569 Emergent States of Matter

Term essays Fall 2011

These essays were written by students taking Physics 569 Emergent States of Matter, Fall 2011, 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: Xiao Chen

Title: Fractional excitation in low dimensional system


The origin of bosons and fermions is a fundamental problem in physics. However, in some low dimensional condensed matter system, the bosons and fermions can be an emergent quasi-particle in some interacting system. The interaction here can changes the exclusion statistics of the particles in the original system. Another interesting emergent phenomenon is the fractionalization in these low dimensional system which is composed by particles with integer charges. I will discuss these emergent phenomenon in fractional hall liquid and some one dimensional systems in a unified picture.

Author: Wenchao Xu

Title: BEC-BCS crossover in ultracold Fermionic gas


By using Feshbach resonance, the atom-atom interaction can be tuned from attractive effect to repulsive, which allows us to study the crossover from Bardeen-Cooper-Schrieffer (BCS) type superfluid with paring in momentum space, to Bose-Einstein condensation (BEC) of bound pairs in real space. In this paper, I will present the mean field approach for both sides at T=0, and then discuss some experimental results in degenerate Fermi gas. Such results demonstrated the existence of these two emergent states and revealed the energy dispersion relationship and momentum distribution for both sides.

Author: Di Zhou

Title:  Bosonization of 1-Dimensional Luttinger  Liquid


Due to the special dimensionality of one-dimensional Fermi system, Fermi Liquid Theory breaks down and we must ?nd a new way to solve this problem. Here I will have a brief review of one-dimensional Luttinger Liquid, and introduce the process of Bosonization for 1-Dimensional Fermionic system. At the end of this paper, I will discuss the emergent state of charge density wave (CDW) and spin density wave (SDW) separation phenomena.

Title: Symmetry Fractionalization and Topological Order

Author: Yizhi You

Abstract:  In this article, I would first introduce a new phase of matter with symmetry fractionalization and symmetry protected topological orders. Such a system is beyond Landau's symmetry breaking theory. For a symmetry protected topological ordered state, even without symmetry breaking, it is still different from a conventional non-symmetry breaking one as it cannot be adiabatically connected to a trivial disordered state as long as the symmetry is protected. I would give the basic rules to classified different symmetry topological phases, based on the Matrix Product State Representation and the group cohomology of the symmetry. Then, a complete set of nonlocal string order would be defined in theses phases, which shows that such s symmetry fractionalization state is different from a trivial disordered state since its local entanglement is protected by symmetry and the irreducible entanglement in these phase of matter is responsible for its nontrivial topology.

Author: Chris Bonnell

Title: Kuramoto Oscillators


The Kuramoto model for systems of oscillators, a first-order system of differential equations used to study systems of phase oscillators, is a useful tool for the study of synchronization. This model occupies an essential niche between triviality and reality, being complex enough to have interesting features and yet admitting solution. In this paper we discuss the formulation of the model for a finite and infinite number of oscillators, its applications to physics and neuroscience, and some recent mathematical developments.

Author: Ponnuraj Krishnakumar

Title: Rotating Bose Einstein Condensates


This paper contains a review of dilute Bose-Einstein gas, both in a box and in a harmonic trap, and when they form condensates. As the Bose- Einstein condensate (BEC) begins to rotate vortices begin to appear and their dynamics are studied. For more rapid rotation, the vortices begin to form regular arrays and for very high rotation rates, one begins to see Landau levels. Eventually as the rotation rate approaches the radial trap frequency, there is an expected quantum phase transition to a highly correlated state analogous to those found in fractional quantum hall e?ect for electrons in a strong external magnetic field.

Author: Mayukh Nilay Khan

Title: Self organization of a Bose Einstein Condensate in an optical cavity

Abstract: Here, we discuss the spatial self organization of a BEC in a single mode optical cavity driven transversely by a laser field. Above a critical pump power, the atoms organize themselves into one of two possible arrangements depending on the initial fluctuations of the system. The system is analyzed at a mean field level. Connections of this system to the Dicke quantum phase transition is drawn. It is realized by two photon processes involving the cavity field and the pump mode. Finally some experimental results are also reported.

Author: V. N. Redmon IV

Title: Scale Invariance, Pattern Formation, and Disorder in Drying Colloids


Drying colloids have been shown to exhibit a rich variety of critical phenomena and pattern formations. They also have a wide range of practical applications. Here, a survey of the phenomena associated with drying colloidal suspension and a brief discussion of interesting applications is presented.

