Topological phases of matter represent a new phase which cannot be understood in terms of Landau’s theory of symmetry breaking and are characterized by non-local topological properties emerging from purely local (microscopic) degrees of freedom. It is the non-trivial topology of the bulk band structure that gives rise to topological phases in condensed matter systems. Quantum Hall systems are prominent examples of such topological phases. Different quantum Hall states cannot be distinguished by a local order parameter. Instead, non-local measurements are required, such as the Hall conductance, to differentiate between various quantum Hall states. A signature of a topological phase is the existence of robust properties that do not depend on microscopic details and are insensitive to local perturbations which respect appropriate symmetries. Examples of such properties are the presence of protected gapless edge states at the boundary of the system for topological insulators and the remarkably precise quantization of the Hall conductance for quantum Hall states. The robustness of these properties can be under-stood through the existence of a topological invariant, such as the Chern number for quantum Hall states which is quantized to integer values and can only be changed by closing the bulk gap. Two other examples of topological phases of matter are topological superconductors and Weyl semimetals. The study of transport in various kinds of junctions of these topological materials is highly interesting for their applications in modern electronics and quantum computing. Another intriguing area to study is how to generate new kind of gapless edge modes in topological systems. In this thesis I have studied various aspects of topological phases of matter, such as electronic transport in junctions of topological insulators and topological superconductors, the generation of new kinds of boundary modes in the presence of granularity, and the effects of periodic driving in topological systems. We have studied the following topics. 1. transport across a line junction of two three-dimensional topological insulators, 2. transport across a junction of topological insulators and a superconductor, 3. surface and edge states of a topological insulator starting from a lattice model, 4. effects of granularity in topological insulators, 5. Majorana modes and conductance in systems with junctions of topological superconducting wires and normal metals, and 6. generation of new surface states in a Weyl semimetal in the presence of periodic driving by the application of electromagnetic radiation. A detailed description of each chapter is given below. • In the first chapter we introduce a number of concepts which are used in the rest of the thesis. We will discuss the ideas of topological phases of matter (for example, topological insulators, topological superconductors and Majorana modes, and Weyl semimetals), the renormalization group theory for weak interactions, and Floquet theory for periodically driven systems. • In the second chapter we study transport across a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time-reversal invariant system, we show that the line junction is characterized by an arbitrary real parameter α; this determines the scattering amplitudes (reflection and transmission) from the junction. The physical origin of α is a potential barrier that may be present at the junction. If the surface velocities have the same sign, edge states exist that propagate along the line junction with a velocity and orientation of the spin which depend on α and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle φ with respect to each other. We study the scattering and differential conductance across the line junction as functions of φ and α. We also show that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on φ. Finally, if the surface velocities have opposite signs, we find that the electrons must necessarily transmit into the two-dimensional interface separating the two topological insulators. • In the third chapter we discuss transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. This junction is more complicated than the line junction discussed in the previous chapter because of the presence of the superconductor. In a topological insulator spin-up and spin-down electrons get coupled while in a superconductor electrons and holes get coupled. Hence we have to use a four-component spinor formalism to describe both spin and particle-hole degrees of freedom. The junction can have three time-reversal invariant barriers on the three sides. We compute the subgap charge conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters which characterize the barriers. We find that the presence of topological insulators and a superconductor leads to both Dirac and Schrodinger-like features in the charge conductances. We discuss the effects of bound states on the superconducting side on the conductance; in particular, we show that for triplet p-wave superconductors such a junction may be used to determine the spin state of its Cooper pairs. • In the fourth chapter we derive the surface Hamiltonians of a three-dimensional topological insulator starting from a microscopic model. (This description was not discussed in the previous chapters where we directly started from the surface Hamiltonians without deriving them form a bulk Hamiltonian). Here we begin from the bulk Hamiltonian of a three-dimensional topological insulator Bi2Se3. Using this we derive the surface Hamiltonians on various surfaces of the topological insulator, and we find the states which appear on the different surfaces and along the edge between pairs of surfaces. The surface Hamiltonians depend on the orientation of the surfaces and are therefore quite different from the previous chapters. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based directly on a lattice discretization of the bulk Hamiltonian in order to find surface and edge states. