Browsing by Subject "Theoretical physics"

In order to analyze the strongly interacting quark gluon plasma in heavy ion collisions, we study different probes by applying the gauge/gravity duality to facilitate our qualitative understandings on such a non-perturbative system. In this dissertation, we utilize a variety of holographic models to tackle many problems in heavy ion physics including the rapid thermalization, jet quenching, photon production, and anomalous effects led by external electromagnetic fields. We employ the AdS-Vaidya metric to study the gravitational collapse corresponding to the thermalization of a strongly coupled gauge theory, where we compute the approximated thermalization time and stopping distances of light probes in such a non-equilibrium medium. We further generalize the study to the case with a nonzero chemical potential. We find that the non-equilibrium effect is more influential for the probes with smaller energy. In the presence of a finite chemical potential, the decrease of thermalization times for both the medium and the light probes is observed.

On the other hand, we also investigate the anisotropic effect on the stopping distance related to jet quenching of light probes and thermal-photon production. The stopping distance and photoemission rate in the anisotropic background depend on the moving directions of probes.

The influence from a magnetic field on photoemission is as well investigated in the framework of the D3/D7 system, where the contributions from massive quarks are involved. The enhancement of photon production for photons generated perpendicular to the magnetic field is found. Given that the mass of massive quarks is close to the critical embedding, the meson-photon transition will yield a resonance in the spectrum. We thus evaluate flow coefficient $v_2$ of thermal photons in a 2+1 flavor strongly interacting plasma. The magnetic-field induced photoemission results in large $v_2$ and the resonance from massive quarks gives rise to a mild peak in the spectrum. Moreover, we utilize Sakai-Sugimoto model to analyze the chiral electric separation effect, where an axial current is generated parallel to the applied electric field in the presence of both the vector and axial chemical potentials. Interestingly, the axial conductivity is approximately proportional to the product of the vector chemical potential and the axial chemical potential for arbitrary magnitudes of the chemical potentials.

We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\CC^3/\ZZ_r$, focusing

on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number

of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the

G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for

N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy

to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that

irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional

worldsheet instanton corrections beyond those from smooth isolated rational curves.

When a normal metal is placed in a good electrical contact to a superconductor, Cooper pairs leak across the interface inducing pair correlations into the normal metal. This corresponds to Andreev scattering of electrons into holes at the interface. With long-range phase coherence, this enables charge interconversion effects. A conventional Andreev scattering is a retroreflection where the hole retraces the electron's trajectory in time-reverse. In graphene, however, a specular Andreev reflection (SAR) is possible where the reflected hole, instead, maintains the forward progression of the electron along the interface (similar to light reflection in a mirror). Thus, confining SAR (e.g. by a second boundary) leads to multiple Andreev reflections in a propagating coherent electron-hole superposition, an Andreev mode. In this dissertation, we consider another variation of this: by breaking time-reversal by quantum Hall effect, the trajectory is also forward progressing due to the cyclotron orbits "skipping" along the interface, the chiral Andreev interface mode. We call the Andreev process in such one-way propagating boundary channels, a chiral Andreev reflection (chAR). In this dissertation, chAR is studied in lattice and continuum models of disorder-free graphene on the lowest Hall plateau coupled to a generic superconducting contact.

At first, we show possibility of transport interference of two conjugate Andreev modes upon varying diverse control parameters, and study particularities of distinct graphene-superconductor boundaries in the transport pattern and surface spectrum. This is done in tight-binding as well as more generically via a parametric family of boundary conditions. We then study more concrete models for the interface properties and parameter dependences of the proximity effect in the chAR. Lastly, we study scattering properties of the same in graphene nanostructures with superconductor coupling of varied interface transparency and geometry, which are to be of experimental relevance.

