12023 research outputs found
Sort by
Convergence of Time-Inhomogeneous Random Walks on Finite Groups with Applications to Universality for Random Groups
Get PDFWe study time-inhomogeneous random walks on finite groups in the case where each random walk step need not be supported on a generating set of the group. When the supports of the random walk steps satisfy a natural condition involving normal subgroups of quotients of the group, we show that the random walk converges to the uniform distribution on the group, and give bounds for the convergence rate using spectral properties of the random walk steps. As applications, we prove a general universality theorem for quotients of the free group on n generators as n → ∞, and another universality theorem for cokernels of random integer matrices with dependent entries
Lorentz Symmetry and Non-Unitary Quantum Field Theories
Get PDFWe know quantum field theory is unitary. However, since the early 1980s, there have been numerous attempts to construct quantum field theories where time evolution is non-unitary. Some of these endeavors aimed to address the issue of black hole information loss, as non-unitary evolution does not necessarily require information preservation. Some wanted to use it as a modification of quantum mechanics to allow objective collapse. Some wanted to construct classical-quantum gravity which could serve as an alternative to quantum gravity.
I embarked on a similar path, attempting to construct a Lorentz covariant non-unitary quantum field theory. At a certain point, I believed we were making significant progress. However, I gradually realized that our construction faced serious problems. We took a lot of assumptions and results from unitary quantum field theory for granted, and used them without justification. After struggling with it for a long time, I decide to make a complete reversal and prove that non-unitary quantum field theories fundamentally conflict with Lorentz covariance.
There are three approaches to constructing a Lorentz covariant non-unitary QFT. The first approach involves constructing a theory based on unitary quantum field theory, where a system is coupled to an environment. If we only consider the system and trace out the environment, the resulting equation of motion appears non-unitary. In this case, unitarity emerges as an emergent property. The second approach is to propose a theory from scratch where the time evolution is fundamentally non-unitary, described by the Lindblad master equation. Both in the emergent and fundamentally non-unitary theories, the dynamics are intended to be Lorentz covariant. The third approach employs the Schwinger-Keldysh formalism to construct a path integral, and examines the symmetry of the Keldysh action within the path integral. It is assumed that, similar to quantum field theory, the non-unitary theory will possess the same symmetry as the Keldysh action.
Regrettably, none of these three classes of theories prove successful. This thesis thoroughly analyzes the issues associated with these three constructions. The most significant problems include:
1, The fundamental assumption that the quantum fields (and their excitations) form a unitary representation of the Lorentz group is invalid, and they cannot form a non-unitary representation either.
2, The system Hamiltonian in the Lindblad equation is ill-defined and does not transform as the first component of a Lorentz four-vector.
3, Even if we overlook the aforementioned inconsistencies, the dynamics fail to produce expected results when applied to phenomena such as particle decay, as they exhibit a preferred reference frame.
4, The symmetry of the Keldysh action does not guarantee the corresponding symmetry in the dynamics. Invariant Keldysh actions can correspond to non-covariant equations of motion.
In conclusion, the Lorentz symmetry is incompatible with non-unitary quantum field theories.</p
Michéline
No full textBackground: How do you tell the story of white supremacy, racial capitalism, settler colonialism, transatlantic chattel slavery, and tell a story that cares for BIPOC (Black, indigenous, and people of color) lives? A story that honors the lives of those who were not supposed to survive, no less thrive? Bernardine Evaristo’s Girl, Woman, Other is a work that successfully embodies such a practice of care amid precarity. While the novel ends with an epilogue, we know, as scholars of Black studies, that the Black diaspora has not ended and that many of the stories of its diverse kin have yet to be told
Holistic Design in High-Speed Silicon Photonics and Low-Power Electronics Platforms
Get PDFHigh-speed interconnects are of vital importance to the operation of high-performance computing and communication systems, determining the ultimate bandwidth or data rates at which the information can be exchanged. Optical interconnects and the employment of high order modulation formats are considered as the solutions to fulfilling the envisioned speed and power efficiency of future interconnects. One area of growing importance in optical interconnects is the design and optimization of energy-efficient transmitters with superior power efficiency. Enhancing the electro-optical bandwidth density while keeping the power efficiency optimized, requires improvement in the optical power penalty of photonic integrated circuits. Moreover, co-optimization of electronics and photonics enables a path towards sub-pJ/b transmission efficiency. In this dissertation, architectural and circuit-level energy-efficient techniques serving these goals are presented.
