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The Classical Limit of Quantum Mechanics

Description: The Feynman path integral formulation of quantum mechanics is a path integral representation for a propagator or probability amplitude in going between two points in space-time. The wave function is expressed in terms of an integral equation from which the Schrodinger equation can be derived. On taking the limit h — 0, the method of stationary phase can be applied and Newton's second law of motion is obtained. Also, the condition the phase vanishes leads to the Hamilton - Jacobi equation. The s… more
Date: December 1977
Creator: Hefley, Velton Wade
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Quantized Hydrodynamics

Description: The object of this paper is to derive Landau's theory of quantized hydrodynamics from the many-particle Schroedinger equation. Landau's results are obtained, together with an additional term in the Hamiltonian.
Date: August 1972
Creator: Coomer, Grant C.
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Virial Theorem for a Molecule

Description: The usual virial theorem, relating kinetic and potential energy, is extended to a molecule by the use of the true wave function. The virial theorem is also obtained for a molecule from a trial wave function which is scaled separately for electronic and nuclear coordinates.
Date: May 1972
Creator: Ranade, Manjula A.
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The Concept of Collision Strength and Its Applications

Description: Collision strength, the measure of strength for a binary collision, hasn't been defined clearly. In practice, many physical arguments have been employed for the purpose and taken for granted. A scattering angle has been widely and intensively used as a measure of collision strength in plasma physics for years. The result of this is complication and unnecessary approximation in deriving some of the basic kinetic equations and in calculating some of the basic physical terms. The Boltzmann equatio… more
Date: May 2004
Creator: Chang, Yongbin
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Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors

Description: Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold. Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a … more
Date: May 2004
Creator: Burns, Michael E.
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Test of Gauge Invariance: Charged Harmonic Oscillator in an Electromagnetic Field

Description: The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probabil… more
Date: August 1980
Creator: Wen, Chang-tai
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Characterization, Properties and Applications of Novel Nanostructured Hydrogels.

Description: The characterization, properties and applications of the novel nanostructured microgel (nanoparticle network and microgel crystal) composed of poly-N-isopropylacrylanmide-co-allylamine (PNIPAM-co-allylamine) and PNIPAM-co-acrylic acid(AA) have been investigated. For the novel nanostructured hydrogels with the two levels of structure: the primary network inside each individual particle and the secondary network of the crosslinked nanoparticles, the new shear modulus, drug release law from hydrog… more
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Date: December 2006
Creator: Tang, Shijun
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The Dynamic Foundation of Fractal Operators.

Description: The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation … more
Date: May 2003
Creator: Bologna, Mauro
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Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor

Description: The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapun… more
Date: August 2005
Creator: Zheng, Yindong
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Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles

Description: This dissertation aims at addressing two important theoretical questions which are still debated in the statistical mechanical community. The first question has to do with the outstanding problem of how to reconcile time-reversal asymmetric macroscopic laws with the time-reversal symmetric laws of microscopic dynamics. This problem is addressed by developing a novel mechanical approach inspired by the work of Helmholtz on monocyclic systems and the Heat Theorem, i.e., the Helmholtz Theorem. By … more
Date: May 2008
Creator: Campisi, Michele
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The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes

Description: We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows … more
Date: August 2008
Creator: Bagci, Gokhan Baris
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Non-Poissonian statistics, aging and "blinking'" quantum dots.

Description: This dissertation addresses the delicate problem of aging in complex systems characterized by non-Poissonian statistics. With reference to a generic two-states system interacting with a bath it is shown that to properly describe the evolution of such a system within the formalism of the continuous time random walk (CTRW), it has to be taken into account that, if the system is prepared at time t=0 and the observation of the system starts at a later time ta>0, the distribution of the first s… more
Date: August 2004
Creator: Aquino, Gerardo
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Decoherence, Master Equation for Open Quantum Systems, and the Subordination Theory

Description: This thesis addresses the problem of a form of anomalous decoherence that sheds light into the spectroscopy of blinking quantum dots. The system studied is a two-state system, interacting with an external environment that has the effect of establishing an interaction between the two states, via a coherence generating coupling, called inphasing. The collisions with the environment produce also decoherence, named dephasing. Decoherence is interpreted as the entanglement of the coherent superposit… more
Date: August 2005
Creator: Giraldi, Filippo
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Theoretical Cross Section for Light Scattering from Superfluid Helium-4

Description: The finite lifetime of the bound roton pair is included in the theoretical light scattering cross section to explain the shape of the peak in the observed Raman light scattering cross section in He II. A model Hamiltonian is used to describe interactions between quasiparticles for the helium system. The equation of motion for the bound roton pair state, which is taken to be a collective mode of quasiparticle pairs, is solved. The cross section for light scattering is then derived using Fermi's … more
Date: May 1976
Creator: Latham, W. Peters, Jr., 1948-2016.
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A Theoretical Investigation of Bound Roton Pairs in Superfluid Helium-4

