Statistical, Nonlinear, and Soft Matter Physics Commons^™

Potential Energy Landscape Formalism For Quantum Liquids, Yang Zhou

Dissertations, Theses, and Capstone Projects

Atomic delocalization due to nuclear quantum effects (NQE) remains poorly understood in low-temperature liquids near the glass state and during vitrification. Many liquids can be described accurately by treating their nuclei as classical particles, but this approximation fails for light elements such as He and H₂, small hydrogen-containing molecules such as water, and systems in which zero-point motion or isotope-substitution effects are important. Developing a general thermodynamic and statistical-mechanical description of such liquids has been challenging. This dissertation extends the potential energy landscape (PEL) formalism, originally developed for classical liquids and glasses, to liquids that obey quantum mechanics and exhibit …

The Grasshopper's Journey To The Bloch Sphere, David Llamas

Graduate Doctoral Dissertations

The Grasshopper Problem asks a simple geometric question. A grasshopper lands on a lawn of fixed area and jumps a fixed distance in a random direction. What shape of lawn maximizes the probability that the grasshopper remains on the lawn after jumping? The jump rule is rotationally symmetric, but the best lawns do not have to be. This dissertation studies how that symmetry breaking occurs, maps the continuum problem to a novel constrained spin system, and uses the spherical Grasshopper Problem to compare quantum singlet correlations with classical local models.

For planar lawns, boundary-integral and perturbative calculations explain why the …

Differentiating The Impossible: Feynman's Trick In Applications Of Modern Physics, Yaohua Zhao

Discovery Day - Daytona Beach

We discuss Feynman’s method of differentiating with respect to a parameter inside an integral and explore its significance on selective topics of modern physics. This powerful technique allows us to integrate functions that may seem impossible. Depending on the underlying parameters, the Feynman method becomes a unifying framework that connects mathematical concepts to many parameter-dependent equations in modern physics. In statistical mechanics, this appears directly in the partition function, where derivatives with respect to temperature-related parameters yield thermodynamic quantities such as internal energy and heat capacity; this demonstrates how parameter dependence gives rise to macroscopic behaviors observable at a larger …

Information Processing In Quantum Thermodynamic Systems, Shou-I Tang

Graduate Masters Theses

This thesis extends the classical autonomous Hamiltonian framework of information thermodynamics to the quantum regime. In this formulation, a composite system consisting of a principal system, a heat bath, a memory, and a work source is described by fully quantum, time-independent Hamiltonian dynamics. By introducing the quantum speed limit (QSL) for the system and memory subsystems, referred to as the Quantum Thermodynamic Speed Limit (QTSL), I establish a connection between the QTSL and Landauer’s principle. This relationship reveals the fundamental constraints on quantum information processing in terms of dynamics and energy costs during the evolution. Furthermore, I present an interpretation …

Nonlinear Diffusion, Hydrodynamic Cascades And Jamming In Kinetically Constrained Systems: Insights From Lattice Gas Models, Abhishek Raj

Dissertations, Theses, and Capstone Projects

This dissertation investigates non-linear diffusion processes and emergent dynamical phenomena in kinetically constrained lattice gases. Two central models are considered: a one-dimensional lattice gas exhibiting a diffusion cascade triggered by hydrodynamic nonlinearities and a triangular ladder exclusion model that undergoes a jamming transition. The former demonstrates stretched exponential decay consistent with non-perturbative long-time tails, while the latter illustrates how classical-quantum mappings yield insight into glassy dynamics and mobility constraints. Through a combination of numerical simulations, analytical perturbation theory, and mean-field approximations, the work uncovers mechanisms underlying anomalous transport, jamming transitions, and the breakdown of perturbative hydrodynamics.

Non-Linear Atom-Laser Interactions Using Rubidium Pump-Probe Spectroscopy, Grace Neil

Beyond: Undergraduate Research Journal

An experiment was performed to demonstrate the pump-probe spectroscopy of Rubidium (Rb) vapor, revealing the nonlinear atom-laser interactions in the 5S1/2 ↔ 5D5/2 transition in Rb that can be used to generate quantum entanglement between two laser beams. The setup included a tunable infrared diode laser, optical mirrors, photodiode-detectors, a beam-splitter, and a temperature- regulated rubidium gas chamber, all of which are controlled by the TeachSpin laser controller and monitor. The output from the laser-diode was split into a pump (90%) and a signal probe (10%), which intersected in counter-propagating directions inside the Rubidium chamber. The analysis shows that in …

