**569 Emergent States of Matter**

**Term essays Fall 2007**

*These essays were written by students taking Physics 569 Emergent States of Matter, Fall 2007, at the University of Illinois at Urbana-Champaign. The copyright of each essay is due to the author. *

*Please acknowledge the essay title, author, and this course in any citation to these articles.*

*The information, opinions and interpretations expressed are those of the authors, not necessarily those of the instructor. *

Superfluid helium 3 - Topological Defects as a Consequence of Broken Symmetry

Author: Matthias Brasse

Abstract:

Superfluid phases in helium 3 were first discovered in 1972. They arise from the pairing of two fermionic helium 3 atoms to a composite boson, although there is a strong, short range repulsion between the atoms. These effects can be described using the Fermi liquid theory developed by Landau. But I will choose a different approach to the problem. Superfluidity is a macroscopic quantum phenomenon exhibiting spontaneous symmetry breaking. This characteristic can be understood by introducing an order parameter. Analyzing the structure of the order parameter you can explain the appearance of different superfluid phases. Furthermore, due to its complexity, superfluid helium 3 has a rich structure of topological defects. In the following I will give a short introduction explaining some general properties of superfluid 3He. After that its broken symmetry and the macroscopic order will be analyzed. Finally, using the concept of order parameter, I will investigate the rich structure of topological defects.

Title: Vulcanization and the Properties of Rubber

Author: Sarang Gopalakrishnan

Abstract:

Rubber is composed of long stringlike polymer molecules, which are pinned together at random points by crosslinks. As the density of crosslinks is increased, the molecules get localized and the system undergoes a phase transition from a liquid to an amorphous solid state. The elastic properties of the resulting solid are very different from those of metals, and are primarily due to changes in the entropy of the chains upon stretching. This paper discusses why rubber solidifies, and why the solid has the properties it does.

Title: Electronic Liquid Crystal Phases in Hole Doped Mott Insulators

Author: Jeremy McMinis

Abstract:

Theoretical, numerical, and experimental studies have suggested the existence of striped electronic phases in doped antiferromagnets such as the high temperature superconductors. In this essay we survey the literature and summarize the results.

Title: The Statistical Mechanics of Scale-Free Networks

Author: Wade DeGottardi

Abstract:

The methods and ideas from the emerging field of scale-free networks have been applied to a diverse group of problems. In this paper we survey some important theoretical developments and look at several prominent studies. Possible future directions in the field are discussed.

Title: Superfluidity in Solid Helium-4

Author: Wen-Pin Hsieh

Abstract:

Superfluidity in solid Helium-4 was predicted in 1969 and has been experimentally realized in 2004. In this essay, I will introduce the discovery of the intriguing emergent state, supersolid in Helium-4, and its recent experimental progress. In addition, since some of the details of the experiments are not yet well understood, theoretical arguments and comments about this quantum phenomenon will also be discussed.

Title: Deconfined Quantum Criticality

Author: Seungmin Hong

Abstract:

This essay reviews the theory of quantum phase transtion in two-dimensional spin system which is conjectured not to fit in the framework of Landau-Ginzburg-Wilson paradigm and discusses recent numerical works that support or disprove the second order conjecture.

Author: Stephanie Law

Title: Pairing symmetry and two-fluid behavior in the heavy fermion superconductor CeCoIn5

Abstract:

CeCoIn5 has recently been the subject of much controversy regarding the symmetry of its order parameter as well as the possibility of multi-band superconductivity. Experiments have been done which show d-wave pairing as well as evidence for two-fluid-like behavior. In this paper, I will first briefly review what is know about heavy fermion superconductors. I will then discuss two majors experiments which have been done recently on CeCoIn5. I will finish by discussing some of the theory explaining the two-fluid model and what could be done to resolve the dispute.

