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In this work we discuss the application of high energy theory methods to the study of condensed matter problems. We focus in particular on the effective field theory (EFT) approach and on the holographic duality. We show that, in certain contexts, both techniques present some relevant advantages with respect to more standard approaches. In particular, we will study holographic superfluids, and make explicit connection between the holographic picture and the EFT one. We also determine for the first time the gravity dual of a solid, and show that it undergoes a first order phase transition, a “holographic melting”. On a more phenomenological ground, we study the motion of vortex lines in a confined superfluid. Using a suitable EFT we successfully reproduce the experimental results, and perform a number of steps forward with respect to traditional methods. Finally, we also discuss possible exciting directions for the future of EFTs and condensed matter.

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Effective theories have applications in many areas of physics, from Newtonian mechanics through to condensed matter physics. In this thesis we discuss effective field theories in the context of constructing nucleon-nucleon interactions in a systematic and model-independent way. We start with the examination of the spin-singlet P-wave, by using distorted wave methods to remove the effects of long-range pion-exchange forces from the empirical 1P1 phase shift. The divergence appearing in this channel is renormalised using a counterterm that is provided by the relevant (Weinberg) power counting. This leaves an effective interaction strength that can be analysed, and from which one can extract an approximate scale for the underlying physics. We determine this scale to be close to the delta-resonance. We then turn to coupled (spin-triplet) waves, focussing predominantly on the 3S1-3D1 wave that contains the deuteron - an important system to understand in the context of nuclear forces. Starting with the 3S1-3D1 scattered waves, we again remove long-range pion-exchange forces from the empirical phase shifts, and extract an effective interaction matrix. The element that suffers from a divergence can be renormalised using counterterms provided by a renormalisation group analysis. Switching to negative energies we look for the deuteron boundstate, which is loosely bound and so pion physics plays an important role. Using the counterterms provided at positive energies, we extrapolate to the boundstate and treat this, two-pion-exchange and recoil one-pion-exchange as a combined perturbation to the system. We then use perturbation theory techniques to calculate the first-order correction to the energy and wave function, from which we calculate some deuteron observables.

Song Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 50-54). / Abstracts in English and Chinese. / THESIS COMMITTEE --- p.ii / ABSTRACT --- p.iii / 中文摘要 --- p.v / ACKNOWLEDGENTS --- p.vi / TABLE OF CONTENTS --- p.vii / LIST OF FIGURES --- p.ix / LIST OF TABLES --- p.x / Chapter CHAPTER 1 --- INTRODUCTION --- p.1 / Chapter 1.1. --- Motivation --- p.1 / Chapter 1.2. --- Properties of Molecular Hydrogen --- p.3 / Chapter 1.3. --- Properties of Solid Hydrogen --- p.5 / Chapter CHAPTER 2 --- THEORY --- p.11 / Chapter 2.1. --- Group Theory --- p.12 / Chapter 2.2. --- Crystal Field Splitting --- p.18 / Chapter 2.3. --- Permanent Multipole Moment --- p.23 / Chapter 2.4. --- Predicted Rovibrational Spectrum --- p.26 / Chapter CHAPTER 3 --- APPLICATION: CARBON MONOXIDE IN SOLID PARAHYDROGEN --- p.28 / Chapter 3.1. --- Permanent Multipole Moment of CO --- p.28 / Chapter 3.2. --- Crystal field splitting --- p.33 / Chapter 3.3. --- Rovibrational Transitions and Relative Intensities --- p.42 / Chapter CHAPTER 4 --- DISCUSSION AND CONCLUSION --- p.46 / REFERENCE --- p.50

by Tsang Yue Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 120-122). / by Tsang Yue Kin. / Contents --- p.ii / List of Figures --- p.iv / List of Tables --- p.vi / Abstract --- p.vii / Acknowledgement --- p.viii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Probability Density Function in Turbulence --- p.2 / Chapter 1.2 --- Scaling Laws in Turbulence --- p.6 / Chapter Chapter 2. --- The Problem --- p.12 / Chapter 2.1 --- Random Advection of a Passive Scalar --- p.12 / Chapter 2.2 --- Numerical Implementation --- p.14 / Chapter Chapter 3. --- Statistics of Scalar Fluctuation --- p.19 / Chapter 3.1 --- Results --- p.19 / Chapter 3.1.1 --- Probability Density Function of Scalar Fluctuation --- p.20 / Chapter 3.1.2 --- Exact Formula for PDF --- p.20 / Chapter 3.1.3 --- Other Velocity Statistics --- p.24 / Chapter 3.2 --- Conditional Averages q(x) and r(x) --- p.25 / Chapter 3.2.1 --- q(x) --- p.25 / Chapter 3.2.2 --- r(x) --- p.39 / Chapter 3.2.3 --- PDF calculated from various forms of q(x) and r(x) --- p.46 / Chapter 3.3 --- Other Velocity Statistics --- p.55 / Chapter Chapter 4. --- Statistics of Scalar Difference --- p.75 / Chapter 4.1 --- PDF of Scalar Difference --- p.75 / Chapter 4.1.1 --- Results --- p.76 / Chapter 4.1.2 --- Relation between PT{x) and 5S2n(T) --- p.80 / Chapter 4.2 --- Scaling of S2n(T) --- p.82 / Chapter 4.3 --- Other Velocity Statistics --- p.90 / Chapter 4.4 --- Discussions --- p.103 / Chapter Chapter 5. --- Conclusion --- p.105 / Appendix A. PDF of Stream Functions --- p.107 / Chapter A.1 --- General Formalism --- p.107 / Chapter A.2 --- Applications --- p.108 / Appendix B. Generation of Random Deviates --- p.112 / Appendix C. Check of Stationarity --- p.114 / Appendix D. Calculations of the coefficients of q(x) and r(x) --- p.117 / Bibliography --- p.120