Term Essays for Emergent States of Matter

Physics 498ESM, Spring 2004.
Department of Physics
University of Illinois at Urbana-Champaign

Author: Joe Altepeter
Title: The Emergent Behaviour of Traffic

This paper describes the basics of freeway traffic, through descriptions of empirical observations and modelling techniques.

Author: Rahul Biswas
Title: Quantum Phase Transitions Outside Landau Ginzburg Wilson paradigm

Abstract :

We review certain aspects of quantum phase transititions. We then report on certain recent theoretical advances in the study of quantum phase transitions in the context of two dimensional quantum magnets, which do not fit into the Ginbzburg-Landau-Wilson (GLW) formalism usually used to study phase transitions.

Author: Pak Yuen Chan
Title: The emergence of money


Money, defined as the media of exchange, is demonstrated to be an emergent property of interacting-agent systems. An agent-based model of markets is discussed.  In the model, agents are able to trade among a set of commodities, none of which has any special feature, i.e. they are symmetric to each other. The symmetry is then spontaneously broken due to fluctuation and money is emerged.  Comparison to other models is discussed and drawback of these models is addressed.

Author: Shu-Wei Chang
Title: Crossover from Bose-Einstein Condensed Molecules to Cooper Pairs by Using Feshbach Resonance


At low temperature, fermionic atoms can either condense into a Bose-Einstein condensate (BEC) by forming bosonic molecules or be loosely paired to form Cooper pairs described by Bardeen, Cooper, and Schrieffer's (BCS) microscopic theory. Experimentalists have claimed the observation of the intermediate regime between BEC and BCS limits by tuning the scattering length with the aid of Feshbach resonance. In this report, we will discuss the idea of using Feshbach resonance to achieve the crossover. Some many-body formulation concerning this crossover will be briefly introduced, but not in detail. The experimental results will be our main concerns and addressed in this report.

Author: Suk Bum Chung
Title: Physics of p-wave spin-triplet pairing with the experimental examples of strontium ruthenate


This essay describes the p-wave spin-triplet pairing with broken time-reversal symmetry and experimental evidence for such pairing in strontium ruthenate. It will also deal with the limitation of this pairing in accounting for strontium ruthenate physics.

Author: James Cook
Title: The Statistical Physics of Traffic Flows


This essay describes the empirical observations and theoretical modeling of traffic flows.

Author: Vasilica Crecea
Title: Collective Phenomena in Photonic Crystals

Abstract :

Photonic crystals have had a great potential for technical applications. The understanding of the underlying mechanism has thus been of great interest to both theoreticians and experimentalists. We present an overview of collective phenomena in PGB materials, with a focus on spontaneous symmetry breaking occuring in superradiance, and an optical spin-glass state of impurity two-level atoms. We also highlight the experimental realization of a tunable photonic bandgap fiber.

Author: Joe Gezo
Title: The Quest for an Excitonic Bose Condensate


The high critical temperature and adjustable symmetry of bound electron- hole pairs make excitonic Bose-Einstein condensation an interesting (though elusive) possibility. Several models have been proposed for the behaviour  of excitons just above the critical density. In the interest of simplicity, these models ignore certain phenomena; namely, the expansion of the exciton gas through a crystal, interconversion between singlet and triplet states, and two- body Auger recombination. Experiments have shown that the Auger process, in particular, is especially prevalent at low temperature and high density, making it even more of a barrier to Bose condensation of excitons than their inevitable photodecay. The models of Snoke, O'Hara, and Banyai are examined here, and modifications to Banyai's model are proposed.

Author: Kenjiro Kimura Gomes
Title: STM Studies of Cuprate Superconductors


The paper summarizes recent STM experiments that have found spatial modulations on the tunneling conductance on BSCCO.

Author: Vikram Jadhao
Title: Superfluid to Mott Insulator transition in optical lattice


This paper describes the experiment which realised a quanutm phase transition from superfluid to mott insulator state in bosonic system. The tuning parameter being strength of the optical lattice potential.

Author: Fatemeh Khalili-Araghi
Title: Condensed phases of Gases inside Nanotube Bundles.


Small molecules absorbed by nanotube bundles undergo temperature dependent transitions from ordered to disordered phases. Depending on thermodynamic condition one or two dimensional behavior is observed for those particles as well as dimensional cross overs. Here an overview of phase behavior for gases exposed to nanotubes is presented.

Author: Minsu Kim
Title: Phase transitions in liquid crystals

Abstract :

Liquid crystals can be classified into 5 phases; Liquid, Nematic, Smetic, Columnar and Crystalline according to their position order and orientational order. To explain these phases, many models have been employed; Landau-de Gennes theory, Onsager-type theory, Maier-Saupe theory and the van der waals type theory. In this paper, I'll explain these theories and their computer simulations. At the end, experiment will be introduced for comparison.