Phase Nanoscopy With Correlated Frequency Combs, Xiaobing Zhu

Optical Science and Engineering ETDs

In this dissertation a sensing method applying to any physical quantity that modifies optical phase is developed. Two pulses are produced inside a synchronously pumped Optical Parametric Oscillator, generating two identical, undistinguishable frequency combs. The physical quantity to be measured applies a small phase shift/round trip to one of the pulses, resulting in a frequency shift of the corresponding comb. The latter frequency is measured as a beat by interfering the two combs on a detector. A world record resolution, close to the quantum limit, of 0.033 nanoradian (corresponding to 0.006 fm in displacement) is achieved. A detailed analysis of …

Experimental Characterization, Computational Investigation, And Structure-Property–Activity Relationship Studies Of Nickel Ferrite Nanostructures, Ali Ben Ahmed

Polytechnic Journal

Intending to predict the multifunctionality of Nickel ferrite in several technological and medical fields, we have prepared nickel ferrite nanostructure by coprecipitation method. X-ray Diffraction (XRD) is used to determine the crystalline structure and phase composition of materials by analyzing the pattern of X-rays scattered by the atoms within the material. Fourier Transform Infrared Spectroscopy (FTIR) provides information about a material's chemical bonds and functional groups by analyzing how it absorbs infrared light at various wavelengths. Scanning Electron Microscopy (SEM) offers high-resolution images of the material's surface morphology and texture by scanning it with a focused beam of electrons. Transmission …

Questioning Reality: The Progressive Development Of Modern Physics, Joshua Lancman

STEM Month

Humanity has a tendency to divide time. The past is distinct from the present which is entirely separate from the future. In supposedly 20-20 vision history is neatly divided into different sections, distinct eras with sharp lines between them. What is present and in the future is always modern. What is past is something else with another name.

Yet time is not divided so neatly. We know this living through it: years and decades blend into one another in a non-uniform progression. To divide human history into separate eras is a necessary simplification, as it helps to ascribe order onto …

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Questioning Reality: The Progressive Development Of Modern Physics, Joshua Lancman

STEM for Success Showcase

Humanity has a tendency to divide time. The past is distinct from the present which is entirely separate from the future. In supposedly 20-20 vision history is neatly divided into different sections, distinct eras with sharp lines between them. What is present and in the future is always modern. What is past is something else with another name.

Yet time is not divided so neatly. We know this living through it: years and decades blend into one another in a non-uniform progression. To divide human history into separate eras is a necessary simplification, as it helps to ascribe order onto …

Progress In Physics: Twentieth Year Of Publication, Florentin Smarandache, Andreas Ries, Pierre Millette, Ebenezer Chifu

Branch Mathematics and Statistics Faculty and Staff Publications

The journal Progress in Physics was created in January 2005 on behalf of many influential scientists with whom we were in correspondence. The main reason was that publications in other journals were allowed only if the submitter was affiliated with a scientific institution or research organization. Given this situation, many working scientists finding themselves partially employed or unemployed, such as in between research grants, find themselves unable to publish their research results. Even e-print archives such as Cornell’s arXiv required scientific affiliation and still follow this policy.

Effective Non-Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics, Vincent Paul Flynn

Dartmouth College Ph.D Dissertations

Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an "effective non-Hermiticity" intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search …

Magnetic Interactions In Open-Shell Conjugated Polymers, Michael Steelman

Dissertations

Most materials are closed shell in which every electron participates in a bond, resulting in unremarkable magnetometry signatures and functionalities. While rare, modern technologies rely on magnetic materials in which unpaired electrons are localized to inorganic atomic centers. In recent decades, a collection of organic open-shell π-conjugated molecules have shown magnetic ordering, albeit at exceedingly low temperatures; a result of weak noncovalent intermolecular interactions limiting long range electronic exchange. Thus, practically applicable sp orbital magnetism that persists at or above room temperature remains a grand challenge for chemistry and physics. Despite the wide variety of chemical structures afforded by organic …

Nonequilibrium And Nonlinear Dynamics In Collective Spin Models And Implementations Using Quantum Feedback Control, Manuel H. Munoz Arias

Physics & Astronomy ETDs

Out-of-equilibrium dynamics generalizes the study of ground states of quantum Hamiltonians at zero temperature, to that of dynamical quasi-steady states of quantum systems far from equilibrium. In this dissertation I discuss dynamical quantum phase transitions and out-of-equilibrium phases of matter in models of collective spins with multi-body interactions. These models, based on collective degrees of freedom, allow an exact description of the thermodynamic limit via the mean-field description. In this limit, the nonequilibrium dynamics of properties of quantum states is mapped to the nonlinear dynamics of classical variables, and thus it can be analyzed using tools from the theory of …

Estimation Of Pure B Power In Polarized Cmb Data Via Gibbs Sampling., Joseph Sterling