Title: Mirror symmetry breaking of the bioorganic world: biogenic and abiogenic approaches

Author: Tatyana Perlova

While inorganic nature contains equal amounts of different chirality type molecules, living nature is chirally pure. This mirror asymmetry of the bioorganic world on the molecular level is one of the unsolved mysteries of biology. A number of approaches to the solution of this problem were developed. Biogenic approaches claim that the property of chiral purity was selected in the course of biological evolution due to competitive advantage acquired by chirally pure organisms relative to racemic ones. According to the abiogenic approaches chiral symmetry was broken during the prebiotic stage of evolution either due to the presence of asymmetric factors or spontaneously.

Author: Arka Banerjee

Title: Electroweak phase transition in the early universe and Baryogenesis

Abstract: In the Standard Model, it is generally accepted that elementary particles get their masses via the Higgs mechanism, which involves a phase transition from the symmetric phase at higher temperatures (close to the Big Bang) to a phase in which the symmetry has been spontaneously broken. One of the outstanding problems in particle physics is to explain the origin of the observed matter-antimatter asymmetry (baryogenesis) which we observe in today's universe. In this term paper, we look at the phase transition associated with the Higgs mechanism and attempt to explain the above asymmetry using the same. If the phase transition is  'first-order' and rapid, it is possible to obtain the observed asymmetry from this model.

Author: Chi Hang Boyce Tsang

Title: Patterns in reaction diffusion system

Reaction-Diffusion systems are important in the field of non-equilibrium phenomena with relevance to biological and synthetic pattern formation. While homogenous distribution of chemicals was always believed to be a stable state, the symmetry-breaking treatment by Turing on such systems in 1951 showed pattern formation could be more stable in certain cases. This paper reviews the treatment by Turing and the subsequent evidences for and against its application.

Author: Philip Chang

Title: Electroweak Phase Transition and Baryogenesis


Our universe is apparently matter dominant. Although CP violation is experimentally proven, the full scenario of baryogenesis remains to be unsolved. Matter asymmetry is discussed brie y in this paper and electroweak phase transition (EWPT) is presented as one possible scenario of baryogenesis. Bounds on the Higgs boson mass for such scenario for Standard Model (SM) and Minimal Supersymmetric extension to Standard Model (MSSM) is discussed. It will be discussed that the LEP experiment has excluded SM as the possibility for matter asymmetry scenario and thus requires new physics beyond SM to explain baryogenesis through EWPT.

Author: Sean Vig

Title: Network Congestion as an Emergent Phenomena in Internet Traffic


This paper investigates the onset of congestion as an emergent phase in Internet networks at the network (IP) layer as a function of packet creation rate, addressing the models used to simulate network traffic and the applicability of these models to analyzing real-world Internet scenarios.

Author: Xiaoxiao Wang

Title: Phases of Liquid Crystals and Their Transitions


A brief introduction of liquid crystals and their phases is provided in this paper. Liquid crystal is a state of matter which has intermediate prosperities between liquid and crystalline solid. Its phases are characterized by their space and point group symmetry. We'll give a description of the symmetry and characteristics of different phase types of liquid crystals. And then talk about their phase transition. In particular, we'll talk about some interesting theoretical and experimental results for N-I, N-SA and SA-SC transition.

Author: Pak On Chan

Title: Quantum Phases and Topological States in Optical Lattices


Optical lattices are periodic potentials giving rise from optical fields. In this review essay, system of cold bosonic atoms sitting in an optical lattice is considered. Different quantum phases in optical lattices are discussed. In particular, we will talk about the superfluid and the Mott insulating phases of the system. Finally, a brief introduction on the topological states found in the optical lattices is given.

Name:  Ian Mondragon

Title: Ginzburg-Landau theory of the fractional quantum Hall e ffect


We present a description of the fractional quantum Hall eff ect (FQHE) in terms of a field theory analogous to the well-known Ginzburg-Landau theory of superconductivity. The key contribution of this theory is that it describes the phenomenology of the FQHE in terms of the behaviour of a charged superfluid. Hence, it provides a unifying understanding of the fractional quantum Hall state in the context of a well-known condensed matter system.

Author: Thomas Tuegel

Title: Pairing in cuprate superconductors

Abstract: Despite 25 years of intense effort and a wealth of experimental data, no clear consensus has emerged regarding the mechanism that allows pairing in the cuprate superconductors at such unprecedentedly high values of Tc . Nevertheless, it is now known, in part through the dramatic, qualitative results of dc SQUID measurements, that the d- wave pairing states are dominant in the cuprates. This result, and the constraints it places on possible microscopic theories of high-TC superconductivity, are discussed. The SO (5) model and the resonating valence bond model are described. Both models lead to an effective t-J model, the implications of which are discussed.

Name:  Raymond Clay

Title:  Solid He4:  A Case Study in Supersolidity


Solid He4 currently is the strongest candidate for realizing the proposed “supersolid” state of matter. Recent experimental results, however, have served to significantly complicate the original picture of solid He4 as a supersolid. In an attempt to get a handle on what has turned out to be a broad and rapidly changing field, I will present the original theoretical understanding as laid out by Andreev and Lifshitz, Chester, and Leggett, summarize the experimental data since Kim and Chan's discovery of non-classical rotational inertia, and then describe how modern theoretical work has developed to accommodate some unusual discoveries. 

