Matching Items (21)

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The History and Importance of the Double-Slit Experiment: From Classical to Quantum Physics

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This paper analyzes the history and impact of the double-slit experiment on the world of physics. The experiment was initially created by Thomas Young in the early nineteenth century to prove that light behaved as a wave, and the experiment’s

This paper analyzes the history and impact of the double-slit experiment on the world of physics. The experiment was initially created by Thomas Young in the early nineteenth century to prove that light behaved as a wave, and the experiment’s findings ended up being foundational to the classical wave theory of light. Decades later, the experiment was replicated once more with electrons instead of light and shockingly demonstrated that electrons possessed a dual nature of behavior in that they acted in some instances as particles and in others as waves. Despite numerous modifications and replications, the dual behavior of electrons has never been definitively explained. Numerous interpretations of quantum mechanics all offer their own explanations of the double-slit experiment’s results. Notably, the Copenhagen Interpretation states that an observer measuring a quantum system, such as the double-slit experiment, causes the electrons to behave classically (i.e. as a particle.) The Many Worlds Interpretation offers that multiple branching worlds come into existence to represent the physical occurrence of all probable outcomes of the double-slit experiment. In these and other interpretations, explanations of the double-slit experiment are key to proving their respective dogmas. The double-slit experiment has historically been very important to the worlds of both classical and quantum physics and is still being modified and replicated to this day. It is clear that it will continue to remain relevant even in the future of physics.

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2021-05

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Solution methods for certain evolution equations

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Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

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2013

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High-quality extended-wavelength materials for optoelectronic applications

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Photodetectors in the 1.7 to 4.0 μm range are being commercially developed on InP substrates to meet the needs of longer wavelength applications such as thermal and medical sensing. Currently, these devices utilize high indium content metamorphic Ga1-xInxAs (x >

Photodetectors in the 1.7 to 4.0 μm range are being commercially developed on InP substrates to meet the needs of longer wavelength applications such as thermal and medical sensing. Currently, these devices utilize high indium content metamorphic Ga1-xInxAs (x > 0.53) layers to extend the wavelength range beyond the 1.7 μm achievable using lattice matched GaInAs. The large lattice mismatch required to reach the extended wavelengths results in photodetector materials that contain a large number of misfit dislocations. The low quality of these materials results in a large nonradiative Shockley Read Hall generation/recombination rate that is manifested as an undesirable large thermal noise level in these photodetectors. This work focuses on utilizing the different band structure engineering methods to design more efficient devices on InP substrates. One prospective way to improve photodetector performance at the extended wavelengths is to utilize lattice matched GaInAs/GaAsSb structures that have a type-II band alignment, where the ground state transition energy of the superlattice is smaller than the bandgap of either constituent material. Over the extended wavelength range of 2 to 3 μm this superlattice structure has an optimal period thickness of 3.4 to 5.2 nm and a wavefunction overlap of 0.8 to 0.4, respectively. In using a type-II superlattice to extend the cutoff wavelength there is a tradeoff between the wavelength reached and the electron-hole wavefunction overlap realized, and hence absorption coefficient achieved. This tradeoff and the subsequent reduction in performance can be overcome by two methods: adding bismuth to this type-II material system; applying strain on both layers in the system to attain strain-balanced condition. These allow the valance band alignment and hence the wavefunction overlap to be tuned independently of the wavelength cutoff. Adding 3% bismuth to the GaInAs constituent material, the resulting lattice matched Ga0.516In0.484As0.970Bi0.030/GaAs0.511Sb0.489superlattice realizes a 50% larger absorption coefficient. While as, similar results can be achieved with strain-balanced condition with strain limited to 1.9% on either layer. The optimal design rules derived from the different possibilities make it feasible to extract superlattice period thickness with the best absorption coefficient for any cutoff wavelength in the range.  

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2013

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Dual-wavelength internal-optically-pumped semiconductor laser diodes

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Dual-wavelength laser sources have various existing and potential applications in wavelength division multiplexing, differential techniques in spectroscopy for chemical sensing, multiple-wavelength interferometry, terahertz-wave generation, microelectromechanical systems, and microfluidic lab-on-chip systems. In the drive for ever smaller and increasingly mobile electronic