Honors Theses

In the search for effective processes to estimate E and B spectra from polarized data, Gibbs Sampling has proven to be a powerful method. In the search for B modes, it is essential to avoid a false positive detection due to contamination from the larger E component. It is therefore of interest to combine Gibbs sampling with methods to “purify” the B modes, ensuring that a B-mode detection is robust. This goal can be achieved by compelling the Gibbs Sampler to estimate a pure B spectrum. The method we chose to implement involves an artificially inflated E spectrum, which “forces” …

Charge Transport And Spin Dynamics Of Color Centers In Diamond, Damon Daw

Dissertations, Theses, and Capstone Projects

Solid state defects in diamond are promising candidates for room temperature quantum information processors (1, 3, 5). Chief among these defects is the nitrogen vacancy center (‘NV center’ or ‘NV’). The NV has long coherence times (at 300K) and its state is easily initialized, manipulated and read out (5). However, the outstanding issue of entangling NV centers in a scalable fashion, at room temperature remains a challenge. This thesis presents experimental and theoretical work aimed at achieving this goal by developing the ‘flying qubit’ framework in (1). This method for remote entanglement utilizes a charge carrier (initialized into a definite …

The Cavity-Embedded Cooper Pair Transistor As A Charge Detector Operating In The Nonlinear Regime, Bhargava Thyagarajan

Dartmouth College Ph.D Dissertations

The cavity-embedded Cooper pair transistor (cCPT) has been shown to be a nearly quantum limited charge detector operating with only a single intracavity photon. Here, we use the inherent Kerr nonlinearity to demonstrate a dispersive charge sensing technique inspired by the Josephson bifurcation amplifier. Operating in the bistable regime close to a bifurcation edge, the cCPT is sensitive to charge shifts of 0.09e in a single-shot readout scheme with a detection time of 3 μs and a detection fidelity of 94%. The readout is implemented with only ∼ 25 intracavity photons in the high oscillation amplitude state, still several orders …

Intracavity Phase Interferometry Based Fiber Sensors, Luke Jameson Horstman

Optical Science and Engineering ETDs

Intracavity Phase Interferometry (IPI) is a detection technique that exploits the inherent sensitivity of a laser's frequency to the parameters of its cavity. Intracavity interferometry is orders of magnitude more sensitive than its extracavity alternatives. This dissertation improves on previous free-space proof-of-concept designs. By implementing the technique in fiber optics, using optical parametric oscillation, and investigating non-Hermitian quantum mechanics and dispersion tailoring enhancement techniques, IPI has become more applicable and sensitive. Ring and linear IPI configurations were realized in this work, both operating as bidirectional fiber optical parametric oscillators. The benefit of using externally pumped synchronous optical parametric oscillation is …

Exclusion Statistics For Particles With A Discrete Spectrum, Stéphane Ouvry, Alexios P. Polychronakos

Publications and Research

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a …

Kinetic Monte Carlo Investigations Involving Atomic Layer Deposition Of Metal-Oxide Thinfilms, David Tyler Magness

Graduate Theses/Dissertations

Atomic Layer Deposition is a method of manufacturing thin film materials. Metal-oxides such as zinc-oxide and aluminum-oxide are particularly interesting candidates for use in microelectronic devices such as tunnel junction barriers, transistors, Schottky diodes, and more. By adopting a 3D Kinetic Monte Carlo model capable of simulating ZnO deposition, the effect of parameters including deposition temperature, chamber pressure, and composition of the initial substrate at the beginning of deposition can be investigated. This code generates two random numbers: One is used to select a chemical reaction to occur from a list of all possible reactions and the second is used …

Thermodynamic Properties Of Transverse Field Quantum Ising Model Using Tensor Network Formalism, Sin Yang Pang

Student Works (2020-2029)

Ising model has been successful in describing ferromagnetism and its phase transition to paramagnet. At the critical point, the free energy density function and its derivatives diverge. Their behaviour near the critical point are described by power-laws with associated critical exponents. In many cases, the critical exponents can be determined from analytic solutions via conventional renormalization groups methods or from Monte Carlo simulations. However, for quantum many-body systems, very few are tractable to analytical solutions. The quantum many-body wavefunction belongs to large dimensional Hilbert space that increases exponentially with system size. If the Hamiltonian is gapped and only local interaction …

Duality In A Model Of Layered Superfluids And Sliding Phases, Steven Vayl

Dissertations, Theses, and Capstone Projects

The intent of my project is to determine if the proposal of sliding phases in XY layered systems has physical ground. It will be done by comparing numerical and analytical results for a layered XY models. Sliding phases were first proposed in the context of DNA complexes and then extended to XY models, 1D coupled wires and superfluid films. The existence of the sliding phase would mean that there is a phase transition from 3D to 2D behavior. Such systems have been studied both in the clean case and with disorder. The idea of the sliding phases is based on …

Numerical And Analytical Bounds On Threshold Error Rates For Hypergraph-Product Codes, Alexey Kovalev, Sanjay Prabhakar, Ilya Dumer, Leonid P. Pryadko

Department of Physics and Astronomy: Faculty Publications

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7%.

