193 research outputs found
Mesoscopic Physics of Quantum Systems and Neural Networks
We study three different kinds of mesoscopic systems – in the intermediate region between macroscopic and microscopic scales consisting of many interacting constituents:
We consider particle entanglement in one-dimensional chains of interacting fermions. By employing a field theoretical bosonization calculation, we obtain the one-particle entanglement entropy in the ground state and its time evolution after an interaction quantum quench which causes relaxation towards non-equilibrium steady states. By pushing the boundaries of the numerical exact diagonalization and density matrix renormalization group computations, we are able to accurately scale to the thermodynamic limit where we make contact to the analytic field theory model. This allows to fix an interaction cutoff required in the continuum bosonization calculation to account for the short range interaction of the lattice model, such that the bosonization result provides accurate predictions for the one-body reduced density matrix in the Luttinger liquid phase.
Establishing a better understanding of how to control entanglement in mesoscopic systems is also crucial for building qubits for a quantum computer. We further study a popular scalable qubit architecture that is based on Majorana zero modes in topological superconductors. The two major challenges with realizing Majorana qubits currently lie in trivial pseudo-Majorana states that mimic signatures of the topological bound states and in strong disorder in the proposed topological hybrid systems that destroys the topological phase. We study coherent transport through interferometers with a Majorana wire embedded into one arm.
By combining analytical and numerical considerations, we explain the occurrence of an amplitude maximum as a function of the Zeeman field at the onset of the topological phase – a signature unique to MZMs – which has recently been measured experimentally [Whiticar et al., Nature Communications, 11(1):3212, 2020]. By placing an array of gates in proximity to the nanowire, we made a fruitful connection to the field of Machine Learning by using the CMA-ES algorithm to tune the gate voltages in order to maximize the amplitude of coherent transmission. We find that the algorithm is capable of learning disorder profiles and even to restore Majorana modes that were fully destroyed by strong disorder by optimizing a feasible number of gates.
Deep neural networks are another popular machine learning approach which not only has many direct applications to physical systems but which also behaves similarly to physical mesoscopic systems. In order to comprehend the effects of the complex dynamics from the training, we employ Random Matrix Theory (RMT) as a zero-information hypothesis: before training, the weights are randomly initialized and therefore are perfectly described by RMT. After training, we attribute deviations from these predictions to learned information in the weight matrices.
Conducting a careful numerical analysis, we verify that the spectra of weight matrices consists of a random bulk and a few important large singular values and corresponding vectors that carry almost all learned information. By further adding label noise to the training data, we find that more singular values in intermediate parts of the spectrum contribute by fitting the randomly labeled images. Based on these observations, we propose a noise filtering algorithm that both removes the singular values storing the noise and reverts the level repulsion of the large singular values due to the random bulk
Determining uncertainty in the functional quantities of fringe projection
Fringe projection systems can acquire a point-cloud of more than a million points in minutes while not needing to ever physically touch the measurement surface and can be assembled using relatively inexpensive off-the-shelf components. Fringe projection system can conduct measurements faster than their tactile counterparts and typically require less training to do so.
The disadvantage of using a fringe projection system is the measurements are less accurate than alternative tactile methods – and typical methods to obtain an uncertainty evaluation within fringe projection require a tactile system as a comparator. Anterior to any measurement, fringe projection systems undergo a calibration, whereby the set of functional quantities (defined in this thesis as the system parameters) are found that define the measurement (the point-cloud) from the indication (a set of images). The accuracy of the estimated parameters will define the accuracy of any measurements made by the system. The calibration process does not evaluate any uncertainty of the estimated system parameters – the accuracy of the estimation of the parameters remains unknown, as is their exact effect on the measurement result.
In this thesis, an investigation into the using the system parameters to evaluate the uncertainty of fringe projection measurements is made. Firstly, a method to localise the centre of ellipses in camera images with an uncertainty is given. This uncertainty is used to derive the uncertainty in the estimated system parameters. The uncertainty in the system parameters is tested by using the system parameters to measure known artefacts, a flatness artefact and two sphere-based artefacts, where the propagated uncertainty is tested against the measurement error. The accuracy of the system parameters are tested by comparing the measurement error of the measurements with measurements made on a commercial system, the GOM ATOS Core 300. In addition, an exhaustive study is undertaken on the calibration, including applying curvature, specificity and parameter stability tests on the non-linear regression used within calibration.
The sphere-based measurements were found to not be robust enough against measurement noise in fringe projection to be able to provide information on errors caused by the system parameters. This thesis raises questions as to the appropriateness of using sphere-based measurements to represent the performance of a fringe projection system. The flatness measurements made using the estimated system parameters achieved an accuracy of approximately 30 "μm" across a 300 "mm"×140 "mm" flatness artefact, which is similar to measurements made by the commercial system. However, the estimated uncertainty was unable to explain all measurement discrepancy between the fringe projection measurements and the tactile measurements. The result specificity test indicated poor specificity of the mathematical model of fringe projection, namely the camera pinhole model with Brown-Conrady distortion. It is concluded that the level of accuracy of the mathematical model has become a limiting factor in the accuracy of fringe projection measurements, instead of the accuracy of the inputs to the calibration. Therefore, the uncertainty of the system parameters cannot be used to evaluate an uncertainty of a measurement made using a fringe projection system
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Random matrix theory and the loss surfaces of neural networks
Neural network models are one of the most successful approaches to machine
learning, enjoying an enormous amount of development and research over recent
years and finding concrete real-world applications in almost any conceivable
area of science, engineering and modern life in general. The theoretical
understanding of neural networks trails significantly behind their practical
success and the engineering heuristics that have grown up around them. Random
matrix theory provides a rich framework of tools with which aspects of neural
network phenomenology can be explored theoretically. In this thesis, we
establish significant extensions of prior work using random matrix theory to
understand and describe the loss surfaces of large neural networks,
particularly generalising to different architectures. Informed by the
historical applications of random matrix theory in physics and elsewhere, we
establish the presence of local random matrix universality in real neural
networks and then utilise this as a modeling assumption to derive powerful and
novel results about the Hessians of neural network loss surfaces and their
spectra. In addition to these major contributions, we make use of random matrix
models for neural network loss surfaces to shed light on modern neural network
training approaches and even to derive a novel and effective variant of a
popular optimisation algorithm.