Author: Marcelo Kuroda
Title: Can we find metal-insulator transitions in 2-dimensional systems?


It has been almost a quarter of a century since the belief of the non-existence metallic
state or the non-occurrence of metal-insulator transition for a two-dimensional system
in the zero magnetic field was accepted. Nevertheless, during the last decade atypical
behavior in semiconductor samples suggested the possibility of those transitions in two
dimensions. In this essay we will review some of the experiments that can evidence such
transtions and the theoretical models proposed to explain the observed phenomena.

Author: Yan Li
Title: Pseudospin Quantum Hall Ferromagnetism


Symmetry breaking ground states occur in quantum Hall effect (QHE) systems when two or more Landau levels become degenerate near the Fermi level. Isotropic, easy-axis or easy plane quantum Hall ferromagnets (QHF) can form depending on the pseudospins of the involved Landau levels consisting of real spin, orbit radius quantum number, subband index or growth direction. Theories based on Hartree-Fock calculation of pseudospin anisotropy energy are introduced, which classify the type of QHFs according to the nature of the degenerate Landau levels. Several representative experimental studies on the emergence of integer QHF in single-layer and doublelayer two dimensional electron systems as well as of fractional QHF are presented. The anisotropy types are identified from the experimental measurements and compared with the prediction from the Hartree-Fock calculation. Discrepancy arises when neglected factors in the simple theoretical model become significant such as charge distribution profiles of different subbands, orbital effect of the in-plane magnetic field, softness of the barrier etc.

Author: Deyu Lu
Title:   Like-charge attraction


As we learned from mean-field theory, like-chared particles repel. However, in the last decade, like-charge polyelectrolyte attraction was observed in the presence of multivalent ions in a variety of biological systems, including DNA, F-actin, microtubules, and filamentous viruses.  Considering the fundermental role DNA played in the life-cycle, we find like-charge attraction is not only physically intriguing, but also of great biological significance. In this paper, the theory based on the short-range electrostatic correlations is reviewed, and we show that it provides a lot of insight to the DNA condensation experiment. Finally, recent experimental progress is discussed.

Author: Xiaoming Mao
Title: Nematic Elastomers: a New State of Matter?


Nematic elastomers (NE's) are polymer liquid crystals. They have mobile directors, which is coupled to the crosslinking network of polymers, thus give very nonlinear behavior in elasticity, like spontaneous change of shape, and nematic- isotropic transition under mechanical pressure. The basic experimental results are reviewed, and some theoretical work based on the neo-classical rubber elastic theory is also studied, with explaining the two categories of experiments.

Author: Abhishek Mukherjee
Title: Turbulence in Fluids


The basic dynamical equations for incompressible fluid flow (the Navier-Stokes equations) are known for the last one and a half centuries. Yet a detailed understanding of flow at high velocities (Reynolds numbers) remains elusive. The basic assumptions of the "classical" theory due to Kolmogorov is not beyond questions. Here I will discuss on Kolmogorov's theory of turbulence and report briefly and selectively on the work that has been done after that.

Author: Sean Robert Nowling

Title: Defect Induced Structure Formation in the Early Universe

Abstract: When describing the early universe as an FRW metric and being filled with perfect fluids, there is no first principle understanding of structure formation. Instead, at high temperatures one must describe the matter as a quantum field theory. As the universe expands, this field theory will undergo phase transitions, and the possibility for topological defects arise. This paper will discuss how topological defects form, and their role in structure formation in the early universe, focusing on cosmic strings.

Author: Aakash Pushp
Title: Phases of NaxCoO2


This paper deals with the various phases of NaxCoO2 ranging from charge ordered insulator to Curie-Weiss metal to superconductor as the stoichiometry is changed and attempts to understand the related theory and experimental results.
It starts with investigating the superconducting properties of this material, intercalated with H2O and goes on to describe the various phases that come into being as x is varied. It then concentrates on another remarkable phase at x = ½ which is an insulator. For all other doping, this material shows metallic behavior. Later, it tries to give a clear account of the various experiments performed including ARPES and discusses its anisotropic hole-type large hexagonal-like Fermi surface and its implications.

Author: Shizhong Zhang
Title : Propagation Modes in Heisenberg Spin Glasses

Abstract: Spin glasses is a fascinating field, from which a variety of theoretical models and concepts were invented. As an emergent state from the random magnetic system, it defers from other statistical systems in several ways. In particular, the quenched variables prevent the system to be ergodic, and the competitive interactions gives rise to non-trivial degeneracies of the ground states as well as the excitations. In this essay, I will briefly discuss these generic features of spin glasses by presenting some of the characteristic experimental results followed by theoretic analysis. The broken symmetries are discussed with compare to other magnetic systems. Hydrodynamic theory, as well as numerical investigations are discussed aiming to identify the low lying excitations.

