis, we investigate theoretically a new model of charge regulation of a single charged planar surface immersed in an aqueous electrolyte solution. Assuming that the adsorbed ions are mobile in the charged plane, we formulate a field theory of charge regulation where the numbers of adsorbed ions can be determined consistently by equating the chemical potentials of the adsorbed ions to that of the ions in the bulk. We analyze the mean-field treatment of the model for electrolyte of...
Show moreIn this thesis, we investigate theoretically a new model of charge regulation of a single charged planar surface immersed in an aqueous electrolyte solution. Assuming that the adsorbed ions are mobile in the charged plane, we formulate a field theory of charge regulation where the numbers of adsorbed ions can be determined consistently by equating the chemical potentials of the adsorbed ions to that of the ions in the bulk. We analyze the mean-field treatment of the model for electrolyte of arbitrary valences, and then beyond, where correlation effects are systematically taken into account in a loop expansion. In particular, we compute exactly various one-loop quantities, including electrostatic potentials, ion distributions, and chemical potentials, not only for symmetric (1, 1) electrolyte but also for asymmetric (2, 1) electrolyte, and make use of these quantities to address charge regulation at the one-loop level. We find that correlation effects give rise to various phase transitions in the adsorption of ions, and present phase diagrams for (1, 1) and (2, 1) electrolytes, whose distinct behaviors suggest that charge regulation, at the one-loop level, is no longer universal but depends crucially on the valency of the ions.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004560, http://purl.flvc.org/fau/fd/FA00004560
- Subject Headings
- Surface chemistry., Intermolecular forces., Electrodynamics., Quantum field theory.
- Format
- Document (PDF)
- Title
- Representation of groups in quantum mechanics.
- Creator
- Paskaleva, Elitza Dimitrova, Florida Atlantic University, Schroeck, Franklin E., Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
In this work, we discuss the conceptual framework of quantum mechanics in the Hilbert space formalism from a group representation point of view. After a brief review of the main results of the theory of groups and their representations, we describe mathematical models of the subject, and show the applications of this theory for getting numerical answers to problems in elementary particle physics.
- Date Issued
- 2000
- PURL
- http://purl.flvc.org/fcla/dt/15758
- Subject Headings
- Quantum theory, Particles (Nuclear physics), Representations of groups, Hilbert space
- Format
- Document (PDF)
- Title
- Hamiltonian Methods in the Quantization of Gauge Systems.
- Creator
- Vaulin, Ruslan, Florida Atlantic University, Miller, Warner A., Charles E. Schmidt College of Science, Department of Physics
- Abstract/Description
-
The new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework...
Show moreThe new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework of either of the approaches are equivalent. The central to the proof of equivalence was the fact that the gauge symmetries resuIt in the constraints of the first class in Dirac's terminology that Iead to redundancy of equations of motion for some of the canonica variables. Nevertheless, analysis of the quantum theories showed that in general, the quantum theory of the dynamical Hamiltonian is inequivalent to those of the extended Hamiltonian and the Hamiltonian reduction. The new method of quantization was applied to a number of gauge systems, including the theory of relativistic particle, the Bianchi type IX cosmological model and spinor electrodynamics along side with the traditional methods of quantization. In all of the cases considered the quantum theory of the dynamical Hamiltonian was found to be well-defined and to possess the appropriate classical limit. In particular, the quantization procedure for the Bianchi type IX cosmological spacetime did not run into any of the known problems with quantizing the theory of General Relativity. On the other hand, in the case of the quantum electrodynamics the dynamical Hamiltonian approach led to the quantum theory with the modified self-interaction in the matter sector. The possible consequence of this for the quantization of the full theory of General Relativity including the matter fields are discussed.
Show less - Date Issued
- 2006
- PURL
- http://purl.flvc.org/fau/fd/FA00000882
- Subject Headings
- Quantum field theory, Mathematical physics, Evolution equations, Nonlinear, Hamiltonian systems
- Format
- Document (PDF)
- Title
- Spin-foam dynamics of general relativity.
- Creator
- Chaharsough Shirazi, Atousa, Engle, Jonathan S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
- Abstract/Description
-
In this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic...
Show moreIn this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic variables in the Plebanski-Holst formulation of gravity from which spin-foam is derived are a Lorentz connection and a Lorentz-algebra valued two-form, called the Plebanski two-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski two-form alone. The spin-foam sum is therefore a discretized version of a Plebanski-Holst path integral in which only the Plebanski two-form appears, and in which the conne ction degrees of freedom have been integrated out. Calculating the measure factor for Plebanksi Holst formulation without the connection degrees of freedom is one of the aims of this dissertation. This analysis is at the continuum level and in order to be implemented in spin-foams one needs to properly discretize and quantize this measure factor. The correct phase is determined by semi-classical behavior. In asymptotic analysis of the Engle-Pereira-Rovelli-Livine spin-foam model, due to the inclusion of more than the usual gravitational sector, more than the usual Regge term appears in the asymptotics of the vertex amplitude. As a consequence, solutions to the classical equations of motion of GR fail to dominate in the semi-classical limit. One solution to this problem has been proposed in which one quantum mechanically imposes restriction to a single gravitational sector, yielding what has been called the “proper” spin-foam model. However, this revised model of quantum gravity, like any proposal for a theory of quantum gravity, must pass certain tests. In the regime of small curvature, one expects a given model of quantum gravity to reproduce the predictions of the linearized theory. As a consistency check we calculate the graviton two-point function predicted by the Lorentzian proper vertex and examine its semiclassical limit.