Author: Gregory Hohensee

Title: Power law behavior in designed and natural complex systems: self-organized criticality versus highly optimized tolerance


Power law scalings are abundant in natural and man-made complex systems, but the presence of a power law in itself is insufficient to specify the mechanism that generates it. It would be particularly valuable to understand the origin of the power law distribution of electrical blackout size versus frequency in national high-voltage power grids, in order to better moderate blackouts. The concept of self-organized criticality (SOC), inspired by the critical dynamics of phase transitions, underlies many cascade models for power grid failures; however, the distinct "highly optimized tolerance" (HOT) mechanism can also replicate empirical statistics. This essay surveys recent SOC and HOT models to compare and contrast the two mechanisms in the context of the power grid system.

Author: Rezvan Shahoei

Title: Emergence and evolution of language


I will try to picture the difficulty and controversiality of the problem of language evolution by a brief history. Then I will report some major opinions on the purpose of language and its evolution. One of the most ambiguous pieces of the language emergence puzzle is the emergence of trust in human societies. I will bring a discussion by Fitch on the evolutionary backgrounds which he believes sheds light on this dark piece. At the end I will explain a mathematical model to study language change based on a linguistic model which in continuous-time limit results in Fokker-Planck equation.

Author: Huihuo Zheng

Title: Quasiparticle excitations in cuprate superconductors and their relations to superconductivity


In superconductors, quasiparticles are created when a Cooper pair of electrons breaks apart. Hence a better understanding of quasiparticle dynamics may help to uncover the mechanism for Cooper pairing in cuprate superconductor. Due to d-wave symmetry of the gap function, the quasiparticle spectra in cuprate are strongly momentum-dependent. The minimum excitation energy is zero for momenta in the “nodal” direction (oriented at 45? relative to the Cu-O bond), and is largest for momenta in “anti-nodal” direction (nearly parallel to the bond). It is found that both these two kind of excitations are closely related to the superconductivity. In our study, we review the experimental studies on the spectra properties and dynamics of these two quasiparticle excitations and examine their underlying relations to superconductivity phenomena.

Author: Hannah Gelman

Title: Applications of substrate ordering in nematic liquid crystals


The defining characteristic of liquid crystals (LCs) is the emergence of orientational order without accompanying positional correlations.  As scientists pursue applications of LCs beyond electronics, they have found not only that LC ordering is sensitive to surface substrate characteristics, but also that LCs themselves can act as ordering substrates.  This essay will review insights into LCs as both ordering targets and substrates and will discuss efforts to apply these insights to the study of biochemical systems. 

Author: K. Michael Martini

Title: From Slime to Networks


The slime mold Physarum plasmodium exhibits some remarkable behavior for a single celled organism. Slime molds can optimize their overall structure to distribute nutrients within themselves in the most efficient manner; essentially solving the Steiner tree problem. In order to minimize the transport distance of nutrients slime molds form tubular networks with shortest total length.  Slime molds have been suggested as a good model for studying the transition from single celled organisms to multicellular organisms. This paper will review some current models for how these networks form in slime molds and how people have begun to use these organisms as unconventional computers.

Author: Farshid Jafarpour

Title: Pattern Formation and Emergence of Collective Behavior in Bacterial Growth


Collective surface migration of bacterial cells on a growth medium can lead to interesting spatiotemporal patterns and dynamical behaviors. Studying the rich behavior of these swarming colonies can provide insight in how the multicellular organisms were originally formed. Bacterial swarming is an example of emergent behavior as a result of interplay between the collective interactions of a population of bacterial cells, colony growth, and hydrodynamic motions. Several models have been proposed to describe bacterial swarming some of which can  qualitatively reproduce a variety of colony shapes observed in experiments. In this paper, some experimental work along with a theoretical model for the mechanism of pattern formation in bacterial swarming that captures some qualitative and quantitative aspects of this phenomenon is reviewed.

Author: Zachary Dell

Title: From White Noise to Fur Elise: What makes music beautiful?


Can an entire symphony be predicted by just one note from just a single instrument in the orchestra? It seems absurd to even ask this question. The power of an orchestral piece is in how the ?utes harmonize with the viola, and how the hardness of percussion counters the softness of the winds. The manner in which all of the notes from all of the instruments come together to produce a collective piece that evokes an emotional response from listeners is a very di?cult subject to investigate. This is due to the complex interactions between the sounds produced and how humans perceive these sounds. In an attempt to describe these processes, current research in music theory has drifted from the traditional interpretation of music in terms of its properties (such as pitch, rhythm, tempo) to a more contemporary approach which tries to involve the neurological aspects of listening and composing. The complex and emergent behavior of music will be investigated with focus on how research has shifted over the past few decades. Emphasis will be placed on the hierarchal structure of interpreting music, and how views of this structure has shifted recently.

