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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 secondary objective of this paper is to study ways of relating quantum mechanics and classical mechanics. The Ehrenfest theorem is applied to a particle in an electromagnetic field. Expressions are found which are the hermitian Lorentz force operator, the hermitian torque operator, and the hermitian power operator.
Date: December 1977
Creator: Hefley, Velton Wade

Coherent Resonant Interaction and Harmonic Generation in Atomic Vapors

Description: This work examines the use of higher order multiphoton resonances in higher harmonic generation together with judicious exploitation of coherent interaction properties to achieve efficient harmonic generation. A detailed experimental study on third harmonic generation in two photon resonant coherent interaction and a theoretical study on four photon resonant coherent interaction have been conducted. Two photon resonant coheren propagation in lithium vapor (2S-4S and 2S-3D interaction) has been studied in detail as a function of phase and delay of the interacting pulse sequence. Under coherent lossless propagation of 90 phase shifted pulse pair, third harmonic generation is enhanced. A maximum energy conversion efficiency of 1% was measured experimentally. This experiment shows that phase correlated pulse sequence can be used to control multiphoton coherent resonant effects. A larger two photon resonant enhancement does not result in more efficient harmonic generation, in agreement with the theoretical prediction. An accurate (to at least 0.5 A°) measurement of intensity dependent Stark shift has been done with the newly developed "interferometric wavemeter." Stark shifts as big as several pulse bandwidths (of picosecond pulses) result in a poor tuning of multiphoton resonance and become a limiting factor of resonant harmonic generation. A complete theory has been developed for harmonic generation in a four photon resonant coherent interaction. A numerical application of the theory to the Hg atom successfully interprets the experimental observations in terms of the phase dependent stimulated Raman scattering. With the intensity required for four photon resonant transition, the calculation predicts a dramatic Stark shift effect which completely destroys the resonance condition. This model provides a basis for the development of future schemes for efficient higher order coherent upconversion.
Date: August 1987
Creator: Mukherjee, Nandini

Collision Broadening in the Microwave Rotational Spectrum of Gaseous Monomeric Formaldehyde

Description: A source-modulation microwave spectrograph was utilized to measure line width parameters for several spectral lines in the pure rotational spectrum of formaldehyde (H₂CO). The spectrograph featured high-gain ac amplification and phase-sensitive detection, and was capable of measuring microwave lines having absorption coefficients as small as 10⁻⁷ cm⁻¹ with a frequency resolution on the order of 30 kHz. Center frequencies of the measured lines varied from 4,830 MHz to 72,838 MHz; hence, most of the observations were made on transitions between K-doublets in the rotational spectrum. Corrections were applied to the measured line width parameters to account for Doppler broadening and, where possible, for deviations due to magnetic hyperfine structure in some of the K-doubled lines. Low modulation voltages and low microwave power levels were used to minimize modulation and saturation broadenings; other extraneous broadenings were found to be insignificant. The primary broadening mechanism at low gas pressure is pressure broadening, and a review of this topic is included. Line width parameters for the several observed transitions were determined by graphing half-widths versus pressure for each spectral line, and performing a linear least-squares fit to the data points. Repeatability measurements indicated the accuracy of the line width parameters to be better than ±10 percent. The reasons for this repeatability spread are discussed, Broadening of each line was measured for self- and foreign-gas broadening by atomic helium and diatomic hydrogen. Effective collision diameters were calculated for each broadening interaction, based on the observed rates of broadening.
Date: December 1973
Creator: Rogers, David Valmore

Complex Numbers in Quantum Theory

Description: In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function.” This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. I identify a freedom/constraint situation encountered by vectors when, employed in accordance with adopted quantum representational methodology, and representing angular momentum states in particular. Complex vectors, quite simply, provide more available adjustable variables than do real vectors. The additional variables relax the constraint situation allowing the theory’s representational program to carry through. This complex number issue, which lies at the deepest foundations of the theory, has implications for important issues located higher in the theory. For example, any unification of the classical and quantum accounts of the settled order of nature, will rest squarely on our ability to account for the introduction of the imaginary unit.
Date: August 2015
Creator: Maynard, Glenn

Complexity as a Form of Transition From Dynamics to Thermodynamics: Application to Sociological and Biological Processes.

Description: This dissertation addresses the delicate problem of establishing the statistical mechanical foundation of complex processes. These processes are characterized by a delicate balance of randomness and order, and a correct paradigm for them seems to be the concept of sporadic randomness. First of all, we have studied if it is possible to establish a foundation of these processes on the basis of a generalized version of thermodynamics, of non-extensive nature. A detailed account of this attempt is reported in Ignaccolo and Grigolini (2001), which shows that this approach leads to inconsistencies. It is shown that there is no need to generalize the Kolmogorov-Sinai entropy by means of a non-extensive indicator, and that the anomaly of these processes does not rest on their non-extensive nature, but rather in the fact that the process of transition from dynamics to thermodynamics, this being still extensive, occurs in an exceptionally extended time scale. Even, when the invariant distribution exists, the time necessary to reach the thermodynamic scaling regime is infinite. In the case where no invariant distribution exists, the complex system lives forever in a condition intermediate between dynamics and thermodynamics. This discovery has made it possible to create a new method of analysis of non-stationary time series which is currently applied to problems of sociological and physiological interest.
Date: May 2003
Creator: Ignaccolo, Massimiliano