Show less - Date Issued
- 2015
- PURL
- http://purl.flvc.org/fau/fd/FA00004488, http://purl.flvc.org/fau/fd/FA00004488
- Subject Headings
- General relativity (Physics), Gravitation, Mass (Physics), Mathematical physics, Quantum gravity, Quantum theory
- Format
- Document (PDF)
- Title
- Initial investigations of the magnetic circular dichroism of isobutene using synchrotron radiation in the vacuum ultraviolet region.
- Creator
- Sanders, Clifford., Charles E. Schmidt College of Science, Department of Chemistry and Biochemistry
- Abstract/Description
-
Ethylene is the simplest alkene. The carbon-carbon double bond is ubiquitous in the field of chemistry. Ethylene serves as the basis for understanding these molecules. Thus, the assignment of the electronic transitions in ethylene is an important endeavor that many scientists have undertaken, but are yet to decipher theoretically or experimentally. Synchrotron Radiation in the vacuum ultraviolet region allows for magnetic circular dichroism (MCD) measurements of ethylene and other simple...
Show moreEthylene is the simplest alkene. The carbon-carbon double bond is ubiquitous in the field of chemistry. Ethylene serves as the basis for understanding these molecules. Thus, the assignment of the electronic transitions in ethylene is an important endeavor that many scientists have undertaken, but are yet to decipher theoretically or experimentally. Synchrotron Radiation in the vacuum ultraviolet region allows for magnetic circular dichroism (MCD) measurements of ethylene and other simple alkenes. Studies of ethylene and propylene revealed that the páap* (AgáaB1u ethylene notation) transition is not the lowest energy transition. The páa3s(R) (AgáaB3u ethylene notation) is the lowest energy transition. To further this investigation, MCD and absorption measurement were carried out on isobutene. The isobutene spectra clearly showed four electronic transitions in the 156 to 212 nm wavelength region. These four isobutene transitions have been assigned as páa3s, páap*, páa3p(Sv (Band páa3px proceeding from lower energy to higher energy. The present results support the assignments in ethylene and propylene.
Show less - Date Issued
- 2009
- PURL
- http://purl.flvc.org/FAU/228772
- Subject Headings
- Bioactive compounds, Testing, Magnetic circular dichroism, Molecular spectroscopy, Spectrum analysis, Quantum theory
- Format
- Document (PDF)
- Title
- Secure Communication by Coherence Modulation at the Photon Counting Level.
- Creator
- Boughanmi, Abdellatif, Rhodes, William T., Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
- Abstract/Description
-
Secure communication is a topic of great importance. The goal of our research reported here is to develop a scheme of secure communication system using coherence modulation at the photon counting level. When operated at the photon counting level, coherence modulation can provide quantifiably secure binary transmission between two entities, security being based on the nonclonability of photons. The objectives of the research are as follows: Show that interferometer-based coherence modulation...
Show moreSecure communication is a topic of great importance. The goal of our research reported here is to develop a scheme of secure communication system using coherence modulation at the photon counting level. When operated at the photon counting level, coherence modulation can provide quantifiably secure binary transmission between two entities, security being based on the nonclonability of photons. The objectives of the research are as follows: Show that interferometer-based coherence modulation can provide physics guaranteed secure binary transmission where each bit is associated with a countable number of photons. Review the operation of conventional high-light-level coherence modulation communication and then show, by means of example, that through the reduction of light intensities to photon-counting levels the system can be made secure. Analyze a particular attack on the system to demonstrate the quantifiability of the scheme’s security. Implement a version of the BB84 quantum key distribution protocol by slightly modifying our scheme in order to achieve a greater security. Identify a variety of issues related to hardware and the challenges of implementing our scheme in the real world.
Show less - Date Issued
- 2017
- PURL
- http://purl.flvc.org/fau/fd/FA00004809, http://purl.flvc.org/fau/fd/FA00004809
- Subject Headings
- Photonics., Statistical communication theory., Optical data processing., Nanotechnology--Technological innovations., Quantum communication.
- Format
- Document (PDF)
- Title
- Quantum Circuits for Cryptanalysis.
- Creator
- Amento, Brittanney Jaclyn, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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Finite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghost-bit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with...
Show moreFinite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghost-bit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with subquadratic depth reported in the literature. Our quantum circuit for the computation of multiplicative inverses is based on the Itoh-Tsujii algorithm which exploits the property that, in a normal basis representation, squaring corresponds to a permutation of the coe cients. We give resource estimates for the resulting quantum circuit for inversion over binary elds F2m based on an elementary gate set that is useful for fault-tolerant implementation. Elliptic curves over nite elds F2m play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with a ne or projective coordinates. In this thesis we show that changing the curve representation allows a substantial reduction in the number of T-gates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in F2m in depth O(mlogm) using a polynomial basis representation, which may be of independent interest. Finally, we change our focus from the design of circuits which aim at attacking computational assumptions on asymmetric cryptographic algorithms to the design of a circuit attacking a symmetric cryptographic algorithm. We consider a block cipher, SERPENT, and our design of a quantum circuit implementing this cipher to be used for a key attack using Grover's algorithm as in [18]. This quantum circuit is essential for understanding the complexity of Grover's algorithm.
Show less - Date Issued
- 2016
- PURL
- http://purl.flvc.org/fau/fd/FA00004662, http://purl.flvc.org/fau/fd/FA00004662
- Subject Headings
- Artificial intelligence, Computer networks, Cryptography, Data encryption (Computer science), Finite fields (Algebra), Quantum theory
- Format
- Document (PDF)