Matching Items (14)

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p-Adic Numbers with an Emphasis on q-Volkenborn Integration

Description

Similar to the real numbers, the p-adic fields are completions of the rational numbers. However, distance in this space is determined based on divisibility by a prime number, p, rather

Similar to the real numbers, the p-adic fields are completions of the rational numbers. However, distance in this space is determined based on divisibility by a prime number, p, rather than by the traditional absolute value. This gives rise to a peculiar topology which offers significant simplifications for p-adic continuous functions and p-adic integration than is present in the real numbers. These simplifications may present significant advantages to modern physics – specifically in harmonic analysis, quantum mechanics, and string theory. This project discusses the construction of the p-adic numbers, elementary p-adic topology, p-adic continuous functions, introductory p-adic measure theory, the q-Volkenborn distribution, and applications of p-adic numbers to physics. We define q-Volkenborn integration and its connection to Bernoulli numbers.

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Agent

Created

Date Created
  • 2020-05

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Quantum Matter Coupled to Classical Gravity

Description

A problem of interest in theoretical physics is the issue of the evaporation of black holes via Hawking radiation subject to a fixed background. We approach this problem by considering

A problem of interest in theoretical physics is the issue of the evaporation of black holes via Hawking radiation subject to a fixed background. We approach this problem by considering an electromagnetic analogue, where we have substituted Hawking radiation with the Schwinger effect. We treat the case of massless QED in 1+1 dimensions with the path integral approach to quantum field theory, and discuss the resulting Feynman diagrams from our analysis. The results from this thesis may be useful to find a version of the Schwinger effect that can be solved exactly and perturbatively, as this version may provide insights to the gravitational problem of Hawking radiation.

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Agent

Created

Date Created
  • 2016-05

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Field Theories à la Gravity: From Navier-Stokes to Superconductivity.

Description

Recent developments inspired by string theoretic considerations provide multiple maps between gravitational and non-gravitational degrees of freedom. In this dis- sertation I discuss aspects of three such dualities, the gauge/gravity

Recent developments inspired by string theoretic considerations provide multiple maps between gravitational and non-gravitational degrees of freedom. In this dis- sertation I discuss aspects of three such dualities, the gauge/gravity duality and how it applies to condensed matter systems, the fluid-gravity duality, and the color-kinematics duality.

The first of these, colloquially referred to as holography, in its simplest form posits a mapping of d-dimensional conformal field theory (boundary) partition functions onto d+1 dimensional gravitational(bulk) partition functions, where the space-time carries a negative cosmological constant. In this dissertation I discuss the results of our calculations examining the emergence of Fermi-surface like structures in the bulk spacetime despite the absence of explicit Fermions in the theory.Specifically the 4+1 dimensional Einstein-Maxwell-Chern-Simons theory with scalar degrees of freedom, with and without symmetry breaking is considered. These theories are gravity duals to spatially modulated gauge theories. The results of calculations presented here indicate the existence of a rich phase space, most prominently Fermi shells are seen.

The second set of dualities considered are the color-kinematic duality, also known as the double-copy paradigm and the fluid-gravity duality. The color-kinematic duality involves identifying spin-2 amplitudes as squares of spin-1 gauge amplitudes. This double copy picture is utilized to construct “single copy” representations for space- times where Einstein’s equations reduce to incompressible Navier-Stokes equations. In this dissertation I show how spacetimes that characterize irrotational fluids and constant vorticity fluids each map to distinct algebraically special spacetimes. The Maxwell fields obtained via the double-copy picture for such spacetimes further provide interesting parallels, for instance, the vorticity of the fluid is proportional to the magnetic field of the associated gauge field.

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Agent

Created

Date Created
  • 2020

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Solving the mechanism of Na+/H+ antiporters using molecular dynamics simulations

Description

Na+/H+ antiporters are vital membrane proteins for cell homeostasis, transporting Na+ ions in exchange for H+ across the lipid bilayer. In humans, dysfunction of these transporters are implicated in hypertension,

Na+/H+ antiporters are vital membrane proteins for cell homeostasis, transporting Na+ ions in exchange for H+ across the lipid bilayer. In humans, dysfunction of these transporters are implicated in hypertension, heart failure, epilepsy, and autism, making them well-established drug targets. Although experimental structures for bacterial homologs of the human Na+/H+ have been obtained, the detailed mechanism for ion transport is still not well-understood. The most well-studied of these transporters, Escherichia coli NhaA, known to transport 2 H+ for every Na+ extruded, was recently shown to bind H+ and Na+ at the same binding site, for which the two ion species compete. Using molecular dynamics simulations, the work presented in this dissertation shows that Na+ binding disrupts a previously-unidentified salt bridge between two conserved residues, suggesting that one of these residues, Lys300, may participate directly in transport of H+. This work also demonstrates that the conformational change required for ion translocation in a homolog of NhaA, Thermus thermophilus NapA, thought by some to involve only small helical movements at the ion binding site, is a large-scale, rigid-body movement of the core domain relative to the dimerization domain. This elevator-like transport mechanism translates a bound Na+ up to 10 Å across the membrane. These findings constitute a major shift in the prevailing thought on the mechanism of these transporters, and serve as an exciting launchpad for new developments toward understanding that mechanism in detail.