Description: The Bogoliubov theory of excitations in superfluid helium is used to study collective modes at zero temperature. A repulsive delta function shell potential is used in the quasiparticle excitation energy spectrum to fit the observed elementary excitation spectrum, except in the plateau region. The linearized equation of motion method is used to obtain the secular equation for a collective mode consisting of a linear combination of one and two free quasiparticles of zero total momentum. It is sho… more
Date: August 1974
Creator: Cheng, Shih-ta
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A Gauge-Invariant Energy Variational Principle Application to Anisotropic Excitons in High Magnetic Fields

Description: A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phas… more
Date: December 1983
Creator: Kennedy, Paul K. (Paul Kevin)
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Photon Exchange Between a Pair of Nonidentical Atoms with Two Forms of Interactions

Description: A pair of nonidentical two-level atoms, separated by a fixed distance R, interact through photon exchange. The system is described by a state vector which is assumed to be a superposition of four "essential states": (1) the first atom is excited, the second one is in the ground state, and no photon is present, (2) the first atom is in its ground state, the second one is excited, and no photon is present, (3) both atoms are in their ground states and a photon is present, and (4) both atoms are e… more
Date: May 1987
Creator: Golshan, Shahram Mohammad-Mehdi
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Linewidth Parameters, Dipole Moments, and Microwave Spectrum of Nitrogen-Substituted Methyl Cyanide

Description: The shape of collision-broadened microwave absorption lines is reviewed, along with a number of other broadening mechanisms. The Anderson and Murphy-Boggs linewidth theories are reviewed in detail. Several published modifications to these theories are reviewed. Computer programs which numerically evaluate linewidths and lineshifts are presented. Approximations are made to reduce the need for extensive use of the modified Bessel functions, thereby reducing computation time. Only dipole-dipole f… more
Date: August 1981
Creator: Messer, James Keith
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CO₂-Laser Induced Hot Electron Magneto-Transport Effects in n-InSb

Description: The effects of optical heating via infrared free carrier absorption on the electron magneto-transport properties of n-InSb at helium temperatures have been studied for the first time. Oscillatory photoconductivity (OPC) type structure is seen in the photon energy dependence of the transport properties. A C0₂ laser (hω = 115 to 135 meV) was used as the optical source. Concentrations between 1 x 10¹⁵ cm⁻³ and 2 x 10¹⁶ cm⁻³ were studied. The conclusions of this study are that the energy relaxatio… more
Date: August 1979
Creator: Moore, Bradley T.
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Theoretical and Experimental Linewidth Parameters in the Rotational Spectrum of Nitrogen Dioxide

Description: Contributions to the second order collision efficiency function S ⁽²⁾ (b), used in semiclassical perturbation approaches to pressure broadening of microwave and infrared spectra, due to several leading terms, dipole and quadrupole components, in the expansion of the intermolecular interaction energy are derived by method of irreducible spherical tensor operators for molecules of arbitrary symmetry. Results are given explicitly in terms of dipole and quadrupole line strengths. General expression… more
Date: December 1982
Creator: Moazzen-Ahmadi, Mohamad Nasser
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Density Profile of a Quantized Vortex Line in Superfluid Helium-4

Description: The density amplitude of an isolated quantum vortex line in superfluid 4He is calculated using a generalized Gross-Pitaevskii (G-P) equation. The generalized G-P equation for the order parameter extends the usual mean-field approach by replacing the interatomic potential in the ordinary G-P equation by a local, static T matrix, which takes correlations between the particles into account. The T matrix is a sum of ladder diagrams appearing in a diagrammatic expansion of the mean field term in an … more
Date: May 1975
Creator: Harper, John Howard
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Distribution of Nighttime F-region Molecular Ion Concentrations and 6300 Å Nightglow Morphology

Description: The purpose of this study is two-fold. The first is to determine the dependence of the molecular ion profiles on the various ionospheric and atmospheric parameters that affect their distributions. The second is to demonstrate the correlation of specific ionospheric parameters with 6300 Å nightglow intensity during periods of magnetically quiet and disturbed conditions.
Date: December 1970
Creator: Brasher, William Ernest, 1939-
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A Calculation of the Excitation Spectrum of Superfluid Helium-4

Description: The Hartree-Fock-Bogoliubov theory of homogeneous boson systems at finite temperatures is rederived using, a free energy variational principle. It is shown that a t-matrix naturally emerges in the theory. Phenomenological modifications are made (1) to remove the energy gap at zero momentum, and (2) to eliminate the Hartree-Fock-like terms, which dress the kinetic energy of the particle. A numerical calculation of the energy spectrum is made over a temperature range of 0.00 to 3.14 K using the M… more
Date: May 1974
Creator: Goble, Gerald W.
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Optical Nonlinearities in Semiconductors for Limiting

Description: I have conducted detailed experimental and theoretical studies of the nonlinear optical properties of semiconductor materials useful for optical limiting. I have constructed optical limiters utilizing two-photon absorption along with photogenerated carrier defocusing as well as the bound electronic nonlinearity using the semiconducting material ZnSe. I have optimized the focusing geometry to achieve a large dynamic range while maintaining a low limiting energy for the device. The ZnSe monolithi… more
Date: May 1990
Creator: Wu, Yuan-Yen
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