National Parks and Development in Sub-Saharan Africa: and Examination of Social and Economic Program Effectiveness in the Development Paradigm

Senior Project submitted to The Division of Social Studies of Bard College

Far-infrared spectra of lateral quantum dot molecules

We study effects of electron-electron interactions and confinement potential on the magneto-optical absorption spectrum in the far-infrared range of lateral quantum dot molecules. We calculate far-infrared (FIR) spectra for three different quantum dot molecule confinement potentials. We use accurate exact diagonalization technique for two interacting electrons and calculate dipole-transitions between two-body levels with perturbation theory. We conclude that the two-electron FIR spectra directly reflect the symmetry of the confinement potential and interactions cause only small shifts in the spectra. These predictions could be tested in experiments with nonparabolic quantum dots by changing the number of confined electrons. We also calculate FIR spectra for up to six noninteracting electrons and observe some additional features in the spectrum.Comment: For better quality Figs download manuscript from http://www.fyslab.hut.fi/~mma/FIR/Helle_qdmfir.ps.g

Goldstone bosons and a dynamical Higgs field

Higgs inflation uses the gauge variant Higgs field as the inflaton. During inflation the Higgs field is displaced from its minimum, which results in associated Goldstone bosons that are apparently massive. Working in a minimally coupled U(1) toy model, we use the closed-time-path formalism to show that these Goldstone bosons do contribute to the one-loop effective action. Therefore the computation in unitary gauge gives incorrect results. Our expression for the effective action is gauge invariant upon using the background equations of motion.Comment: 27 pages, 2 figures, published version with minor correction

Large-k Limit of Multi-Point Propagators in the RG Formalism

Renormalized versions of cosmological perturbation theory have been very successful in recent years in describing the evolution of structure formation in the weakly non-linear regime. The concept of multi-point propagators has been introduced as a tool to quantify the relation between the initial matter distribution and the final one and to push the validity of the approaches to smaller scales. We generalize the n-point propagators that have been considered until now to include a new class of multi-point propagators that are relevant in the framework of the renormalization group formalism. The large-k results obtained for this general class of multi-point propagators match the results obtained earlier both in the case of Gaussian and non-Gaussian initial conditions. We discuss how the large-k results can be used to improve on the accuracy of the calculations of the power spectrum and bispectrum in the presence of initial non-Gaussianities.Comment: 30 page

Control of many electron states in semiconductor quantum dots by non-Abelian vector potentials

Adiabatic time evolution of degenerate eigenstates of a quantum system provides a means for controlling electronic states since mixing between degenerate levels generates a matrix Berry phase. In the presence of spin-orbit coupling in n-type semiconductor quantum dots the electron Hamiltonian is invariant under time reversal operation and the many body groundstate may be doubly degenerate. This double degeneracy can generate non-Abelian vector potentials when odd number of electrons are present. We find that the antisymmetry of many electron wavefunction has no effect on the matrix Berry phase. We have derived equations that allow one to investigate the effect of electron correlations by expressing the non-Abelian vector potentials for many electron system in terms of single electron non-Abelian vector potentials.Comment: minor changes included, accepted in Phys. Rev.

Microstrip superconducting quantum interference device amplifiers with submicron Josephson junctions: enhanced gain at gigahertz frequencies

We present measurements of an amplifier based on a dc superconducting quantum interference device (SQUID) with submicron Al-AlOx-Al Josephson junctions. The small junction size reduces their self-capacitance and allows for the use of relatively large resistive shunts while maintaining nonhysteretic operation. This leads to an enhancement of the SQUID transfer function compared to SQUIDs with micron-scale junctions. The device layout is modified from that of a conventional SQUID to allow for coupling signals into the amplifier with a substantial mutual inductance for a relatively short microstrip coil. Measurements at 310 mK exhibit gain of 32 dB at 1.55 GHz.Comment: Version with high resolution figures at: http://physics.syr.edu/~bplourde/bltp-publications.ht

Nontrivial damping of quantum many-body dynamics

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schr\"odinger picture. We show that a nontrivial damping in the Schr\"odinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system

The Nonlinear Cosmological Matter Power Spectrum with Massive Neutrinos I: The Halo Model

Measurements of the linear power spectrum of galaxies have placed tight constraints on neutrino masses. We extend the framework of the halo model of cosmological nonlinear matter clustering to include the effect of massive neutrino infall into cold dark matter (CDM) halos. The magnitude of the effect of neutrino clustering for three degenerate mass neutrinos with m_nu=0.9 eV is of order ~1%, within the potential sensitivity of upcoming weak lensing surveys. In order to use these measurements to further constrain--or eventually detect--neutrino masses, accurate theoretical predictions of the nonlinear power spectrum in the presence of massive neutrinos will be needed, likely only possible through high-resolution multiple particle (neutrino, CDM and baryon) simulations.Comment: v2: matches PRD versio