First, an integrated DAC-less PAM-4 transmitter in a multi-micron silicon photonics platform using 2 binary-driven uneven-length SiGe EAMs in an unbalanced MZI is presented. The optical transmitter exhibits 5.5dB ER at 100 Gb/s with 2.1dB SNR improvement compared to single EAMs driven by PAM-4 signals. Also, A DAC-less 200Gb/s QAM-16 transmitter in a multi-micron silicon-photonics platform using 4 binary-driven SiGe EAMs in an unbalanced MZI is presented. The transmitter exhibits bit-error rates of 3×10-4 and 2.8×10-4 for square and hexagonal constellations.
Second, a 100Gb/s PAM4 optical transmitter system implemented in a 3D-integrated Silicon Photonics-CMOS platform is presented. The photonics chip includes a push-pull segmented Mach-Zehnder Modulator (MZM) structure using highly capacitive (415fF to 1.1pF), yet optically efficient (VπL= 0.8 V.cm) metal-oxide-silicon capacitor (MOSCAP) phase modulators. Two pairs of U-shaped modulator segments with effective lengths of 170µm and 450µm are driven at 50 Gbaud by a dual-channel 28nm CMOS driver, which is flip-chip bonded to the photonics chip. The driver cores utilize digitally controllable pre-distortion and inductive peaking to achieve sufficient electro-optical bandwidth. The drivers deliver 1.2Vppd swing to modulators using a 0.9V supply and on-chip serializers that generate 50Gb/s data streams. The electronics chip consumes 240mW achieving 2.4pJ/bit energy efficiency. The overall electro-optical bandwidth (EOBW), without any pre-distortion, is increased by approximately 56% and 48% for the 170µm and 450µm segments, respectively, when compared to their EOBW measured by 65GHz 50-Ohm terminated probes. The optical input power to the photonics chip is +10dBm and an erbium-doped fiber amplifier amplifies output signals by 11dB. The 50Gb/s NRZ optical raw eye diagram exhibits 4.3dB extinction ratio (ER) and 1.2dBm of optical modulation amplitude (OMA). The 100Gb/s PAM4 optical raw eye diagram shows 4.3dB ER and 1.4dBm OMA with a transmitter dispersion eye closure quaternary (TDECQ) of 1.53dB after a 5-tap feed-forward-equalization (FFE) filter. The PAM4 TDECQ changes by 53% when the temperature is increased from 30ºC to 90 ºC at the optimum forward bias voltage of 1V.
Third, an efficient cold-starting energy harvester system, fabricated in 65nm CMOS is presented. The proposed harvester uses no external electrical components and is compatible with biofuel-cell voltage and power ranges. A power-efficient system architecture is proposed to keep the internal circuitry operating at 0.4V while regulating the output voltage at 1V using switched-capacitor DC-DC converters and a hysteretic controller. A startup enhancement block is presented to facilitate cold startup with any arbitrary input voltage. A real-time on-chip 2D maximum power point tracking with source degradation tracing is also implemented to maintain power efficiency maximized over time. The system performs cold startup with a minimum input voltage of 0.39V and continues its operation if the input voltage degrades to as low as 0.25V. Peak power efficiency of 86% is achieved at 0.39V of input voltage and 1.34μW of output power with 220nW of average power consumption of the chip. The end-to-end power efficiency is kept above 70% for a wide range of loading powers from 1μW to 12μW. The chip is integrated with a pair of lactate biofuel-cell electrodes with 2mm of diameter on a prototype printed circuit board (PCB). Integrated operation of the chip with the electrodes and a lactate solution is demonstrated
Noncanonical Amino Acid Synthesis by Evolved Tryptophan Synthases
Get PDFThe β-subunit of tryptophan synthase (TrpB) is responsible for the final step of ʟ-tryptophan biosynthesis in all of known biology. Recognized for this important role and its powerful chemistry, TrpB has more recently been used for the in vitro synthesis of tryptophan analogs and other noncanonical amino acids (ncAAs). This thesis describes some of these efforts as well as the application of TrpB for developing new methods in directed enzyme evolution. Chapter I first establishes important topical background. It begins with a general account of directed enzyme evolution by exploring the emergence of new catalytic functions in natural and laboratory settings, and how this information and chemical intuition can be used to create enzymes for desired reactions. This is followed by a description of the state of the field of ncAA synthesis, with a special focus on biocatalytic approaches using engineered enzymes. Chapters II and III examine targeted engineering campaigns to create enzymes that can efficiently synthesize valuable blue-fluorescent ncAAs such as 4-cyanotryptophan (Chapter II) and β-(1-azulenyl)-ʟ-alanine (AzAla, Chapter III) from accessible starting materials. In Chapter IV, the native function of TrpB for ʟ-tryptophan biosynthesis is used as a selection pressure