Author: Kai Sun
Title: Explanation of Log-Normal Distributions and Power-Law Distributions in Biology and Social Science


In many biological and social systems, where the ideal of heritance and aberrance exist at the same time, normal distribution failed in describing the distributions of variables. In stead, many real data as well as simulations indicate that log-normal distribution and power-law distribution can characterize many properties of this kind of systems. In this paper, the failure of normal distribution is studied and a general phenomenological model including both heritance and aberrance is set up. Using Fokker-Plank equation, it turns out that, log-normal distribution will be favored if the system has an optimum value for the variable we are studying, but power-law distribution will be favored for discrete variables.

Author: Ting-Pong Choy
Title: Fractional charge in the fractional quantum hall system


The Luttinger liquid is believed to be the emergent hehaviors of 1D interacting electron gas on the edge of the fractional quantum hall (FQH) system. A brief summary of the Luttinger liquid is given. And tunneling of the Luttinger liquid between edges is shown to enable a direct measurement of the fractional charge of the quasiparticle.

Author: Victor Vakaryuk
Title: Vortex lattice pinning in HTc superconductors.


Vortex matter in high temperature superconductors has many peculiar properties such as melting of the vortex lattice, creation of new vortex-liquid phases etc. These effects are not seen in conventional superconductors. This is mainly due to the fact that HTc compounds are strongly type two superconductors with Ginzburg-Landau ratio up to ~110 that makes thermal and quantum fluctuations more profound. Another class of unusual vortex matter properties in HTc materials is related to their structural features. Most important are strong layering and structure defects such as dislocations and grain boundaries. Moreover structure defects can be introduced artificially irradiating samples with high-energy ions. In this term paper I am going to discuss effect of structural defects on vortex lattice behavior in particular on vortex lattice pinning.

Name: Daniel Vandervelde
Title: Emergent Phenomenon in Congested Traffic Flow


The existence of phase transitions and other emergent phenomena in small particle systems has been studied for some time. The application of this field of study to traffic is a somewhat novel approach to the problem. Here the approach of three different groups using this method will be examined and discussed.

Author: Xin Lu
Title: Towards Bose-Einstein Condensation of Excitons


A new method to produce long life-time excitons has been employed using the band-gap engineering quantum hetero- structures of 2D coupled quantum wells. Just as atom condensation were performed on atomic gases, confined in the potential traps, the quasi 2D excitons are collected in an in-plane potential trap and PL measurements show that they are indeed condensed at the bottom of the traps, giving rise to a statistically degenerate Bose gas. Meanwhile, the PL kinetics, which is determined by the bosonic stimulated scattering of indirect excitons in CQWs, also indicates condensation to the low energy states. A macroscopically ordered exciton state has been observed. The spatially resolved measurements reveal fragmentation of the ring- shaped emission pattern into circular structures that form periodic arrays over length up to 1mm.  

Author: Ruqing Xu
Title: Observing Condensations in Atomic Fermi Gases


Observing condensation in a gas of fermions has been another interesting topic after the realization of the Bose-Einstein Condensation in atomic gases. The condensation of fermions may happen either in the BEC or the BCS manner, depending on how the fermions are paired to each other. This paper gives a brief review on the recent breakthroughs in this area.

Author: Yang Liu
Title: Vortex Matter Driven by Alternating Current


Experimentally, it has been found that in a well-defined range of fields, temperatures and driving amplitudes, the vortex matter displays novel types of nonlinear response. As is the case with ordinary solids, it appears that unidirectional drives tend to disorder the system, while shaking tends to order it. A numerical result states that the oscillatory motion of vortices, provided that its amplitude is of the order of the lattice constant, can favor an ordered structure, even when the motion of the vortices is plastic when the same force is applied in a constant way.

Author: Yu, Zhenhua
Title:  Stock market crashes


This paper begins with introducing the concept of crash in stock market.  Different spatial and temporal scales in stock markets are to be discussed.  In order to clearly manifest that crashes are emergent state, the concept of drawdowns is introduced as a superior way to the traditional returns of price.  Afterwards, the mechanisms leading to positive feedbacks, such as imitative behavior and herding between investors are reviewed.  A simplified spin model is constructed to make the picture easy to capture. Based upon preceding preparation, as a mathematical model, a phenomenological approach to stock market crashes is constructed.

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