Graphene Fermi velocity makes a strong proximity effect possible despite large sharp potential step from superconductor Fermi wave mismatch unlike in systems of single lattice type. Thus, the strong effect is compatible with metallicity of the superconductor and is only weakly sensitive to graphene parameters. Single-channel chAR is found to be stronger and more robust to reduced transparency interfaces compared to the conventional multimode Andreev retroreflection at the same graphene doping. Intervalley scattering in nanostructures is important and allows for significant electron-hole conversion in weak transparency junctions even despite suppressed interface pairing. At this weak transparency, in nanostructures with two intervalley corners, an interference of chAR with up to full conversion amplitude is shown. The interferometer in the proposed nanostructure should be fairly available in a range of atomistic corners without much finetuning.

Effective field theory (EFT) has evolved as a powerful model-independent theoretical framework for illuminating complicated interactions across a wide range of physics areas and subfields. It takes advantage of the scale separation exsiting in physical systems to invoke a systematic expansion to capture the physics at a certain energy scale. The symmetries of the high-energy/short-distance theory constrain these interactions, limiting the number of unknown low-energy coefficients (LECs) that must be extracted from the experiment or calculated directly from the underlying theory.

The utilization of EFTs in nuclear physics has facilitated our understanding of atomic nuclei and bridged the gap between quantum chromodynamics (QCD), the theory of strong interactions, and nuclear structure and interactions. In particular, EFTs have been proven successful in describing the structure and dynamics of few-body nuclei. In this dissertation, we present several studies on applying the EFT technique to research problems in nuclear physics. We first apply pionless EFT (\eftnopi) to study parity violation in two-nucleon systems and the dark matter scattering off light nuclei. The operators contributing to these elusive processes are accompanied by unknown LECs. We show that the large-\Nc expansion can systematically separate these LECs into those that occur at leading order in $N_c$ and those that occur at next-to-leading order in \Nc. The large-\Nc ordering could provide a powerful reduction in the number of experiments needed to understand these processes at every order in this combined expansion, as well as help prioritize future experiments and lattice QCD calculations.

In the second part, we consider the low-energy proton–deuteron and deuteron-Helium-4 systems at low energies in cluster EFT. Below the deuteron breakup threshold, the deuteron and Helium-4 can be treated as structureless degrees of freedom. In particular, we focus on the deuteron + Helium-4 cluster configuration of the Lithium-6 nucleus. We illustrate how to directly extract the asymptotic normalization coefficient, $\mathcal{C}_0$, and the asymptotic $D/S$ ratio, $\eta_{sd}$, from the three electromagnetic form factors of Lithium-6. The fitting to these form factor data yields $C_0\approx 2.20$ fm$^{-1/2}$ and $\eta_{sd}\approx -0.0224$.

Quantum entanglement lies at the heart of modern physics and pervades various research fields. In the field of quantum many-body physics, celebrated area and log-area laws have been established for the entanglement entropy of ground states. However, there exists a long-standing question regarding the transition of eigenstate entanglement entropy from the ground state to the highly excited states. Our study fills this gap and elucidates a crossover behavior with universal scaling properties. In the study of quantum matters, knowledge about the entanglement structure can be used to guide the design of tensor network state simulations. For example, we may iteratively eliminate short-range entanglement in a so-called entanglement renormalization scheme so that the entangled ground state is mapped to a product state and then resolved exactly. This idea can be adapted to hybrid quantum-classical algorithms and speed up the simulation of strongly correlated quantum many-body systems.

In the first part of this dissertation, we investigate eigenstate entanglement scaling in quantum many-body systems and characterize the crossover from the ground-state entanglement regime at low energies and small subsystem sizes to extensive volume laws at high energies or large subsystem sizes. We first establish a weak eigenstate thermalization hypothesis (ETH) for translation-invariant systems, argue that the entanglement entropies of (almost) all energy eigenstates are described by a single crossover function whenever the (weak) ETH applies, and point out the universal scaling properties in the quantum critical regime. We then comprehensively confirm these scaling properties by analyzing large classes of quantum many-body systems. Particularly, we give the eigenstate entanglement scaling functions in analytical form for critical one-dimensional systems based on conformal field theory and for $d$-dimensional fermionic systems with Fermi surfaces. For $d=1,2,3$ non-interacting fermions, the scaling functions are numerically verified, and for $d=1,2,3$ harmonic lattice models (free scalar field theory), they are numerically determined. ETH is confirmed with Monte Carlo methods by sampling energy eigenstates or squeezed states for fermions or bosons with $d=1,2$. We also probe and confirm the described scaling properties and the applicability of the ETH in integrable and non-integrable interacting spin-1/2 chains by using exact diagonalization. All the evidence appearing here strongly suggests the existence of crossover functions. Their transition from ground-state scaling to extensive scaling, as well as the universal scaling properties in quantum-critical regimes, are generic.