to develop an in vivo continuous evolution system. Despite a selection pressure for only ʟ-tryptophan synthesis the orthologous TrpB variants generated by this system have varying promiscuous activities for ʟ-tryptophan analogs, paralleling the sequence-function diversity of natural enzyme homologs. Chapter V describes evSeq, an inexpensive and simple method for sequencing all protein variants generated during an engineering campaign, demonstrated by collecting ~800 TrpB sequence-function data points. Finally, in Chapter VI, directed evolution and chemical intuition are used to convert TrpB from a tryptophan synthase to a novel tyrosine synthase (TyrS). This enzyme can irreversibly and regioselectively alkylate simple phenol analogs to synthesize valuable tyrosine analogs, including the blue-fluorescent ncAA β-(1-naphthol-4-yl)-ʟ-alanine (NaphAla) and 3-methyl-ʟ-tyrosine at gram scales. Because TyrS synthesizes a primary metabolite, this transformation represents a noncanonical method for the biosynthesis of ʟ-tyrosine. This is the first example of a feasible new route for de novo aromatic amino acid biosynthesis, which occurs through a universally conserved set of chemistry across all of life. In total, the work described here expands the fields of chemical synthesis and synthetic biology by presenting new enzymes—and methods for producing these enzymes—that are capable of synthesizing important amino acids in vitro and in vivo.</p
Polyelectrolytes Near Solid Surfaces
Get PDFPolyelectrolytes are ubiquitous in nature and in the products we use daily. The combination of their connectivity and charge lead to many useful properties in solution and near surfaces. Electrostatic forces dominate much of the behavior of charged species near solid surfaces; however, nonelectrostatic forces arising ion specific interactions or from varying polymer chemistry play an important role in tuning electrolyte and polyelectrolyte properties. The balance of these forces depends on factors like the salt concentration, solution pH, and properties of the surface. The current work outlines the thermodynamics of charged systems and investigates the structure and phase behavior of polyelectrolytes near solid surfaces. In particular, the work covers the thermodynamic aspects of preferential adsorption of small ions in electric double layers, polyelectrolyte adsorption, polymer-mediated interactions of surfaces using strong and weak electrolytes, surface phase transitions and contact angles of complex coacervates on solid surfaces, complexation-induced conformational phase transitions of polyelectrolyte brushes, and electro-swelling of weak polyelectrolyte brushes. The wide variety of problems addressed here reflects the variety of applications of polyelectrolytes and contexts in which polyelectrolytes appear.</p
A Novel Platform for Mechanochemical Multicolor Lithography and Models for Solution-Phase Mechanophore Activation
Get PDFThe use of mechanical force to trigger chemical reactions has generated many exciting applications in stimuli-responsive materials. Advancement of this area of study requires the development of fundamental models for mechanical activation as well as the design of new force-responsive units, termed mechanophores. This thesis investigates models for solution-phase activation kinetics and activation efficiency and details the development of a novel mechanophore platform for multicolor mechanochemical lithography
Explore the Nature of Dark Matter in the Context of Galaxy Formation
Get PDFThe nature of dark matter (DM) is a fundamental question in modern cosmology. Despite its significant role in various physical processes throughout the Universe, the particle nature of DM remains elusive. With the non-detection of classical candidates (e.g. WIMPs), the theoretical space for DM is becoming increasingly open. This thesis revolves around studying the nature of DM in the context of structure formation and we will focus on a category of DM with self-interactions (SIDM), which can be constrained only through astrophysical probes if DM has no coupling with the standard model particles. Utilizing advanced cosmological hydrodynamical simulations, we examine the effects of DM elastic and dissipative self-interactions on galaxy structure and their interplay with baryonic physics processes. Our numerical studies encompass a range of systems, such as Local dwarf galaxies, massive galaxy clusters in the Local Universe, and rare massive quasar-host galaxies at high redshift (z ≳ 6). In Local dwarf galaxies, we analyze the unique signatures of dissipative self-interacting DM (dSIDM) with typical self-interaction cross-section σ/m ~ 0.1-10 cm² g⁻¹ and dissipation factor ~ 0.5. We find a universal cuspy central density profile and systematic changes in halo morphology in dSIDM. By comparing our results with observations, we derive constraints for effective