Simulating The Electrical Properties Of Random Carbon Nanotube Networks Using A Simple Model Based On Percolation Theory, Roberto Abril Valenzuela

Physics

Carbon nanotubes (CNTs) have been subject to extensive research towards their possible applications in the world of nanoelectronics. The interest in carbon nanotubes originates from their unique variety of properties useful in nanoelectronic devices. One key feature of carbon nanotubes is that the chiral angle at which they are rolled determines whether the tube is metallic or semiconducting. Of main interest to this project are devices containing a thin film of randomly arranged carbon nanotubes, known as carbon nanotube networks. The presence of semiconducting tubes in a CNT network can lead to a switching effect when the film is electro-statically …

Vibrational Relaxation Theory For Systems Embedded In Microscopically Specified Reservoirs, Anastasia Aemilia Ierides

Physics & Astronomy ETDs

This dissertation is a study of the theoretical framework of the practical as well as fundamental problem of the process of relaxation to equilibrium of quantum mechanical systems. The fundamental aspect is concerned with the simultaneous occurrence of decoherence and population equilibration. The practical aspect deals with experimental observations of vibrational relaxation of molecules embedded in liquids or solids. The systems include, but are not limited to, the nondegenerate dimer and harmonic oscillator, in one case weak and in the other strong, interaction with a thermal bath. The time dependence of the energy and the temperature dependence of the relaxation …

Subsystem Eigenstate Thermalization Hypothesis, Anatoly Dymarsky, Nima Lashkari, Hong Liu

Physics and Astronomy Faculty Publications

Motivated by the qualitative picture of canonical typicality, we propose a refined formulation of the eigenstate thermalization hypothesis (ETH) for chaotic quantum systems. This formulation, which we refer to as subsystem ETH, is in terms of the reduced density matrix of subsystems. This strong form of ETH outlines the set of observables defined within the subsystem for which it guarantees eigenstate thermalization. We discuss the limits when the size of the subsystem is small or comparable to its complement. In the latter case we outline the way to calculate the leading volume-proportional contribution to the von Neumann and Renyi entanglment …

The Inferential Design Of Entropy And Its Application To Quantum Measurements, Kevin Vanslette

Legacy Theses & Dissertations (2009 - 2024)

This thesis synthesizes probability and entropic inference with Quantum Mechanics and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools \emph{designed} for the purpose of updating probability distributions and density matrices, respectively [1]. The derivation of the standard and quantum relative entropy are completed in tandem following the same inferential principles and design criteria. This provides the first design derivation of the quantum relative entropy while also reducing the number of required design criteria to two.

Spontaneous Parametric Down Conversion Of Photons Through Β-Barium Borate, Luke Horowitz

Physics

An apparatus for detecting pairs of entangled 405nm photons that have undergone Spontaneous Parametric Down Conversion through β-Barium Borate is described. By using avalanche photo-diodes to detect the low-intensity converted beam and a coincidence module to register coincident photons, it is possible to create an apparatus than can be used to perform quantum information experiments under a budget appropriate for an undergraduate physics lab.

Event Generator Tunes Obtained From Underlying Event And Multiparton Scattering Measurements, Cms Collaboration, Ekaterina Cms Avdeeva, Kenneth A. Bloom, S. Bose, Daniel Claes, Aaron Dominguez, Caleb Fangmeier, Rebeca Gonzalez Suarez, Rami Kamalieddin, J. Keller, D. Knowlton, Ilya Kravchenko, F. Meier, Jose Monroy, F. Ratnikov, J. E. Siado, Gregory Snow

Kenneth Bloom Publications

New sets of parameters (“tunes”) for the underlying-event (UE) modelling of the PYTHIA8, PYTHIA6 and HERWIG++ MonteCarlo event generators are constructed using different parton distribution functions. Combined fits to CMS UE proton–proton (pp) data at √s = 7 TeV and to UE proton–antiproton (pp) data from the CDF experiment at lower √s, are used to study the UE models and constrain their parameters, providing thereby improved predictions for proton–proton collisions at 13 TeV. In addition, it is investigated whether the values of the parameters obtained from fits to UE observables are consistent with the values determined from fitting observables sensitive …