In the second part of this dissertation, we present a quantum-classical tensor network state algorithm for condensed matter systems. First, we describe this algorithm, which is based on the multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimizations. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale quantum (NISQ) devices and still describe large systems. We show that the number of required qubits is independent of the system size, increasing only to logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translational invariance can be used to make the computational cost square-logarithmic with respect to the system size and to describe the thermodynamic limit. The method is particularly attractive for ion-trap devices with ion shuttling capabilities. We then demonstrate it numerically for MERA with Trotterized disentanglers and isometries and find that the computational cost of such MERA quantum eigensolvers is substantially lower than that of the corresponding classical algorithms. In particular, numerical results in various strongly-correlated quantum magnet models show that it has a polynomial quantum advantage over the classical approach. In the experimental implementation, small angles in the employed two-qubit quantum gates are advantageous. We find that, by adding an angle penalty term to the energy functional, the average absolute values of the angles can be moderately reduced without significantly affecting the energy accuracies. Finally, we propose that the Trotter-type circuit in each tensor can be replaced by a parallel random circuit. However, this replacement does not seem to result in further gains as long as the tensor-network bond dimensions are small.

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Heavy-flavor particles are excellent probes of the properties of the hot and dense nuclear medium created in the relativistic heavy-ion collisions. Heavy-flavor transport coefficients in the quark-gluon plasma (QGP) stage of the collisions are particularly interesting, as they contain important information on the strong interaction at finite temperatures. Studying the heavy-flavor evolution in a dynamically evolving medium requires a comprehensive multi-stage modeling approach of both the medium and the probes, with an accurate implementation of the physical ingredients to be tested. For this purpose, I have developed a new partonic transport model (Linear-Boltzmann-plus-Diffusion-Transport-Model) LIDO and applied it to heavy quark propagation inside a QGP. The model has an improved implementation of parton in-medium bremsstrahlung and a flexible treatment of the probe-medium interactions, combining both large angle scatterings and diffusion processes. The model is then coupled to a high-energy event-generator, a hydrodynamic medium evolution and a hadronic transport model. Finally, applying a Bayesian analysis, I extract the heavy quark transport coefficients from a model-to-data comparison. The results, with uncertainty quantification, are found to be consistent with earlier extraction of the light-quark transport coefficients at high momentum and with first-principle calculations of the heavy-flavor diffusion constant at low momentum.

Boundary quantum phases ---a special type of quantum phenomena--- occur in the boundary part of the system. The boundary part can be a surface of a bulk material, an interface between two distinct system, and even it can be a single impurity or a impurity cluster embedded into a bulk system. The properties of the boundary degree of freedom can be affected by many strong electron correlation effects, mesoscopic effects, and topological effects, which, therefore, induce a vast variety of exotic boundary quantum phases. Many techniques for precise fabrication and measurement in nanostructures had been developed,

which can provide ways to prob, understand, and control those boundary quantum phases.

In this thesis, we focus on three types of the boundary quantum phases : Kondo effects, boundary quantum phase transitions, and Majorana fermions. Our motivation is to design and prob those effects by using a important type of nanostructures, i.e. quantum dots. A vast variety of models related to quantum dots (QDs) are studied theoretically, which includes a QD coupled to a mesoscopic bath, a quadruple QD system with metallic leads, a QD with dissipative environments, and a QD coupled to a Majorana fermion zero mode.