parameters of dSIDM and identify the parameter space where it remains viable and exhibits interesting observational implications. For a similar type of dSIDM with fairly low σ/m ≾ 0.05 cm² g⁻¹, we also explore the possibility that the direct collapse of dSIDM halos at high redshift can seed supermassive black holes and serve as progenitors for massive bright quasars observed at high redshift. This scenario predicts a large population of quiescent supermassive black holes (SMBHs) at high redshift, which could be tested by future LISA observations. Lastly, in Local massive galaxy clusters, we compare the X-ray morphology of hot gas in observed clusters with simulations of elastic SIDM. Although SIDM models with large interaction cross-sections (σ/m ≳ 0.5 cm² g⁻¹) are favored, uncertainties from cooling and feedback physics in galaxy clusters must be taken into account. This thesis summarizes the findings and constraints on DM properties, with a particular emphasis on its potential self-interactions, as derived from a combination of research projects
The Effects of Disorder and Interaction in Metallic Systems
Get PDFMetallic states in two-dimensional quantum matter have a long history and pose extremely challenging problems. A generic metallic state is described by a gapless system with a finite density of particles, along with disorders and interactions. Such correlated many-body systems are usually difficult to study, both analytically and numerically. In this thesis, we are dedicated to certain simplified cases which enable us to study via analytical approaches. Firstly, we study the effects of quenched disorder and a dissipative Coulomb interaction in the Dirac composite fermion theory describing the quantum phase transition of integer quantum Hall plateau and magnetic-field tuned 2D supercondutor
The renormalization group study is presented, by considering the quantum effect of disorder and gauge fluctuation. Secondly, we present a study of integer quantum Hall plateau transition using a mean-field theory of composite fermions with a gyromagnetic ratio equal to two. We investigate the stability problem in terms of semi-classical approach and derive the corresponding nonlinear sigma model. Thirdly, we study a single 2D Dirac fermion at finite density, subjected to a quenched random magnetic field. The low-energy theory can be mapped onto an infinite collection of 1D chiral fermions coupled by a random vector potential matrix. The theory is exactly solvable, and the electrical response is computed non-perturbatively. Lastly, we shift our focus to a disorder-free system formed by a collection of 1D wires. We provide an example of an Ersatz Fermi liquid by deforming the chiral Wess-Zumino-Witten model with level k greater than unity
Tunability of Gas Adsorption Enthalpies in Carbonaceous Materials for Energy-Related Applications
Get PDFCarbonaceous materials provide a porous, high surface area framework for the adsorption of gases through physisorption. Physisorption operates through van der Waals forces, resulting in highly reversible, densified gas storage. The density of adsorbed gas species approaches the bulk liquid density, providing a method to increase the volumetric energy density of hydrogen and natural gas at conditions where the adsorbate is a non-liquid in the bulk phase. This dissertation explores the tunability of the strength of gas adsorption to surfaces of carbon adsorbents, known as the enthalpy of adsorption. Two methods are studied: modification of the surface atomic composition and microstructural changes to the carbon porosity. Applications are considered for both energy storage and carbon capture applications.
The first chapter presents a brief overview of the energy storage field, with emphasis on non-conventional methods to store gases efficiently. Chapter 2 provides the thermodynamic and statistical mechanical derivations used throughout this work, and the assumptions that go into the models used to analyze adsorption data. Chapter 3 reports work on a copper-modified commercial carbon MSC-30 for hydrogen storage, which exhibits an activated dissociative chemisorption desorption feature around ambient temperature. Chapter 4 presents the densification of a novel architected carbon structure, zeolite-templated carbon, for adsorbed natural gas storage. Through the pelletization process, the pore morphology of the underlying adsorbent framework is compressed, resulting in increased adsorption enthalpies with applied pelletization pressure. Chapter 5 focuses on the tunability of pore structure through potassium hydroxide activation, and the resulting adsorption properties pertinent to carbon dioxide capture from a simulated flue-gas stream. The last chapter provides insight into the work as a whole and identifies areas of future work that would improve the fundamental understanding and broader impact of adsorbent materials.</p