569 Emergent States of Matter

Term essays Spring 2006

These essays were written by students taking Physics 569 Emergent States of Matter, Spring 2006, 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.

Author: Inaki Anduaga

Title: Spin transport in the square lattice vortex state of rotational He3-A superfluid


We obtained a theoretical description of rotating superfluid in the He3-A phase in two dimensions. Experimentally, it is known that the vortices appear under rotation, so by requiring our order parameter to reflect that, we derived the form of the excitation eigenstates. Then we considered the presence of a magnetic field along the rotation axis, and found that the excitations evolve adiabatically with an extra phase (Berry phase) besides the dynamical one. Finally we considered the spin current carried by the excitations and found that it is quantized under certain conditions.

Author: Keiko I Kircher

Title: Emergent Behavior of Rock-Paper-Scissors Game


When rock-paper-scissors game is played by many people, there is an emergent behavior. Analytic model suggests that there are three phases, and computer simulation shows that phases are determined by how local interactions are. In this paper, analytic and computational model of RPS game, as well as applications to biological systems (E.coli and side- blotched lizards) are discussed.

Author: Zach Etienne

Title: Emergence in the World Wide Web


The World Wide Web (WWW) is a directionally linked network of $\sim10^9$ nodes (web pages).  Unlike a simple random network in which links are distributed with uniform probability between nodes, the probability $P(k)$ that there are $k$ (web) links to or from a given node on the WWW behaves as a power law in $k$ over many orders of magnitude, with exponent $\approx -2.1$ for links to a node, and $\approx -2.45$ for outbound links [1],[2]. This emergent property implies that the WWW has evolved into a scale-free (i.e., ``self-similar'') network. In this paper, we will review these observations and discuss two models that attempt to explain the power-law behavior of $P(k)$.

Author: Guy Tal

Title: Emergent Properties of the Net


The purpose of this paper is to discuss the unexpected, emergent properties of the Internet and the World Wide Web. Such properties include a fractal distribution of nodes, a scale-free power law, resiliency to breakdown under randomized attack, and threat of breakdown under specifically directed attack. Experimental evidence is surveyed and a few models are presented.  The potential usefulness of such information for defense purposes and better functioning of the Internet is outlined.

Author: Jiansheng Wu

Title:   Random Dimer Model: Escape from Localization


The Anderson localization is introduced as well as the scaling theory of localization. These predict the absence of the metallic state in 1 and 2 dimensions.  In such a theoretical background, the random dimmer model is shown to be novel due to its ability to escape from localization. This model is also shown to be applicable to describe the insulator-metal transition in a wide range of conducting polymer, such as polyaniline.

Author:  Jen Hsin

Title:  Emergence of Vortex Swarming in Daphnia


Swarming formation is a commonly observed group behavior in various biological systems.  It is an example of emergent global pattern in a collection of individuals who follows simple-minded rules.  In this paper we will discuss a special phenomenon of swarming, vortex swarming, that is observed in high- density population of Daphnia.  Particular interest lays in the transition from a low-density, normal swarming state, in which rotation direction is equally probable among the Daphias, to the high-density, vortex swarming state, in which nearly all Daphnias rotate in one direction.  We will examine the observations, mathematical models and simulations for both states, and discuss the possible parameters controlling the activation of vortex swarming formation.

Author: Kuei Sun

Title: Giant vortices in rapidly rotating Bose-Einstein condensates


In this essay, we will talk about two different ways in experiments to produce a giant vortex in BECs, and discuss the features of each kind of giant vortex separately. Besides, we also give the results and predictions from numerical simulations, comparing them with experiments.

Author: Ruizhe Yang

Title: Discovery of Quark Gluon Plasma at RHIC


Recent experimental results from Relativistic Heavy Ion Collider (RHIC) have shown the evidence of a new state of matter at high energy density. Physicists believe that the new state of matter is "Quark Gluon Plasma" (QGP) that they have been seeking for long time. This paper will survey both theoretical and experimental studies on QGP.


Author: Chandra Shekhar Mohapatra


We aim to study Integral Quantum Hall Effect in MBE-grown thin films like Graphene,Bismuth,GaAs and FeSiO2.We aim to look at how the quantum size effects dominate the electrical transport properties like the resistivity, hall coefficient, magnetoresistance coefficient and low-frequency electrical noise. We are also interested to look at the measurements on the MBE-grown AlGaAs/GaAs heterojunctions which indicate a difference of nearly an order of magnitude in the transport properties.

Author: Matthew Pasienski

Title: Kosterlitz-Thouless Transition in RF Dressed Ultra-Cold Gases


This essay reviews briefly the Kosterlitz-Thouless transition (KTT). The study of this transition in recent ultra-cold atomic gases is then discussed. Finally, a new, potentially advantageous, method to study 2D physics, including the KTT, with RF dressed Bose-Einstein condensates is suggested.

Author:   G. H. Lai

Title: Quantum Phase Transitions


Characteristics of QPT are discussed and some possible  applications of QPT in physics and biology are considered.

Author: Miguel Morales

Title: Superfluid 3He.


In this report I will discuss the main properties of the superfluid phases of Helium 3. First, a brief description of the experimental observations and the phase diagram of Helium 3 is made. This is followed by a discussion of the superfluid phases from a theoretical point of view based on the generalized BCS theory in the weak coupling regime. 