Complexity as Aging Non-Poisson Renewal Processes

Description: The search for a satisfactory model for complexity, meant as an intermediate condition between total order and total disorder, is still subject of debate in the scientific community. In this dissertation the emergence of non-Poisson renewal processes in several complex systems is investigated. After reviewing the basics of renewal theory, another popular approach to complexity, called modulation, is introduced. I show how these two different approaches, given a suitable choice of the parameter involved, can generate the same macroscopic outcome, namely an inverse power law distribution density of events occurrence. To solve this ambiguity, a numerical instrument, based on the theoretical analysis of the aging properties of renewal systems, is introduced. The application of this method, called renewal aging experiment, allows us to distinguish if a time series has been generated by a renewal or a modulation process. This method of analysis is then applied to several physical systems, from blinking quantum dots, to the human brain activity, to seismic fluctuations. Theoretical conclusions about the underlying nature of the considered complex systems are drawn.
Date: May 2007
Creator: Bianco, Simone

A Comprehensive Model for the Rotational Spectra of Propyne CH₃CCH in the Ground and V₁₀=1,2,3,4,5 Vibrational States

Description: The energy states of C₃ᵥ symmetric top polyatomic molecules were studied. Both classical and quantum mechanical methods have been used to introduce the energy states of polyatomic molecules. Also, it is shown that the vibration-rotation spectra of polyatomic molecules in the ground and excited vibrational states can be predicted by group theory. A comprehensive model for predicting rotational frequency components in various v₁₀ vibrational levels of propyne was developed by using perturbation theory and those results were compared with other formulas for C₃ᵥ symmetric top molecules. The v₁₀=1,2,3 and ground rotational spectra of propyne in the frequency range 17-70 GHz have been reassigned by using the derived comprehensive model. The v₁₀=3 and v₁₀=4 rotational spectra of propyne have been investigated in the 70 GHz, and 17 to 52 GHz regions, respectively, and these spectral components assigned using the comprehensive model. Molecular constants for these vibrationally excited states have been determined from more than 100 observed rotational transitions. From these experimentally observed components and a model based upon first principles for C₃ᵥ symmetry molecules, rotational constants have been expressed in a form which enables one to predict rotational components for vibrational levels for propyne up to v₁₀=5. This comprehensive model also appears to be useful in predicting rotational components in more highly excited vibrational levels but data were not available for comparison with the theory. Several techniques of assignment of rotational spectra for each excited vibrational state are discussed. To get good agreement between theory and experiment, an additional term 0.762(J+1) needed to be added to Kℓ=1 states in v₁₀=3. No satisfactory theoretical explanation of this term has been found. Experimentally measured frequencies for rotational components for J→(J+1)=+1 (0≤J≤3) in each vibration v₁₀=n (0≤n≤4) are presented and compared with those calculated using the results of basic perturbation theory. The v₉=2 rotational ...
Date: December 1986
Creator: Rhee, Won Myung

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 equation has a five-fold integral collision term that is complicated. Chandrasekhar and Spitzer's approaches to the linear Fokker-Planck coefficients have several approximations. An effective variable-change technique has been developed in this dissertation as an alternative to scattering angle as the measure of collision strength. By introducing the square of the reduced impulse or its equivalencies as a collision strength variable, many plasma calculations have been simplified. The five-fold linear Boltzmann collision integral and linearized Boltzmann collision integral are simplified to three-fold integrals. The arbitrary order linear Fokker-Planck coefficients are calculated and expressed in a uniform expression. The new theory provides a simple and exact method for describing the equilibrium plasma collision rate, and a precise calculation of the equilibrium relaxation time. It generalizes bimolecular collision reaction rate theory to a reaction rate theory for plasmas. A simple formula of high precision with wide temperature range has been developed for electron impact ionization rates for carbon atoms and ions. The universality of the concept of collision strength is emphasized. This dissertation will show how Arrhenius' chemical reaction rate theory and Thomson's ionization theory can be unified as one single theory under the concept of collision strength, and how many important physical terms in different disciplines, such as activation energy in chemical reaction theory, ionization energy in Thomson's ionization theory, and the Coulomb logarithm in ...
Date: May 2004
Creator: Chang, Yongbin

A Continuously Sensitive Cloud Chamber

Description: A continuous cloud chamber would be a valuable asset to laboratory work in nuclear and atomic physics. For this reason the construction and investigation of a continuously sensitive diffusion cloud chamber has been undertaken. It is the purpose of this paper to report the design and operating characteristics of such a chamber.
Date: 1951
Creator: Hughes, James E.