Quantum dots provide a way to study the interplay of Kondo effects and mesoscopic fuctuations. In chapter 5, we consider a model including an Anderson impurity (small QD) coupled to a mesoscopic bath (large QD). Both the weak and strong coupling Anderson impurity problems are characterized by Fermi-liquid theories with weakly interacting quasiparticles. We find that the fluctuations of single particle properties in the two limits are highly correlated and universal : The distributions of the spectrum within the Kondo temperature collapse to universal forms; and the strong coupling impurity changes the wave functions corresponding to the spectrum within the Kondo temperature.

Quantum dots also bring the possibility to study more complex quantum impurities (multi-QDs) and the competition among dierent interactions, which may induce exotic effects: boundary quantum phase transitions and novel Kondo effects. In chapter 7, we design a quadruple quantum dot system to study the competition among three types of interactions: Kondo, Heisenberg, and Ising. We find a rich phase diagram containing two sharp features : a Berezinsky-Kosterlitz-Thouless type quantum phase transition between a charge-ordered phase and a charge liquid phase and a U(1)XU(1) Kondo state with emergent symmetry from Z2 to U(1). In chapter 8, we study a dissipative resonant level model in which the coupling of a fermionc bath competes with a dissipation-induced bosonic bath. we establish an exact mapping from this dissipative resonant level model to a model of a quantum dot embedded into a Luttinger liquid wire, and we also find two kinds of boundary quantum phase transitions (a Berezinsky-Kosterlitz-Thouless type and a second order type).

Finally, in chapter 9, we propose an experimental system to detect Majorana fermion zero modes. This system consists of a spinless quantum do coupled to a Majorana fermion which exists in the end of a p-wave superconductor wire. The Majorana Fermion strongly infuence the transport properties of the quantum dot. The zero temperature conductance peak value (when the dot is on resonance and symmetrically coupled to the leads) is e^2/2h. In contrast, if the wire is in its topological trivial phase, the result is e^2/h; if the side-coupled mode is a regular fermionic zero mode, the result is zero. Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. This result can be used to detect the existence of Majorana fermions.

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Transcription and translation describe the flow of genetic information from DNA to mRNA to protein. Recent studies show that at a single cell level, these processes are stochastic, which results in the variation of the number of mRNA and proteins even under identical environmental conditions. Because the number of mRNA and protein in each single cell are actually very small, these variations can be crucial for cellular function in diverse contexts, such as development, stress response, immunological and nervous system function. Most studies examine the origin and effects of stochastic gene expression using computer simulations. My goal is to develop a theoretical framework to study activity-dependent gene expression using simplified models that capture essential features.

I have examined the dynamics of stochastic gene regulation in three contexts. First, I examine how fluctuations in promoter accessibility lead to "bursty" transcription, during which genes are turned "on" or "off" stochastically. I describe a mathematical formalism to represent bursty gene expression in a coarse-grained manner as a Markov process and derive a master equation for the time evolution of the probability distribution of the number of mRNA molecules. This allows us to examine how transcript number responds to time varying stimuli. This model forms a basic building block for understanding the signal transmission and noise of the transcription process to time varying inputs as would be sensed by cells in dynamic environments. In addition to synthesis, gene expression is subject to additional modes of regulation. One such mechanism that controls transcript numbers is by microRNAs (miRNAs), which pair with target mRNAs to repress protein production following transcription. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks still remains unclear. I explore the functional roles of feedback regulation by miRNAs and show that protein fluctuations strongly depend on the mode of miRNA-mediated repression. I discuss the functional implications of protein fluctuations arising from miRNA-mediated repression on gene regulatory networks. Finally, I examine the impact of fluctuations on alternative splicing, which is a major source for proteomic complexity in higher eukaryotes. Although the proteins regulating alternative splicing have been extensively studied, little is known about how noise arising from the stochastic nature of alternative splicing contributes to the entire gene expression process. I explore the functional roles and noise properties of alternative splicing, focusing on the case of exon skipping and intron retention. I show that while the overall counts of the mRNAs of the two isoforms are independent and Poisson distributed, diffusion and binding of the splicing factors contributes to the variance in the abundance of the isoforms.