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Agent

Created

Date Created
  • 2016

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Holography in Rindler space

Description

This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1

This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1 dimensions from the perspective of a dual quantum field theory living in d dimensions. We begin by considering Rindler space which is the part of Minkowski space seen by an observer with a constant proper acceleration. Because it has an event horizon, Rindler space has been studied in great detail within the context of quantum field theory. However, a quantum gravitational treatment of Rindler space is handicapped by the fact that quantum gravity in flat space is poorly understood. By contrast, quantum gravity in anti-de Sitter space (AdS), is relatively well understood via the AdS/CFT correspondence. Taking this cue, we construct Rindler coordinates for AdS (Rindler-AdS space) in d + 1 spacetime dimensions. In three spacetime dimensions, we find novel one-parameter families of stationary vacua labeled by a rotation parameter β. The interesting thing about these rotating Rindler-AdS spaces is that they possess an observer-dependent ergoregion in addition to having an event horizon. Turning next to the application of AdS/CFT correspondence to Rindler-AdS space, we posit that the two Rindler wedges in AdSd+1 are dual to an entangled conformal field theory (CFT) that lives on two boundaries with geometry R × Hd-1. Specializing to three spacetime dimensions, we derive the thermodynamics of Rindler-AdS space using the boundary CFT. We then probe the causal structure of the spacetime by sending in a time-like source and observe that the CFT “knows” when the source has fallen past the Rindler horizon. We conclude by proposing an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space. Towards the end, we consider the concept of weak measurements in quantum mechanics, wherein the measuring instrument is weakly coupled to the system being measured. We consider such measurements in the context of two examples, viz. the decay of an excited atom, and the tunneling of a particle trapped in a well, and discuss the salient features of such measurements.

Contributors

Agent

Created

Date Created
  • 2012

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Path Integral Quantum Monte Carlo Method for Light Nuclei

Description

I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both

I describe the first continuous space nuclear path integral quantum Monte Carlo method, and calculate the ground state properties of light nuclei including Deuteron, Triton, Helium-3 and Helium-4, using both local chiral interaction up to next-to-next-to-leading-order and the Argonne $v_6'$ interaction. Compared with diffusion based quantum Monte Carlo methods such as Green's function Monte Carlo and auxiliary field diffusion Monte Carlo, path integral quantum Monte Carlo has the advantage that it can directly calculate the expectation value of operators without tradeoff, whether they commute with the Hamiltonian or not. For operators that commute with the Hamiltonian, e.g., the Hamiltonian itself, the path integral quantum Monte Carlo light-nuclei results agree with Green's function Monte Carlo and auxiliary field diffusion Monte Carlo results. For other operator expectations which are important to understand nuclear measurements but do not commute with the Hamiltonian and therefore cannot be accurately calculated by diffusion based quantum Monte Carlo methods without tradeoff, the path integral quantum Monte Carlo method gives reliable results. I show root-mean-square radii, one-particle number density distributions, and Euclidean response functions for single-nucleon couplings. I also systematically describe all the sampling algorithms used in this work, the strategies to make the computation efficient, the error estimations, and the details of the implementation of the code to perform calculations. This work can serve as a benchmark test for future calculations of larger nuclei or finite temperature nuclear matter using path integral quantum Monte Carlo.

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Agent

Created

Date Created
  • 2020

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Topics in cosmology and gravitation

Description

Two ideas that extends on the theory of General Relativity are introduced and then the phenomenology they can offer is explored. The first idea shows how certain types of $f(R)$

Two ideas that extends on the theory of General Relativity are introduced and then the phenomenology they can offer is explored. The first idea shows how certain types of $f(R)$ gravity allows for traversable wormholes among its vacuum solutions. This is surprising to find in such simple setting as these type of solutions usually requires fairly complex constructions to satisfy the equations of motion of a gravitational theory. The second idea is the matter bounce description of the early universe where a fairly unique feature of the model is identified. Consequences of this feature could allow the paradigm to distinguish itself from other alternative descriptions, such as inflation, through late time observations. An explicit example of this claim is worked out by studying a model involving an interaction in the dark sector. Results of a more astrophysical nature, where a careful analysis of the morphology of blazar halos is performed, are also presented in the Appendix. The analysis determined that the $Q$-statistic is an appropriate tool to probe the properties of the intergalactic magnetic fields responsible for the halos formation.