Title: High-Temperature Superfluidity

Author: Tomoki Ozawa

Abstract:

With the recent advancement of the technique of cooling atomic gases, it is now possible to make fermionic atom gases into superfluid state. Although the critical temperature of the superfluidity is only around 50nK, the superfluid state of fermionic atom gas is sometimes called "High-Temperature Superfluidity" in a sense that the critical temperature of the superfluid normalized by the Fermi temperature is high, even much higher than any known high-temperature superconductors. In this paper, I will discuss the basic theory of superfluidity in fermionic atom gases and present several experimental realizations of it. I will also mention the relation between ultracold fermionic gas and high temperature superconductors.

Title: Through Kaleidoscope Eyes: Spin Glasses Experimental Results and Theoretical Concepts

Author: Benjamin Hsu

Abstract:

A spin glass describes a system of spins on a lattice (or a crystal) where the interactions are frustrated as well as disordered. Studying such systems presents many theoretical difficulties, but over the last twenty years considerable advances have been made. In this paper I will discuss some of the experimental results that motivated theorists and some of the concepts that were developed to deal with the physics of disordered system. Specifically, the Edwards-Anderson model and their formulation the the relevant order parameters will be discussed as well as the Sherrington-Kirkpatrick model which gave a mean field, exactly soluble version of Edwards-Anderson model. I will also talk about Parisi's solution and the non-trivial ergodicity breaking that occurs in spin glasses. Spin glasses and the physics of disordered systems have found a wide range of applicability and it is the goal to review some of the experimental features and theoretical concepts developed.

Title: New phases of liquid He3 at low temperature

Author: Jitong Yu

Abstract:

This paper introduces the properties of superfluid Helium 3 by a brief review of the history of experimental discovery and theoretical understanding of the new phases. Experiments that leaded to the discovery and confirmation of the new phases are introduced and discussed.

Title: Vehicular Traffic: A Forefront Socio-Quantitative Complex System

Author: Jaron Krogel

Abstract:

We present the motivation for studying traffic systems from a physical perspective. We proceed to classify the myriad of theoretical approaches applied to the problem. Experimental methodology and observed phenomena are then presented. Next comparisons are made with relevant theoretical results. Finally, an attempt is made at evaluating the progress of theory in meeting its internally stated objectives.

Title: Glashow-Weinberg-Salam Model: An Example of Electroweak Symmetry Breaking

Author: Xianhao Xin

Abstract:

In this essay, The generalization of the gauge theory for electromagnetic interaction of superconductivity to that for the weak interaction is discussed in detail , which is named as Glashow-Weinberg-Salam Model. It turns out that the concept of symmetry spontaneous breaking plays an important role for the theory of eletroweak interaction. Consequencly, the broken symmetry SU(2)\times U(1)_Y \to U(1)_{EM} gives the prediction of the massive particle W and Z bosons, which have already been found at the correct mass in 1983.

Title: Bioconvection

Author: Hefei Hu

Abstract:

Bioconvection patterns, which are a collective phenomenon, usually appear due to upswimming of micro-organisms that are a little denser than water in suspensions. When the upper surface of the suspensions becomes too dense due to the gathering of micro-organisms, it becomes unstable and micro-organisms fall down to cause bioconvection. This essay will review the theoretical models and simulations, as well as experiments of bioconvection patterns.

Title: Emergence in Urban Growth

Author: John Nichol

Abstract:

Cities exhibit emergent properties. For example, the distribution of the number of cities with respect to population is a power law across multiple spatial, temporal, and cultural scales. Specific emergent phenomena of urban development are discussed. Current theories of urban development are described and evaluated with regard to how well they model emergent properties of urban growth.

Author: Greg Thompson

Title: Emergence and Applications of Artificial Neural Networks

Abstract:

Although conventional computers are capable of performing many tasks at rates far exceeding human capabilities their abilities in solving certain classes of complex problems are still dwarfed by the massively parallel human brain. This motivated the advent of artificial neural networks in which a large number of equivalent components communicate using weighted connections attempt to mimic these properties of the brain. Computational properties such as stable memories, ability to generalize, and error robustness emerge from the simple network. The spontaneous appearance and various applications of these properties are discussed in this paper.