Overall, this thesis provides important contributions to cement the place of
random matrix theory in the theoretical study of modern neural networks,
reveals some of the limits of existing approaches and begins the study of an
entirely new role for random matrix theory in the theory of deep learning with
important experimental discoveries and novel theoretical results based on local
random matrix universality.Comment: 320 pages, PhD thesi
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity
Towards a circular economy: fabrication and characterization of biodegradable plates from sugarcane waste
Bagasse pulp is a promising material to produce biodegradable plates. Bagasse is the fibrous residue that remains after sugarcane stalks are crushed to extract their juice. It is a renewable resource and is widely available in many countries, making it an attractive alternative to traditional plastic plates. Recent research has shown that biodegradable plates made from Bagasse pulp have several advantages over traditional plastic plates. For example, they are more environmentally friendly because they are made from renewable resources and can be composted after use. Additionally, they are safer for human health because they do not contain harmful chemicals that can leach into food. The production process for Bagasse pulp plates is also relatively simple and cost-effective. Bagasse is first collected and then processed to remove impurities and extract the pulp. The pulp is then molded into the desired shape and dried to form a sturdy plate. Overall, biodegradable plates made from Bagasse pulp are a promising alternative to traditional plastic plates. They are environmentally friendly, safe for human health, and cost-effective to produce. As such, they have the potential to play an important role in reducing plastic waste and promoting sustainable practices. Over the years, the world was not paying strict attention to the impact of rapid growth in plastic use. As a result, uncontrollable volumes of plastic garbage have been released into the environment. Half of all plastic garbage generated worldwide is made up of packaging materials. The purpose of this article is to offer an alternative by creating bioplastic goods that can be produced in various shapes and sizes across various sectors, including food packaging, single-use tableware, and crafts. Products made from bagasse help address the issue of plastic pollution. To find the optimum option for creating bagasse-based biodegradable dinnerware in Egypt and throughout the world, researchers tested various scenarios. The findings show that bagasse pulp may replace plastics in biodegradable packaging. As a result of this value-added utilization of natural fibers, less waste and less of it ends up in landfills. The practical significance of this study is to help advance low-carbon economic solutions and to produce secure bioplastic materials that can replace Styrofoam in tableware and food packaging production
Review of Particle Physics
The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143
new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the
recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical
particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search
limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs
Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology,
Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily
revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances.
The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume
2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented
in the Listings.
The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov)
and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary
Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version
optimized for use on phones, and as an Android app.United States Department of Energy (DOE) DE-AC02-05CH11231government of Japan (Ministry of Education, Culture, Sports, Science and Technology)Istituto Nazionale di Fisica Nucleare (INFN)Physical Society of Japan (JPS)European Laboratory for Particle Physics (CERN)United States Department of Energy (DOE
Non-Hermitian approaches for pair-excitation in quantum Boson dynamics
The topic of this thesis is the mathematical analysis of physically motivated modelsfor a trapped dilute Bose gas with repulsive pairwise atomic interactions at zero temper-
ature. Our goal is to develop the spectral theory for excited many-body quantum states
of these systems by accounting for the scattering of atoms in pairs from the macroscopic
state (condensate). This general methodology, known as pair-excitation, was introduced
in the physics literature in the 1960s – the work of this thesis provides the first compre-
hensive mathematical treatment of many aspects of pair-excitation. This includes, e.g.,
the spectral theory for pair-transformed approximate Hamiltonians, a general existence
theory for the pair-excitation kernel, and the connection between the pair-excitation for-
malism to quasiparticle excitations in the Bose gas.
We formulate the method of pair-excitation for several historical models of the Bosegas from the physics literature. In particular, we focus on the seminal works of Wu, Fetter,
Griffin, and Lee, Huang, and Yang. Each of these models introduce unique features
to the mathematical analysis, but the general strategy remains the same: transform the
approximate Hamiltonian using a suitably-defined pair-excitation operator. This operator
is not determined a priori, but is chosen as part of the problem in order to simplify the
expression of excited states of the transformed system.
The study begins with models for the Bose gas in the non-translation-invariant set-ting, where the particles are spatially-confined in an external trapping potential. In this
setting, formulating the pair-excitation method entails solving a nonlinear integro-partial-
differential equation for the pair-excitation kernel. We provide a general existence theory
for this kernel via a variational approach. The kernel which we find allows us to connect
the pair-excitation method to the more widely-studied unitary transformation of quadratic
Hamiltonians via Bogoliubov rotation. The theory for the kernel also allows us to write a
simple formula for excited many-body states, which can be adapted to the various models
which we consider in this work.
We then study the problem for the pair-excited transformed approximate Hamilto-nian for Bosons in a periodic box. In this setting, the description of the effective Hamil-
tonian in the momentum basis is particularly simple. However, the lack of particle con-
servation means that the pair-excitation transform is unbounded in operator norm, and
spectral methods developed in earlier chapters are enriched with new tools
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