Noise in gene expression may be of particular relevance in the nervous system. Environmental stimuli drive the rapid remodeling of neural circuitry in part by inducing the activation of genes to make proteins that modify neuronal excitability and connectivity, ultimately influencing higher order brain function. Finally, I examine the implications of our studies for activity dependent gene expression in the nervous system.

In this dissertation, we study the phase structures and the quantum critical phenomena of relativistic lattice fermions with $\O(2N_f)$ symmetry in one and two spatial dimensions, motivated by the ability to perform efficient Monte Carlo simulations. Close to a quantum critical point, physics is universal and can be described by continuum quantum field theories. We perform a perturbative analysis of all independent four-fermion interactions allowed by the $\O(2N_f)$ symmetry near the free-fermion fixed point. We then analyze the resulting continuum field theories using various techniques. In one spatial dimension, we use the powerful tools from conformal field theory and non-abelian bosonization to understand the renormalization group flows, the correlation functions, and the spectra. In the case of $N_f=2$, we find that by tuning a Hubbard coupling, our model undergoes a second-order phase transition, which can be described by an $\SU(2)_1$ Wess-Zumino-Witten model perturbed by a marginal coupling. We confirm these results using the meron-cluster algorithm, and locate the critical point precisely using exact diagonalization based on the spectrum of the Wess-Zumino-Witten model. In two spatial dimensions, we analyze the model using $\varepsilon$ expansion, large $N_f$ expansion and effective potential methods. In the case of $N_f=2$, we find a novel critical point where the anti-ferromagnetic order and superconducting-CDW order become simultaneously quantum critical, which seems to have been missed in literature. We compare these predictions with the numerical results obtained using the fermion-bag algorithm by Emilie Huffman.

The question of ``What is Dark Matter?" has been a focus of cosmological research since the turn of the 20th century. Though the composition of Dark Matter is unknown, the existence of Dark Matter is crucial to the modern theory of cosmology. We focus on a theory of Dark Matter referred to as \textit{Scalar Field Wave Dark Matter} (SF$\psi$DM), which has received an increasing amount of interest from the research community since the late 2000s. SF$\psi$DM is a peculiar theory in which Dark Matter is composed of ultralight bosonic particles. As a result, SF$\psi$DM has an astronomically large deBroglie wavelength, generating complicated wave dynamics on the largest cosmological scales.

This thesis focuses on describing the status of SF$\psi$DM theory, SF$\psi$DM halos, and how SF$\psi$DM halos are affected by the wave-like features of the scalar field. In particular, we offer an analysis of galactic rotation curves and how they relate to SF$\psi$DM excited states. This analysis yields a novel model for an observed galactic trend referred to as the Baryonic Tully-Fisher Relation. Furthering this model, we formulate an eigenfunction decomposition which can be used to describe superpositions of excited states.

Cutting edge research problems require the use of complicated and computationally expensive computer models. I will present a practical overview of the design and analysis of computer experiments in high energy nuclear and astro phsyics. The aim of these experiments is to infer credible ranges for certain fundamental parameters of the underlying physical processes through the analysis of model output and experimental data.

To be truly useful computer models must be calibrated against experimental data. Gaining an understanding of the response of expensive models across the full range of inputs can be a slow and painful process. Gaussian Process emulators can be an efficient and informative surrogate for expensive computer models and prove to be an ideal mechanism for exploring the response of these models to variations in their inputs.

A sensitivity analysis can be performed on these model emulators to characterize and quantify the relationship between model input parameters and predicted observable properties. The result of this analysis provides the user with information about which parameters are most important and most likely to affect the prediction of a given observable. Sensitivity analysis allow us to identify what model parameters can be most efficiently constrained by the given observational data set.

In this thesis I describe a range of techniques for the calibration and exploration of the complex and expensive computer models so common in modern physics research. These statistical methods are illustrated with examples drawn from the fields of high energy nuclear physics and galaxy formation.