Dual-wavelength laser sources have various existing and potential applications in wavelength division multiplexing, differential techniques in spectroscopy for chemical sensing, multiple-wavelength interferometry, terahertz-wave generation, microelectromechanical systems, and microfluidic lab-on-chip systems. In the drive for ever smaller and increasingly mobile electronic devices, dual-wavelength coherent light output from a single semiconductor laser diode would enable further advances and deployment of these technologies. The output of conventional laser diodes is however limited to a single wavelength band with a few subsequent lasing modes depending on the device design. This thesis investigates a novel semiconductor laser device design with a single cavity waveguide capable of dual-wavelength laser output with large spectral separation. The novel dual-wavelength semiconductor laser diode uses two shorter- and longer-wavelength active regions that have separate electron and hole quasi-Fermi energy levels and carrier distributions. The shorter-wavelength active region is based on electrical injection as in conventional laser diodes, and the longer-wavelength active region is then pumped optically by the internal optical field of the shorter-wavelength laser mode, resulting in stable dual-wavelength laser emission at two different wavelengths quite far apart. Different designs of the device are studied using a theoretical model developed in this work to describe the internal optical pumping scheme. The carrier transport and separation of the quasi-Fermi distributions are then modeled using a software package that solves Poisson's equation and the continuity equations to simulate semiconductor devices. Three different designs are grown using molecular beam epitaxy, and broad-area-contact laser diodes are processed using conventional methods. The modeling and experimental results of the first generation design indicate that the optical confinement factor of the longer-wavelength active region is a critical element in realizing dual-wavelength laser output. The modeling predicts lower laser thresholds for the second and third generation designs; however, the experimental results of the second and third generation devices confirm challenges related to the epitaxial growth of the structures in eventually demonstrating dual-wavelength laser output.

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2011

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Solvable time-dependent models in quantum mechanics

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In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which

In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrödinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrödinger equation in R^n with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrödinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

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2011

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Ab initio study of tantalum nitride and silver adatoms

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In 2022, integrated circuit interconnects will approach 10 nm and the diffusion barrier layers needed to ensure long lasting devices will be at 1 nm. This dimension means the interconnect will be dominated by the interface and it has been

In 2022, integrated circuit interconnects will approach 10 nm and the diffusion barrier layers needed to ensure long lasting devices will be at 1 nm. This dimension means the interconnect will be dominated by the interface and it has been shown the interface is currently eroding device performance. The standard interconnect system has three layers - a Copper metal core, a Tantalum Adhesion layer and a Tantalum Nitride Diffusion Barrier Layer. An alternate interconnect schema is a Tantalum Nitride barrier layer and Silver as a metal. The adhesion layer is removed from the system along with changing to an alternate, low resistivity metal. First principles are used to assess the interface of the Silver and Tantalum Nitride. Several stoichiometric 1:1 Tantalum Nitride polymorphs are assessed and it is found that the Fe2P crystal structure is actually the most stable crystal structure which is at odds with the published phase diagram for ambient crystal structure. The surface stability of Fe2P-TaN is assessed and the absorption enthalpy of Silver adatoms is calculated. Finally, the thermodynamic stability of the TaN-Ag interconnect system is assessed.

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2012

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Symplectic topology and geometric quantum mechanics

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The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.

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2011

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Structural and optical properties of molecular beam epitaxy grown inAsBi bulk layers and quantum wells

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InAsBi is a narrow direct gap III-V semiconductor that has recently attracted considerable attention because its bandgap is tunable over a wide range of mid- and long-wave infrared wavelengths for optoelectronic applications. Furthermore, InAsBi can be integrated with other

InAsBi is a narrow direct gap III-V semiconductor that has recently attracted considerable attention because its bandgap is tunable over a wide range of mid- and long-wave infrared wavelengths for optoelectronic applications. Furthermore, InAsBi can be integrated with other III-V materials and is potentially an alternative to commercial II-VI photodetector materials such as HgCdTe.

Several 1 μm thick, nearly lattice-matched InAsBi layers grown on GaSb are examined using Rutherford backscattering spectrometry and X-ray diffraction. Random Rutherford backscattering measurements indicate that the average Bi mole fraction ranges from 0.0503 to 0.0645 for the sample set, and ion channeling measurements indicate that the Bi atoms are substitutional. The X-ray diffraction measurements show a diffraction sideband near the main (004) diffraction peak, indicating that the Bi mole fraction is not laterally uniform in the layer. The average out of plane tetragonal distortion is determined by modeling the main and sideband diffraction peaks, from which the average unstrained lattice constant of each sample is determined. By comparing the Bi mole fraction measured by random Rutherford backscattering with the InAsBi lattice constant for the sample set, the lattice constant of zinc blende InBi is determined to be 6.6107 Å.

Several InAsBi quantum wells tensilely strained to the GaSb lattice constant with dilute quantities of Bi are characterized using photoluminescence spectroscopy. Investigation of the integrated intensity as a function of carrier excitation density spanning 5×1025 to 5×1026 cm-3 s-1 indicates radiative dominated recombination and high quantum efficiency over the 12 to 250 K temperature range. The bandgap of InAsBi is ascertained from the photoluminescence spectra and parameterized as a function of temperature using the Einstein single oscillator model. The dilute Bi mole fraction of the InAsBi quantum wells is determined by comparing the measured bandgap energy to that predicted by the valence band anticrossing model. The Bi mole fraction determined by photoluminescence agrees reasonably well with that estimated using secondary ion mass spectrometry.