Title: Ordered states of Manganite and Dynamical mean-field theory

Author: Young Il Joe

Abstract:

Pure LaMnO_3is an insulator. But, when doped with appropriate amount of doubly valenced impurities, it becomes a conductor retaining the ferromagnetism. Notion of double exchange has been devised to explain this phenomena. Along with this ferromagnetic conductivity, manganites show a variety of physical properties. Some of spin, charge, and orbital orderings are illustrated. Neutron scattering and electron diffraction is useful tool investigate the spin and charge ordered state of manganites. Also, resonance X-ray scattering can give a direct evidence of orbital orderings. Some aspect of Dynamical mean field theory is presented. In some sense, it has a analogue to classical mean-field theory. But it retinas the local fluctuation. This formalism is applied to the colossal magneto-resistance of manganite.

Title: Bosonisation and Fractional Statistics

Author: Stanimir Kondov

Abstract:

In this essay I will justify the applicability of 1-d physics to real systems like optical lattices, carbon nanotubes, and Hall effect setups. More specifically, I will introduce the idea of bosonization to help understand the phenomenon of fractional statistics.

Title: The Emergence of Modularity in Biological Systems

Author: Zhenyu Wang

Abstract:

Modularity is a ubiquitous phenomenon in various biological systems, both in genotype and in phenotype. Biological modules, which consist of components relatively independent in functions as well as in morphologies, have facilitated daily performance of biological systems and their long time evolution in history. How did modularity emerge? A mechanism with horizontal gene transfer and a biological version of spin-glass model is addressed here. When the spontaneous symmetry is broken in an evolving environment, here comes modularity. Further improvement is also discussed at the end.

Title: Exotic Goldstone Particles

Author: Guang Bian

Abstract:

This essay describes two exotic Goldstone particles. One is the pseudo-Goldstone boson which is related to spontaneous breaking of an approximate symmetry. The other is the Goldstone fermion which is a natural result of spontaneously broken global supersymmetry. Their realization and implication in high energy physics are examined.

Author: Beau Meredith

**
**Title: Quark Gluon Plasma

Hadronic matter at normal energy densities is composed of confined, color neutral quarks and gluons. At very high energy densities, theoretical models predict a transition should occur wherein the hadrons "melt" together to form a weakly coupled deconfined plasma of quarks and gluons, i.e. quark gluon plasma (QGP). Experimental evidence suggests that the state of matter formed in the high energy Au-Au collisions at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is actually a strongly coupled plasma. In this paper I shall discuss some of the basic features of QGP as well as experimental evidence from the RHIC experiments (PHENIX, STAR, BRAHMS, PHOBOS) that supports its existence.

Title: Luttinger liquids

Author: Nick Bronn

Abstract:

The Fermi liquid theory of interacting electrons in one dimension breaks down due to the Peierls instability. Hence a different theory that takes into

account explicitly the one-dimensional nature of the system must be found.

This theory was pioneered by J.M. Luttinger, who was able to describe low-lying excitations in a one-dimensional electron gas in terms of bosons. Haldane

completed the constructive approach to the theory and named it Luttinger liquid theory. More recently, advances in experimental techniques and the discovery of carbon nanotubes allowed effectively one-dimensional electron systems to be probed in the laboratory.

Title: Pattern formation by swimming microorganisms

Author: Jeffrey Robert Comer

Abstract:

In still water, the motion of many species of bacteria and algae is biased in a particular direction by the action of gravity or the presence of oxygen, light, or nutrients. A sufficiently dense population of such organisms alters the motion of the fluid in which the organisms are suspended which in turn alters their behavior, leading to a fluid instability known as bioconvection. In this paper, I discuss experimental observations of bioconvection and models that have been proposed to describe it. The emergence of the bioconvective instability from the equations of fluid mechanics and those describing organism behavior is demonstrated. Pattern formation and the existence of topological phase transitions are discussed.

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