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge are studied as a function of the edge potential. We show that a magnetic field applied in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states. • In the fifth chapter we study a system made of topological insulator (TI) nanocrystals which are coupled to each other. Our theoretical studies are motivated by the following experimental observations. Electrical transport measurements were carried out on thin films of nanocrystals of Bi2Se3 which is a TI. The measurements reveal that the entire system behaves like a single TI with two topological surface states at the two ends of the system. The two surface states are found to be coupled if the film thickness is small and decoupled above a certain film thickness. The surface state penetration depth is found to be unusually large and it decreases with increasing temperature. To explain all these experimental results we propose a theoretical model for this granular system. This consists of multiple grains of Bi2Se3 stacked next to each other in a regular array along the z-direction (the c-axis of Bi2Se3 nanocrystals). We assume translational invariance along the x and y directions. Each grain has top and bottom surfaces on which the electrons are described by Hamiltonians of the Dirac form which can be derived from the bulk Hamiltonian known for this material. We introduce intra-grain tunneling couplings t1 between the opposite surfaces of a single grain and inter-grain couplings t2 between nearby surfaces of two neighboring grains. We show that when t1 < t2 the entire system behaves like a single topological insulator whose outermost surfaces have gapless spectra described by Dirac Hamiltonians. We find a relation between t1, t2 and the surface state penetration depth λ which explains the properties of λ that are seen experimentally. We also present an expression for the surface state Berry phase as a function of the hybridization between the surface states and a Zeeman magnetic field that may be present in the system. At the end we theoretically studied the surface states on one of the side surfaces of the granular system and showed that many pairs of surface states can exist on the side surfaces depending on the length of the unit cell of the granular system. • In the sixth chapter we present our work on junctions of p-wave superconductors (SC) and normal metals (NM) in one dimension. We first study transport in a system where a SC wire is sandwiched between two NM wires. For such a system it is known that there is a Majorana mode at the junction between the SC and each NM lead. If the p-wave pairing changes sign at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the subgap conductance between the leads and the SC. We derive an analytical expression as a function of and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the energies oscillate and decay exponentially as L is increased. The energies exactly match the locations of the peaks in the conductance. We find that the subgap conductances do not change noticeably with the sign of . So there is no effect of the extra Majorana modes which appear inside the SC (due to changes in the signs of Δ) on the subgap conductance. Next we study junctions of three p-wave SC wires which are connected to the NM leads. Such a junction is of interest as it is the simplest system where braiding of Majorana modes is possible. Another motivation for studying this system is to see if the subgap transport is affected by changes in the signs of . For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads. In addition, depending on the signs of the Δ’s in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various subgap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next we study the effects of interactions between electrons (in the NM leads) on the transport. We use a renormalization group approach to study the effect of interactions on the conductance at energies far from the SC gap. Hence the earlier part of this chapter where we studied the transport at an energy E inside the SC gap (so that − < E < Δ) differs from this part where we discuss conductance at an energy E where |E| ≫ . For the latter part we assume the region of three SC wires to be a single region whose only role is to give rise to a scattering matrix for the NM wires; this scattering matrix has both normal and Andreev elements (namely, an electron can be reflected or transmitted as either an electron or a hole). We derive a renormalization group equation for the elements of the scattering matrix by assuming the interaction to be sufficiently weak. The fixed points of the renormalization group flow and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. Using the stability analysis we discuss the dependence of the conductances on the various length scales of the problem. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs. • In the seventh chapter we show that the application of circularly polarized electro-magnetic radiation on the surface of a Weyl semimetal can generate states at that surface. The surface states can be characterized by their momenta due to translation invariance. The Floquet eigenvalues of these states come in complex conjugate pairs rather than being equal to ±1. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the Floquet eigenvalues of the surface states lie at the extrema of the Floquet eigenvalues of the bulk system when the latter are plotted as a function of the momentum perpendicular to the surface, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk Floquet eigenvalues have extrema. For the case of zero surface momentum, we can analytically derive interesting scaling relations between the decay lengths of the surface states and the amplitude and penetration depth of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the surfaces; these states have much larger decay lengths (which can be tuned by the radiation amplitude) than the topological surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states even for trivial insulators.