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2016

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Growth, optical properties, and optimization of infrared optoelectronic materials

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High-performance III-V semiconductors based on ternary alloys and superlattice systems are fabricated, studied, and compared for infrared optoelectronic applications. InAsBi is a ternary alloy near the GaSb lattice constant that is not as thoroughly investigated as other III-V alloys

High-performance III-V semiconductors based on ternary alloys and superlattice systems are fabricated, studied, and compared for infrared optoelectronic applications. InAsBi is a ternary alloy near the GaSb lattice constant that is not as thoroughly investigated as other III-V alloys and that is challenging to produce as Bi has a tendency to surface segregate and form droplets during growth rather than incorporate. A growth window is identified within which high-quality droplet-free bulk InAsBi is produced and Bi mole fractions up to 6.4% are obtained. Photoluminescence with high internal quantum efficiency is observed from InAs/InAsBi quantum wells. The high structural and optical quality of the InAsBi materials examined demonstrates that bulk, quantum well, and superlattice structures utilizing InAsBi are an important design option for efficient infrared coverage.

Another important infrared material system is InAsSb and the strain-balanced InAs/InAsSb superlattice on GaSb. Detailed examination of X-ray diffraction, photoluminescence, and spectroscopic ellipsometry data provides the temperature and composition dependent bandgap of bulk InAsSb. The unintentional incorporation of approximately 1% Sb into the InAs layers of the superlattice is measured and found to significantly impact the analysis of the InAs/InAsSb band alignment. In the analysis of the absorption spectra, the ground state absorption coefficient and transition strength of the superlattice are proportional to the square of the electron-hole wavefunction overlap; wavefunction overlap is therefore a major design parameter in terms of optimizing absorption in these materials. Furthermore in addition to improvements through design optimization, the optical quality of the materials studied is found to be positively enhanced with the use of Bi as a surfactant during molecular beam epitaxy growth.

A software tool is developed that calculates and optimizes the miniband structure of semiconductor superlattices, including bismide-based designs. The software has the capability to limit results to designs that can be produced with high structural and optical quality, and optimized designs in terms of maximizing absorption are identified for several infrared superlattice systems at the GaSb lattice constant. The accuracy of the software predictions are tested with the design and growth of an optimized mid-wave infrared InAs/InAsSb superlattice which exhibits superior optical and absorption properties.

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2016

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Quantum Transport and Scattering in Dirac Materials and Molecular Systems

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This dissertation aims to study the electron and spin transport, scattering in two dimensional pseudospin-1 lattice systems, hybrid systems of topological insulator and magnetic insulators, and molecule chain systems. For pseudospin-1 systems, the energy band consists of a pair of

This dissertation aims to study the electron and spin transport, scattering in two dimensional pseudospin-1 lattice systems, hybrid systems of topological insulator and magnetic insulators, and molecule chain systems. For pseudospin-1 systems, the energy band consists of a pair of Dirac cones and a flat band through the connecting point of the cones. First, contrary to the conditional wisdom that flatband can localize electrons, I find that in a non-equilibrium situation where a constant electric field is suddenly switched on, the flat band can enhance the resulting current in both the linear and nonlinear response regimes compared to spin-1/2 system. Second, in the setup of massive pseudospin-1 electron scattering over a gate potential scatterer, I discover the large resonant skew scattering called super skew scattering, which does not arise in the corresponding spin-1/2 system and massless pseudospin-1 system. Third, by applying an appropriate gate voltage to generate a cavity in an alpha-T3 lattice, I find the exponential decay of the quasiparticles from a chaotic cavity, with a one-to-one correspondence between the exponential decay rate and the Berry phase for the entire family of alpha-T3 materials. Based on the hybrid system of a ferromagnetic insulator on top of a topological insulator, I first investigate the magnetization dynamics of a pair of ferromagnetic insulators deposited on the surface of a topological insulator. The spin polarized current on the surface of topological insulator can affect the magnetization of the two ferromagnetic insulators through proximity effect, which in turn modulates the electron transport, giving rise to the robust phase locking between the two magnetization dynamics. Second, by putting a skyrmion structure on top of a topological insulator, I find robust electron skew scattering against skyrmion structure even with deformation, due to the emergence of resonant modes. The chirality of molecule can lead to spin polarized transport due to the spin orbit interaction. I investigate spin transport through a chiral polyacetylene molecule and uncover the emergence of spin Fano resonances as a manifestation of the chiral induced spin selectivity effect.

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2021