Undergraduate Honors Program - Physics and Astronomy Departmenthttp://hdl.handle.net/1803/5692024-03-29T08:16:10Z2024-03-29T08:16:10ZDeformed Explicitly Correlated GaussiansBeutel, Matthewhttp://hdl.handle.net/1803/183112023-08-02T16:15:07Z2022-12-01T00:00:00ZDeformed Explicitly Correlated Gaussians
Beutel, Matthew
Strong coupling of cavity electromagnetic modes and molecules has emerged as
an area of intense theoretical and experimental interest. Such systems are of
particular interest due to their ability to modify the physical and chemical properties of materials. In this work, I use a stochastic variational method (SVM)
to construct optimized light-matter coupled wave function. By using SVMs to
select the best basis states, we are able to achieve highly accurate energies and
wave functions. In this work, I will be solving for the Pauli-Fierz (PF) nonrelativistic QED Hamiltonian. In this work I will introduce a new basis type
Deformed Explicitly Correlated Gaussians (DECGs). DECGs are a modified
form of explicitly correlated Gaussians (ECGs) where the basis is chosen such
that the dipole self-interaction term can be eliminated. These calculations will
be compared to those performed with traditional ECGs, demonstrating their
superiority in cases where a non-spherical potential exists, such as the dipole
self-interaction term.
2022-12-01T00:00:00ZExpected Host Galaxy Properties of PTA Detectable Massive Black Hole BinariesCella, Katharinehttp://hdl.handle.net/1803/169972022-01-14T20:15:52Z2021-12-06T00:00:00ZExpected Host Galaxy Properties of PTA Detectable Massive Black Hole Binaries
Cella, Katharine
Massive black hole binaries (MBHB) produce gravitational waves (GW) that will be detectable with pulsar timing arrays within the next few years. We determine the properties of the host galaxies of MBHB at the time they are producing detectable GW. The population of MBHB systems we evaluate is from the Illustris cosmological simulations taken in tandem with post processing semi-analytic models of environmental factors in the evolution of binaries. Upon evolving to the frequency regime detectable by pulsar timing arrays, we calculate the detection probability of each system using a variety of different values for red and white noise. We average over multiple realizations of the universe by re-sampling the host galaxy properties using a kernel density estimator to approximate the statistical distributions of the universe. Excitingly, we find that detectable systems have host galaxies that are clearly distinct from the overall population. With conservative noise factors, we found that stellar metallicity, for example, peaks at approximately twice solar metallicity as opposed to the total population of galaxies which peaks at approximately solar metallicity. Additionally, the most detectable systems are brighter and more red in color than the overall population. These results can be used to develop effective search strategies for identifying host galaxies and electromagnetic counterparts following GW detections.
2021-12-06T00:00:00ZAnalytic Solutions of Two Electrons in Harmonic Confinement in an Optical CavityHuang, Chenhanghttp://hdl.handle.net/1803/169962022-01-13T23:56:30Z2021-12-01T00:00:00ZAnalytic Solutions of Two Electrons in Harmonic Confinement in an Optical Cavity
Huang, Chenhang
The possibility to control quantum systems with photons has stimulated
recent interest in the study of quantum optical systems. While
simple classical quantum systems admit well-known solutions, analysis
of light-coupling quantum regimes remains lacking. In this work,
we obtain analytic solutions for a light-coupling electron pair in harmonic
confinement in a cavity by separating center-of-mass (CM) and
relative motions. The CM part can be calculated in closed form or
by exact diagonalization of the Hamiltonian, and the relative part is
quasi-exactly solvable. We analyze the 2D results produced by the
exact diagonalization method and reach conclusions on the effects of
different system parameters. We also present 1D numerical simulations
by Stochastic Variational Method (SVM) using Explicitly Correlated
Gaussian (ECG) bases, which agree with our analysis in 2D. Our analytic
solutions may provide a valuable calibration point for simulations
in the quantum optical regime.
Vanderbilt physics honor thesis of Chenhang Huang, in partial fulfillment of the requirements for the honor degree of
Bachelor of Arts in Physics. Advisor: Kalman Varga.
2021-12-01T00:00:00ZAxionlike Dark Energy and Particle Decay in theFuture of the Accelerating UniverseNorton, Cameronhttp://hdl.handle.net/1803/164882021-05-07T13:49:01Z2021-04-30T00:00:00ZAxionlike Dark Energy and Particle Decay in theFuture of the Accelerating Universe
Norton, Cameron
The 1998 discovery that the universe was accelerating in its expansion has yet to be explained
theoretically, meriting the continual theoretical and observational study of this phenomena.
In this thesis, we undergo a phenomenological study of the cosmological implications of this
“dark energy” in two different ways.
In the first part of this thesis, we examine the cosmological evolution of ultralight axionlike (ULA) scalar fields with potentials of the form V (φ) = m2f
2
[1 − cos (φ/f)]2
, with
particular emphasis on the deviation in their behavior from the corresponding small-φ powerlaw approximations to these potentials: V (φ) ∝ φ
2n
. We show that in the slow-roll regime,
when φ˙2/2 V (φ), the full ULA potentials yield a more interesting range of possibilities for
quintessence than do the corresponding power law approximations. For rapidly oscillating
scalar fields, we derive the equation of state parameter and oscillation frequency for the ULA
potentials and show how they deviate from the corresponding power-law values. We derive
an analytic expression for the equation of state parameter that better approximates the ULA
value than does the pure power-law approximation.
In the second part, we study particle decay in the future of the accelerating universe. We
generalize the result that in a cosmological constant dominated universe, the decay of matter
into relativistic particles can never cause radiation to once again dominate over matter. We
study both models of dark energy comprised of quintessence and cosmologies ending in a “big
rip” in this context.
2021-04-30T00:00:00Z