Cooperation-induced Criticality in Neural Networks

Description: The human brain is considered to be the most complex and powerful information-processing device in the known universe. The fundamental concepts behind the physics of complex systems motivate scientists to investigate the human brain as a collective property emerging from the interaction of thousand agents. In this dissertation, I investigate the emergence of cooperation-induced properties in a system of interacting units. I demonstrate that the neural network of my research generates a series of properties such as avalanche distribution in size and duration coinciding with the experimental results on neural networks both in vivo and in vitro. Focusing attention on temporal complexity and fractal index of the system, I discuss how to define an order parameter and phase transition. Criticality is assumed to correspond to the emergence of temporal complexity, interpreted as a manifestation of non-Poisson renewal dynamics. In addition, I study the transmission of information between two networks to confirm the criticality and discuss how the network topology changes over time in the light of Hebbian learning.
Date: August 2013
Creator: Zare, Marzieh

Criticality in Cooperative Systems

Description: Cooperative behavior arises from the interactions of single units that globally produce a complex dynamics in which the system acts as a whole. As an archetype I refer to a flock of birds. As a result of cooperation the whole flock gets special abilities that the single individuals would not have if they were alone. This research work led to the discovery that the function of a flock, and more in general, that of cooperative systems, surprisingly rests on the occurrence of organizational collapses. In this study, I used cooperative systems based on self-propelled particle models (the flock models) which have been proved to be virtually equivalent to sociological network models mimicking the decision making processes (the decision making model). The critical region is an intermediate condition between a highly disordered state and a strong ordered one. At criticality the waiting times distribution density between two consecutive collapses shows an inverse power law form with an anomalous statistical behavior. The scientific evidences are based on measures of information theory, correlation in time and space, and fluctuation statistical analysis. In order to prove the benefit for a system to live at criticality, I made a flock system interact with another similar system, and then observe the information transmission for different disturbance values. I proved that at criticality the transfer of information gets the maximal efficiency. As last step, the flock model has been shown that, despite its simplicity, is sufficiently a realistic model as proved via the use of 3D simulations and computer animations.
Date: May 2012
Creator: Vanni, Fabio

Cross-Section at 15.6 and 16.1 MeV

Description: The intent of this investigation is the determination of the values of the Cs-133 (n,2n)Cs-132 cross-section at neutron energies of 15.6 and 16.1 MeV. Neutrons of this energy are produced with comparative ease by means of the D-T reaction, in which deuterons of energy 500 and 750 keV, respectively, are impingent upon a tritium target.
Date: May 1969
Creator: Pepper, George H.

Cross Section Measurements in Praseodymium-141 as a Function of Neutron Bombarding Energy

Description: Using the parallel disk method of activation analysis, the (n,2n) reaction cross section in 141-Pr was measured as a function of neutron energy in the range 15.4 to 18.4 MeV. The bombarding neutrons were produced from the 3-T(d,n)4-He reaction, where the deuterons were accelerated by the 3-MV Van de Graff generator of the North Texas Regional Physics Laboratory in Denton, Texas.
Date: May 1971
Creator: Marsh, Stephen Addison

A Decay Scheme for 164 Ho

Description: The present investigation was prompted by several considerations. In previous studies there was considerable variance with regard to the reported values for the half-lives of the isomeric and ground states in 164 Ho. There was also considerable variance with regard to the values reported for the branching ratios and the relative intensities of the transitions. Thus a further study of the problem was needed.
Date: December 1972
Creator: Guertin, James

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 superposition of these two states with the environment. The joint action of inphasing and dephasing generates a Markov master equation statistically equivalent to a random walker jumping from one state to the other. This model can be used to describe intermittent fluorescence, as a sequence of "light on" and "light off" states. The experiments on blinking quantum dots indicate that the sojourn times are distributed with an inverse power law. Thus, a proposal to turn the model for Poisson fluorescence intermittency into a model for non-Poisson fluorescence intermittency is made. The collision-like interaction of the two-state system with the environment is assumed to takes place at random times rather than at regular times. The time distance between one collision and the next is given by a distribution, called the subordination distribution. If the subordination distribution is exponential, a sequence of collisions yielding no persistence is turned into a sequence of "light on" and "light off" states with significant persistence. If the subordination function is an inverse power law the sequel of "light on" and "light off" states becomes equivalent to the experimental sequences. Different conditions are considered, ranging from predominant inphasing to predominant dephasing. When dephasing is predominant the sequel of "light on" and "light off" states in the time asymptotic limit becomes an inverse power law. If the predominant dephasing involves a time scale much larger than the ...
Date: August 2005
Creator: Giraldi, Filippo

Design and Testing of a Corona Column and a Closed Gas Distribution System for a Tandem Van de Graaff Voltage Generator

Description: The purpose of this study had been to design and test a corona column and an insulating gas distribution system for a small tandem Van de Graaff. The intent of this paper is to describe the gas handling system and to compare experimentally the effects of corona electrode shape on the corona current carried between adjacent sections of the column.
Date: June 1962
Creator: Gray, Thomas Jack