NAME: Geoffrey Poore

TITLE: Emergent Phenomena in Vehicular Traffic

ABSTRACT: Traffic jams and other features observed in vehicular traffic are examples of emergent phenomena. The current understanding of vehicular traffic is reviewed, with special emphasis on traffic jams. Empirical studies have revealed the presence of multiple phases in traffic, and have shown that traffic jams may form spontaneously. Several methods from physics have been applied to modeling traffic, and the general empirical features have been reproduced.

Author: John Koster
Title: The Color Glass Condensate


The color glass condensate is a proposed new form of matter present in high-energy hadrons that offers great promise to explain 40 year old puzzles in nuclear physics.  This paper will examine the recent theoretical and experimental work on this topic.

Author: Vadas Gintautas

Title: Synchronization of Chaos in Coupled Oscillators


This essay describes the experimental observation as well as numerical simulation and theory of synchronized chaos in systems of coupled oscillators.  This work explores examples of this phenomenon in coupled electronic circuits and optoelectronic systems, as well as possible applications to secure communication.

Author: Onur Hosten

Title: Superfluid state for photons?


Photons, which are bosons, can form a 2D superfluid due to Bose-Einstein condensation inside a nonlinear Fabry-Perot cavity filled with atoms in their ground states. The effective mass and chemical potential for a photon inside this fluid are non-vanishing. The dispersion relation for this photon gas is identical in form to the Bogoliubov relation describing elementary excitations of weakly- interacting bosons. I will summarize the basics behind and the ongoing numerical and experimental tests on the possibility of a superfluid state for photons.

Author: Pinghan Chu

Title: Color superconductivity

Author:  Rogan Carr

Title:  Networks in Biology


This essay describes the recent trend in studying networks and its application to biology.  It begins with an overview of network theory and its applicable results and concludes with a specific look at the network of protein-protein interactions.

Author: Daniela Lindner

Title: Electron doped cuprates


High temperature superconductivity in the copper-oxide ceramics obtains upon hole or electron doping the parent Mott insulating material. While the pairing symmetry of the order parameter in the hole-doped materials is well accepted to be of the d_{x^2-y^2}-type, the situation is far from settled in the electron-doped materials. This paper will analyze the evidence for a complex order in the electron doped materials and explore the possibility that a quantum phase transition exists at a critical doping. In addition, the "odd" occurence of $T^2$ electrical resistivity of the normal state of the electron-doped cuprates will be examined.

Author: Soheil Baharian

Title: Quantum Hall States of Rapidly Rotating Bose-Einstein Condensates


This essay is a review of the topic of vortices in rapidly rotating BECs, where the system is in a quantum Hall-like regime and the density profile is of the Thomas-Fermi form. Also, in this paper, deviations from a triangular lattice is being considered while the system condensates into the lowest Landau levels.

Author: Patricio Jeraldo

Title: The genetic code


In this paper I will review the genetic code. An overview of its functions and inner workings will be given. Also the current theories on the origin and emergence of the canonical genetic code from early codes will be explored.

Author: David Mertens

Title: The Verwey Transition in Magnetite


The historical development and theories explaining the Verwey transition in Magnetite are discussed.  An overview of current experimental work is included. Also examined are multiple charge ordering theories and more sophisticated considerations of Jahn-Teller effects which attempt to explain this long-standing problem in strongly-correlated electron systems.

Author: Daniel Sinkovits

Title: Flocking behavior


Flocking is the phenomenon in which self-propelled individuals, using only limited environmental information and simple rules, organize into an ordered motion. This ordering even occurs at two dimensions where ordering is not possible equilibrium systems. This paper will explain the biological and physical motivation for studying flocking, and the computational, theoretical, and experimental efforts undertaken to explore this phenomenon.

Author: David Ferguson

Title: The Commensurate Incommensurate Transition


What happens when you have a system where particles interact harmonically with an equilibrium length a are placed in a periodic external structure of length scale b? This is the question posed by the Frenkel-Kontorova model and the answer is quite a lot. When the mismatch is small enough the particles will keep themselves in registry with the lattice by compressing the springs into a local topological blob, which then become an interesting emergent degree of freedom. This paper explores this transition termed the "Commensurate Incommensurate Transition," while at the same time trying to glean general lessons that can be applied to other systems that undergo an analogous transition between competing orders. Is this system a good model in that it instructs you to find for any given model its interesting topological structure? Or is it just a one dimensional anomaly, in a general case where the dynamics is so complicated it defies an explanation even in principle. These are great questions that the FK makes one wonder.

Author: Weicheng LV

Title: Electron Pairing in High-$T_c$ Superconductors


In high-$T_c$ cuprate superconductors, the pairing state of electrons is still spin-singlet, as in conventional BCS superconductors. But the orbital part of the wavefunction, order parameter or gap function, has a $d_{x^2-y^2}$ symmetry, rather than the isotropic s-wave symmetry. This exotic symmetry has been confirmed by various experiments, especially the phase-sensitive ones. But the underlying mechanism of $d$-wave pairing remains controversial. Investigations on Hubbard model provide some ideas.

Author: Tom Butler

Title: Horizontal gene transfer and the emergence of Darwinian evolution


In this article I discuss the broader view of evolution that is growing out of our increased understanding of the role played by Horizontal Gene Transfer (HGT) in early evolution. Darwinian evolution, where genetic information and variation are passed to an organism by its ancestors, is seen to be only one aspect of evolution, and to have emerged from a world where the primary mode of evolution was the horizontal transfer of genetic information between organisms.

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