Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 24 for “"Uncertainty Principle"”.
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A generalization of the Beurling-Hedenmalm uncertainty principle
We study the uncertainty principles of Hardy and of Beurling, and functions that "only just" satisfy the inequalities of uncertainty principles. More specifically, we show that if a function and its Fourier transform have nearly gaussian decay, the the coefficients of its Hermite expansion decay …
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Rapid Implicit Diagonalization of Variable-Coefficient Differential Operators Using the Uncertainty Principle
… potential method can be realized. Through the Uncertainty Principle, we will formulate highly accurate estimates of eigenvalues, and then through the QR algorithm, we will use these estimates to formulate highly accurate eigenvalues and eigenfunctions. Ultimately, we will produce a more …
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Higher dimensional fractal uncertainty
… we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher dimensional Beurling and Malliavin multiplier theorem, which allows us to construct band-limited functions that decay rapidly on line porous sets. To prove this theorem, we first explicitly …
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A room temperature optomechanical squeezer
… reaches very high precision, the Heisenberg uncertainty principle comes into play. In GW detectors, this uncertainty manifests itself in the quantum nature of the light. Due to its quantum nature, light (or electromagnetic field) has an uncertain amplitude and phase.
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Quantum mechanics on phase space : geometry and motion of the Wigner distribution
… they hint at what is required beyond the uncertainty principle in order for a Wigner function to be valid. Next we design and implement numerical methods to propagate Wigner functions via the quantum Liouville equation. Using these methods we study the quantum mechanical phenomena of …
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Bi-fractional transforms in phase space
… these bi-fractional transforms to the Heisenberg uncertainty principle, photon statistics and future applications are discussed.
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Broadband Squeezed Microwaves and Amplification with a Josephson Traveling-Wave Parametric Amplifier
… standard quantum limit imposed by the Heisenberg uncertainty principle. It has been widely adopted in research fields to achieve scientific breakthroughs from gravitational wave detection to biological microscopy enhancement. The generation of highly-squeezed states using superconducting …
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Signal decomposition for nonstationary processes
… than the lower bound defined by the Heisenberg uncertainty principle. The application examples demonstrate the great potential of the MPSE method for tracking and analyzing time-varying processes. To deal with the time-varying characteristics caused by linearization of nonlinear processes, the …
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Next-Generation Earth Radiation Budget Instrument Concepts
… is a deterministic model based upon Heisenberg's uncertainty principle and the particle theory of light. This method is applicable to either Fraunhofer or Fresnel diffraction situations, but is incapable of predicting the secondary fringes in a diffraction pattern. Also presented is a second …
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Investigation into compactifed dimensions : Casimir energies and phenomenological aspects.
… fluctuations as a consequence of the Heisenberg Uncertainty Principle. These fluctuations give rise to a number of phenomena; however, two are particularly striking. First, the Casimir Effect, which will be examined in detail in this dissertation is arguably the most salient manifestation of the …
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An Analysis of Three Path-Integral Based Approximations to Quantum Dynamics
… quantum time-correlation functions: constant-uncertainty molecular dynamics (CUMD), the fitted harmonic approximation (FHA) and windowed centroid molecular dynamics (WCMD). The CUMD method has been proposed as a simple and efficient method to incorporate nuclear quantum effects in molecular …
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Quantum noise and radiation pressure effects in high power optical interferometers
… position measurements imposed by the Heisenberg Uncertainty Principle. Most notably, gravitational wave interferometers, such as the Laser Interferometer Gravitational wave Observatory (LIGO), operate within a factor of 10 of the standard quantum limit. Here we characterize and manipulate quantum …
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Generating pictures from waves : aspects of image formation
… tradeoffs that surpass the traditional Fourier uncertainty principle by leveraging time-frequency distributions. We show that the number of sensors in a coherent imaging array defines a stable operating point relative to the phase noise. We introduce a digital phase tightening algorithm to …
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Quantum noise reduction using squeezed states in LIGO
… have the minimum noise allowed by Heisenberg's uncertainty principle, [Delta]X1 [Delta]X2 >/=1, where the two quadratures X1 and X2 are non-commuting observables responsible for the two forms of quantum noise, shot noise and radiation pressure noise. By replacing the vacuum fluctuations entering …
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Optical studies of ion-bombarded gallium arsenide
… the excited-state energy. An alternative uncertainty-principle argument is also given in terms of the confinement-induced k-space broadening of electron states. The near-surface structural disorder in Ar⁺-etched GaAs has been investigated using a combination of Raman scattering and optical …
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Nonsingular and deformed black holes Fundamental aspects and phenomenology
… the smearing of the singularity in terms of the uncertainty principle. Finally, we analyze a model in which black holes are medelled as sets of oscillators whose typical frequencies are given by the quasinormal modes of the systems. Under some assumptions,we are able to obtain the …
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Multiscale analysis of financial volatility
… (motivated from a discussion on Heisenberg's uncertainty principle) namely Wavelet method is defined. A complete account of discrete and continuous wavelet transformations, and wavelet variation is provided and the advantages of wavelet-multiresolution analysis over Fourier methods are …
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Squeezing the Quantum Noise of LIGO below the Standard Quantum Limit
… is fundamental physics dictated by Heisenberg’s uncertainty principle. In the case of continuous measurement like LIGO, the quantum back-action leads to an apparent sensitivity limit known as the Standard Quantum Limit (SQL). It tells us how precisely we can measure an object with light. The SQL …
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