Lab measurements and Monte Carlo simulations have been carried out for the evaluation of the Straw-type detectors used in the NA62 experiment at CERN. In addition, analyses of experiment data was used in corrections to improve the reconstruction of particle tracks, ultimately leading to improved resolution of the detector system as a whole. 97.7 percent of the Straws were aligned to within 30 microns, quantified as the deviation from zero of the mean of the inherent residual distribution of each Straw. A drift time dependence on where along the Straw the particle ionized have been corrected for; before the correction the dependence was as big as 6 ns. A radius-drift time relation based on the leading edge timing distribution has been deduced and implemented. Upon implementation artifacts from the piecewise fits used became evident. An alternative approach using residuals has been put forward.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2015-12-16T13:33:15Z No. of bitstreams: 1 bernardosottomaiorperalva.pdf: 8631621 bytes, checksum: e4e7f3d592c91e719474b259727bab6c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2015-12-16T15:15:06Z (GMT) No. of bitstreams: 1 bernardosottomaiorperalva.pdf: 8631621 bytes, checksum: e4e7f3d592c91e719474b259727bab6c (MD5) / Made available in DSpace on 2015-12-16T15:15:06Z (GMT). No. of bitstreams: 1 bernardosottomaiorperalva.pdf: 8631621 bytes, checksum: e4e7f3d592c91e719474b259727bab6c (MD5) Previous issue date: 2015-09-11 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese apresenta técnicas de processamento de dados para a detecção de sinais e estimação de energia usando calorimetria de altas energias. Os calorímetros modernos possuem milhares de canais de leitura e operam sob alta taxa de eventos. Tipicamente, a reconstrução da energia envolve etapas de detecção e estimação, e é baseada na medida da amplitude do sinal (digitalizado) recebido. Os métodos empregados, atualmente, em experimentos de altas energias são baseados em técnicas de minimização da variância e selecionam os sinais de interesse a partir da estimação da energia. Este trabalho explora o uso de filtros casados para a detecção de sinais e faz uso de uma calibração para a estimação da energia dos sinais. Na abordagem proposta, os parâmetros aleatórios do pulso processado (fase e deformação) e a estatística do ruído de fundo são considerados no projeto do filtro digital, aumentando seu desempenho. No caso particular de experimentos onde a probabilidade de empilhamento de sinais é alta, uma outra solução, baseada na desconvolução linear de sinais para estimação de energia, é discutida. As técnicas propostas nesta tese foram implementadas offline e aplicadas no calorímetro de telhas (TileCal) do ATLAS no LHC. Foram utilizados sinais simulados, assim como dados reais adquiridos durante a operação nominal do LHC. Os estimadores propostos apresentaram menor erro quando comparados aos métodos empregados em calorímetros modernos e estão, atualmente, sendo validados para serem utilizados no TileCal. / This thesis presents data processing techniques of signal detection and energy estimation for high energy calorimetry. Modern calorimeters have thousands of readout channels and operate at high event rate conditions. Typically, the energy reconstruction involves both detection and estimation tasks, and it is based on the amplitude estimation of the received digitized signal. The current methods employed by high energy experiments are based on variance minimization techniques, and the valid signals are selected based on the energy estimation. This work explores the use of a technique based on Matched Filter for signal detection, and it makes use of a calibration factor to estimate the energy. In the proposed approach, the stochastic parameters of the pulse (phase and deformation) and the statistics from the background are considered for the filter design in order to increase performance. In particular cases, where the signal pile-up is likely to occur, another promising technique, based on linear signal deconvolution is discussed. The techniques proposed in this thesis were implemented offline and applied on the ATLAS Tile Calorimeter (TileCal) at LHC. Both simulated signals and real data acquired during nominal LHC operation were used. The proposed estimators presented smaller error with respect to the methods currently used in modern calorimeter systems, and they have been extensively tested to be used in TileCal.