Contributors

Agent

Created

Date Created
  • 2017

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Emergence of Spacetime: From Entanglement to Einstein

Description

Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law

Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law of thermodynamics applied to local holographic screens. This is accomplished by essentially reversing the steps of Hawking's area theorem, leading to the Ricci convergence condition as an input, from which an application of Einstein's equations yields the NEC. Using the same argument, I show logarithmic quantum corrections to the Bekenstein-Hawking entropy formula do not alter the form of the Ricci convergence condition, but obscure its connection to the NEC. Then, by attributing thermodynamics to the stretched horizon of future lightcones -- a timelike hypersurface generated by a collection of radially accelerating observers with constant and uniform proper acceleration -- I derive Einstein's equations from the Clausius relation. Based on this derivation I uncover a local first law of gravity, connecting gravitational entropy to matter energy and work. I then provide an entanglement interpretation of stretched lightcone thermodynamics by extending the entanglement equilibrium proposal. Specifically I show that the condition of fixed volume can be understood as subtracting the irreversible contribution to the thermodynamic entropy. Using the AdS/CFT correspondence, I then provide a microscopic explanation of the 'thermodynamic volume' -- the conjugate variable to the pressure in extended black hole thermodynamics -- and reveal the super-entropicity of three-dimensional AdS black holes is due to the gravitational entropy overcounting the number of available dual CFT states. Finally, I conclude by providing a recent generlization of the extended first law of entanglement, and study its non-trivial 2+1- and 1+1-dimensional limits. This thesis is self-contained and pedagogical by including useful background content relevant to emergent gravity.

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Agent

Created

Date Created
  • 2020

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The Pauli-Lubanski Vector in a Group-Theoretical Approach to Relativistic Wave Equations

Description

Chapter 1 introduces some key elements of important topics such as; quantum mechanics,

representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´

tivistic wave equations

Chapter 1 introduces some key elements of important topics such as; quantum mechanics,

representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´

tivistic wave equations that will play an important role in the work to follow. In Chapter 2,

a complex covariant form of the classical Maxwell’s equations in a moving medium or at

rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum

tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its

connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´

netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.

Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s

equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell

and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´

operators of the Poincare group. A connection between the spin of a particle/field and ´

consistency of the corresponding overdetermined system is emphasized in the massless

case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which

is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨

evolution of exact wave functions of the generalized harmonic oscillators is determined

in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is

shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem

for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the

methods introduced in Chapter 5 a model for the quantization of an electromagnetic field

in a variable media is analyzed. The concept of quantization of an electromagnetic field

in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode

of radiation for this model is used to find time-dependent photon amplitudes in relation

to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the

uncertainty relation, are explicitly given in terms of the Ermakov-type system.

Contributors

Agent

Created

Date Created
  • 2016

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Anomalous Chiral Plasmas in the Hydrodynamic Regime

Description

Chiral symmetry and its anomalous and spontaneous breaking play an important role

in particle physics, where it explains the origin of pion and hadron mass hierarchy

among other things.

Despite its

Chiral symmetry and its anomalous and spontaneous breaking play an important role

in particle physics, where it explains the origin of pion and hadron mass hierarchy

among other things.

Despite its microscopic origin chirality may also lead to observable effects

in macroscopic physical systems -- relativistic plasmas made of chiral

(spin-$\frac{1}{2}$) particles.

Such plasmas are called \textit{chiral}.

The effects include non-dissipative currents in external fields that could be present

even in quasi-equilibrium, such as the chiral magnetic (CME) and separation (CSE)

effects, as well as a number of inherently chiral collective modes

called the chiral magnetic (CMW) and vortical (CVW) waves.

Applications of chiral plasmas are truly interdisciplinary, ranging from

hot plasma filling the early Universe, to dense matter in neutron stars,

to electronic band structures in Dirac and Weyl semimetals, to quark-gluon plasma

produced in heavy-ion collisions.

The main focus of this dissertation is a search for traces of chiral physics

in the spectrum of collective modes in chiral plasmas.

I start from relativistic chiral kinetic theory and derive

first- and second-order chiral hydrodynamics.

Then I establish key features of an equilibrium state that describes many

physical chiral systems and use it to find the full spectrum of collective modes

in high-temperature and high-density cases.

Finally, I consider in detail the fate of the two inherently chiral waves, namely

the CMW and the CVW, and determine their detection prospects.

The main results of this dissertation are the formulation of a fully covariant

dissipative chiral hydrodynamics and the calculation of the spectrum of collective

modes in chiral plasmas.

It is found that the dissipative effects and dynamical electromagnetism play

an important role in most cases.

In particular, it is found that both the CMW and the CVW are heavily damped by the usual

Ohmic dissipation in charged plasmas and the diffusion effects in neutral plasmas.

These findings prompt a search for new physical observables in heavy-ion collisions,

as well as a revision of potential applications of chiral theories in

cosmology and solid-state physics.

Contributors

Agent

Created

Date Created
  • 2019