Este trabalho descreve o desenvolvimento de um simulador para as câmaras de expansão temporal / detectores de radiação de transição (TEC / TRD) do experimento PHENIX, instalado no Colisor de Íons Pesados Relativisticos (RHIC) do Laboratório Nacional de Brookhaven (BNL) nos EUA. O programa do RHIC prevê a produção e caracterização de um estado da matéria conhecido como plasma de quarks e glúons (QGP), através de colisões entre prótons, dêuterons e íons pesados com energias de centro de massa sqrt(s_NN) entre 20 e 200 GeV. O PHENIX, um dos quatro experimentos instalados no acelerador, é especializado na medida de sinais eletrofracos provenientes das colisões e o TEC / TRD é o único subsistema do PHENIX capaz de identificar elétrons de forma eficiente para momentos acima de 5 GeV/c. Um simulador para reprodução da resposta do detector à passagem de partículas foi desenvolvido e comparado a dados de um detector proporcional monofilar construído no Laboratório de Instrumentação e Partículas da USP, e aos dados do próprio TEC / TRD. Os resultados mostram um acordo razoável entre medidas e simulações. O uso do simulador deverá permitir o estudo de novos métodos e melhoras na capacidade de identificação de elétrons do sistema. / The present work describes the development of a simulator for the Time Expansion Chambers / Transition Radiation Detectors (TEC / TRD) of the PHENIX experiment, installed at the Relativistic Heavy Ion Collider (RHIC) of Brookhaven National Laboratory (BNL). The main goal of the RHIC project is the production and study of a state of matter known as Quark Gluon Plasma (QGP), through collisions of protons, deuterons and heavy ions at center of mass energies sqrt(s_NN) ranging between 20 and 200 GeV. PHENIX, one of the four experiments of the accelerator, is dedicated to measuring electroweak signals arising from the collisions, and TEC / TRD is the only subsystem capable of identifying efficiently electrons with momenta above 5 GeV/c. A simulator to reproduce the detector response to the passage of particles was developed and compared to data from a single wire proporcional counter and from TEC / TRD itself. The results show reasonable agreement between measurements and simulations. The use of the simulator allows studies of new methods and possibly improvements in the electron identification capability of the system.

Presented is a search for the rare hadronic B meson decay B0 -&amp;gt; eta phi. It is based on 86 x 10^6 BB pairs recorded by the BABAR experiment at the Stanford Linear Accelerator Center between 1999 and 2002. phi mesons are reconstructed in the channel phi -&amp;gt; K+ K-. eta mesons are reconstructed in the channels eta -&amp;gt; gamma gamma and eta -&amp;gt; pi+ pi- pi0. Signal events are identified by a candidate counting and a maximum-likelihood method. To ensure an unbiased measurement, the number of signal events is blinded throughout the analysis. Although no significant signal is found by either method, the maximum-likelihood method obtains a smaller statistical uncertainty. In this method, the branching fraction of the decay B0 -&amp;gt; eta phi is determined by the upper limit BR (B0 -&amp;gt; eta phi) &amp;lt; 3.28 x 10^-6 (90%). This value includes a systematic uncertainty of 6.2%. The cited upper limit is consistent with recent theoretical predictions. Therefore, this search gives no indication for particle interactions that are not described by the Standard Model of particle physics. / Vorgestellt wird eine Suche nach dem seltenen hadronischen B-Meson-Zerfall B0 -&amp;gt; eta phi. Sie basiert auf 86 x 10^6 BB-Paaren, die zwischen 1999 und 2002 vom BABAR-Experiment am Stanford Linear Accelerator Center aufgezeichnet wurden. phi-Mesonen werden im Kanal phi -&amp;gt; K+ K- rekonstruiert. eta-Mesonen werden in den Kanälen eta -&amp;gt; gamma gamma und eta -&amp;gt; pi+ pi- pi0 rekonstruiert. Zur Identifikation von Signalereignissen wird eine Abzählmethode und eine Maximum-Likelihood-Methode verwendet. Um eine unvoreingenommene Messung zu gewährleisten, bleibt die Anzahl der Signalereignisse während der gesamten Analyse blind. Durch keine der verwendeten Methoden wird ein signifikantes Signal nachgewiesen. Die Maximum-Likelihood-Methode liefert jedoch eine kleinere statistische Unsicherheit. In dieser Methode ist das Verzweigungsverhältnis des Zerfalls B0 -&amp;gt; eta phi durch die obere Grenze BR (B0 -&amp;gt; eta phi) &amp;lt; 3.28 x 10^-6 (90%) gegeben. Dieser Wert enthält eine systematische Unsicherheit von 6.2%. Die angegebene obere Grenze ist mit aktuellen theoretischen Vorhersagen konsistent. Damit gibt diese Untersuchung keine Hinweise auf Wechselwirkungen, die nicht durch das Standardmodell der Elementarteilchenphysik beschrieben werden.

In this thesis we present new results for the 99.9% confidence level flux upper limits on the pulsed VHE gamma ray signal coming from the Crab pulsar. In order to achieve optimum hadronic background suppression we implement a new neural network based selection technique and apply it to Cherenkov shower imaging data from the WHIPPLE 10m IACT telescope at Mount Hopkins Arizona. Special emphasis will be given to the fact that the neural network selector is trained with real data exclusively. An energy estimator for gamma ray induced extensive air shower events has been derived from Monte Carlo simulations using the Monte Carlo framework GrISU. This estimator, applied to the image data, serves as input to the neural set selector and is needed to determine the energy dependent flux upper limits. We compare our results to the results from previous studies and the performance of our neural network selection technique to the so-called Supercuts and Optimized Supercuts methods.The new flux upper limits and the new technique show the potential to settle the question about the production mechanism of pulsar radiation. However, the current analysis does not answer this question fully.

No description available.

[pt] Apesar de ser considerada uma teoria de sucesso no campo das partículas e interações fundamentais, o Modelo Padrão é considerado incompleto porque ainda deixa uma série de questões em aberto. Para abordar algumas delas, é necessário estudar processos tais como decaimento de partículas. Em particular, os decaimentos de hádrons pesados, como os mésons D e B, podem ser sensíveis à física além do Modelo Padrão, como novas fontes de violação de carga-paridade e novas interações. No entanto, com massas na faixa de poucos GeV, onde os cálculos perturbativos da cromodinâmica quântica são limitados, modelos fenomenológicos são necessários para descrever seus decaimentos hadrônicos. Nesta dissertação, um estudo da dinâmica de decaimento de 3 corpos do canal Ds+ em K−K+K+ é apresentado pela primeira vez e utiliza duas abordagens fenomenológicas para descrever a amplitude do decaimento: o Modelo Isobárico e a chamada Quasi-Model Independent Partial Wave Analysis (QMIPWA). As amostras utilizadas correspondem aos dados coletados na run 2 do experimento LHCb (entre os anos 2016-2018) com colisões prótonpróton a uma energia de centro de massa de 13 TeV. A análise é realizada após um processo de seleção para reduzir o background, levando a uma amostra final com cerca de 100 mil decaimentos. Para realizar a análise de amplitudes no Dalitz plot do decaimento, o background remanescente e a eficiência ao longo do gráfico de Dalitz são parametrizados. No caso em que a amplitude de decaimento é descrita pelo Modelo Isobárico, os resultados obtidos mostram uma dominância da ressonância phi(1020) e uma composição de ressonâncias escalares, f0(980) como a mais clara, sendo formada como estados intermediários, e uma pequena mas não desprezível contribuição das ressonâncias de spin-2. O Modelo Isobárico oferece uma descrição qualitativa da dinâmica de decaimento, mas não fornece um ajuste de boa qualidade, mesmo quando uma variedade de possíveis estados intermediários são adicionados ao modelo de amplitude. Por outro lado, o QMIPWA como ferramenta para descrever o setor escalar revelou-se difícil para a região de massa K−K+ acima de 1.3 GeV e sensível às ressonâncias de spin mais alto adicionadas ao modelo, tornando difícil e menos confiável a interpretação dos resultados obtidos. Ainda com as limitações encontradas nos dois modelos, a análise apresentada aqui representa um passo importante para o entendimento da dinâmica deste decaimento, abrindo caminho para estudos com maior estatística no run 3 do LHCb. / [en] Despite of being considered a successful theory in the field of fundamental particles and interactions, the Standard Model is considered incomplete because it still leaves a number of open questions. In order to address some of these, it is necessary to study physical processes such as particle decays. In particular, the decays of heavy hadrons such as D and B mesons can be sensitive to physics beyond the Standard Model, such as new sources of charge-parity violation and new interactions. Nevertheless, at masses at the few GeV range, where perturbative calculations of quantum chromodynamics are limited, phenomenological models are needed to describe their hadronic decays. In this dissertation, a study of the 3-body decay dynamics of the Ds+ to K-K+K+ channel is presented for the first time and uses two phenomenological approaches to describe the decay amplitude: the Isobar Model and the Quasi-Model Independent Partial Wave Analysis (QMIPWA). The samples used corresponds to the data collected in Run 2 of the LHCb experiment (between the years 2016-2018) with proton-proton collisions at a center-of-mass energy of 13 TeV. The analysis is performed after a selection process to reduce background, leading to a final sample of about 100 thousand decays. To perform the amplitude analysis fit to the Dalitz plot of the decay, the remaining background and the efficiency across the Dalitz plot are parametrized. In the case of the Isobar Model, the results obtained show a dominance of the phi(1020) resonance and a composition of scalar resonances, f0(980) as the most clear one, being formed as intermediate states, and a small but not negligible contribution of spin-2 resonances. The Isobar Model offers a qualitative description of the decay dynamics but does not provide a good quality fit, even when a variety of possible intermediate states are added to the amplitude model. On the other hand, the QMIPWA as a tool to describe the scalar sector revealed itself difficult for the region of K−K+ mass above 1.3 GeV and sensitive to the higher-spin resonances added to the model, making it difficult and less reliable to interpret the results obtained. Even with the limitations found through both models, the analysis presented here represent an important step towards the understanding of the dynamics of this decay, opening the path to further studies with higher statistics in run 3 of LHCb.

<p>As successful as the Standard Model has been in describing particle interactions, there are still many open questions it does not answer; the strong CP violation and the existence of dark matter among them. To address these issues many extensions to the Standard Model have been devised. Some of these extensions propose a new force mediating particle; a massive particle results in a potential described by a Yukawa-like interaction, while a massless exchange particle leads to power law type potentials. Limits on the strength of these interactions at the sub-micron range of separation between two particles are poorly characterized, but previous experiments conducted at IUPUI placed the best limits to date on the strength of a Yukawa-like interaction. Those experiments used a spherical test mass and a planar source mass. However, if a cylindrical test mass was used, the increased interaction volume of the cylinder would result in an increased sensitivity of about an order of magnitude over the spherical test mass experiment. Building such a system presents many challenges, namely the alignment of the cylinder with respect to the planar source mass. A capacitance based scheme to determine the alignment of a cylinder with respect to a plane will be discussed. The thesis concludes with an outline for a new type of measurement system. The new experiment attempts to induce a gravitational Π-pulse in a nanoshphere to probe extensions to the Standard Model.</p> <p> </p>

<p dir="ltr">Complexity has played an increasingly important role in recent years. In this dissertation, we study some notions of complexity in systems that exhibit critical behaviour. Our results show that complexity as it is generally understood in holographic and lattice models of criticality can have several ambiguities. But despite these ambiguities, there are some features that are universally true. On the phase diagram of the system, it is the critical point which has the most complex ground state. States of physical systems with a large complexity tend to be hard to simulate using quantum circuits. Near the critical point, there is a part of complexity which is non-analytic and scales universally, i.e, the scaling is independent of the microscopic details of the Hamiltonian but depends only on the dimensionality of the system, and of the deforming operator. The coefficient of this term is unambiguous, i.e, it is not affected by the various changes in the definition of complexity which plague all the analytic terms near the critical point. We show this in lattice, field-theoretic and holographic calculations. These results were first presented in our earlier studies.</p>