Name: Vikyath Deviprasad Rao

Title: Robustness in biological systems


The systems approach to biology aims to address problems using a holistic approach that focuses on emergent properties, namely those that cannot be attributed to a single part of a biological system, but rather, arise from complex, collective processes at the molecular level. An important feature of these emergent properties is robustness---the emergent phenomena are, to a considerable extent, insensitive to changes in the parameters of the microscopic processes that give rise to the phenomena in the first place. In this paper, we examine the general features of robustness as it appears in biology. We also present a model for adaptation in bacterial chemotaxis as an example of how robustness can influence the process of understanding systems-level phenomena by model building.

Author: Barbara Stekas

Title: Emergence of Altruism is Public Goods Games

Abstract: Much of evolutionary and economic theory is based on the idea that humans, animals, and even genes are inherently selfish and make decisions based on what is in their own best interest. But we know that humans and animals make self-sacrificing choices regularly, not just for the benefit of their own progeny but also to help complete strangers, through charity for example. This paper will provide an overview of public goods games (PGG) and how altruism, though harmful in the short term to the practitioners, tends to be beneficial overall . It will also explore whether altruism is evolutionarily favored and what factors can lead to its dominance or failure compared to selfishness in these models.

Author: Andrew Murphy

Title: Blue Phases in Liquid Crystals


The blue phases are a set of thermodynamically distinct phases that occur between the helical phase and isotropic phase of highly chiral liquid crystals. They display many striking properties, brought about by a defect lattice in their structure. In this essay, I briefly introduce liquid crystals, describe some of the properties of the blue phases, look at the theory of blue phases while avoiding mathematical details, and then describe a few of the important experiments which have helped define the blue phases and reveal their structure.

Author: Yulia Maximenko

Title: Superconducting Phase Transition

Abstract: In the current essay we will try to study superconducting-normal phase transition for both types of superconductors, using mostly Landau theory of second order phase transition, or particularly Ginzburg-Landau (GL) functional for superconductivity. A review on the time-dependent GL theory, numerical simulations and problems arising will be reported. One possible technological application in accelerator physics will be discussed as well.

Author: Juan Alberto Garcia

Title: Color Flavor Locked Quark matter properties

Abstract: Quark matter at its highest densities is expected to be a color superconductor and be at a phase called color flavor locking (CFL). Because of asymptotic freedom, the theory becomes weaker at high densities and some kind of superconductivity can be expected . At the CFL phase it behaves as a superfluid and has Chiral Symmetry breaking. Finally, possible observations or experimental evidence will be discussed such as measurements of temperature and energy of neutron stars which give information about the interior Sand gravity wave detection giving information about the density of the stars.

Author: Wathid Assawasunthonnet

Title: Liquid Crystal Phase in DNA


Liquid crystal phase is an emergent phase in many of the condensed matter and biological systems it has properties between those of normal crystalline solid and liquid. In this paper a brief introduction to different types of liquid crystal ordering is given. Features and properties observed in liquid crystals are presented. The rest will discuss a specific system namely the liquid crystal phases due to the helix-helix interaction in DNA. Qualititavely I will argue that DNA in electrolyte should exhibit liquid crytal phase transition. Experimental results confirming the existence are presented. A theory based on mean field approach will also be discussed

Author: Michael LeBlanc

Title: Spontaneous symmetry breaking in non-abelian gauge theories


This term paper explores the phenomenon of spontaneous symmetry breaking in systems with non-abelian gauge symmetry. The most famous example comes from the standard model of particle physics, wherein symmetry breaking is responsible for the masses of the W and Z bosons and the corresponding short range of the weak nuclear force. The electroweak theory will be discussed as well as a more ambitious (but less successful) attempt to unify the strong, weak and electromagnetic forces in which symmetry breaking also plays a key role.

Author: Charles Steiner

Title: Heavy Fermion Superconductivity


Heavy fermion superconductors were the first class of unconventional superconductors discovered. The epxerimental and theoretical work done on them has important implications both for the basic physics and for how we understand othe types of unconventional superconductors. In this paper I give a brief overview of the history and microscopic model of heavy fermion materials. A diverse selection of heavy fermion superconductors is presented, along with a brief discussion of how proposed mechanisms fit in with this diversity.

Author: Douglas Packard

Title: Particle-Hole symmetry in the nu=5/2 QHE state


This paper discusses the quantum hall effect, the concept of Landau Levels as an explanation for the integer effect, and the analogy made for composite fermions to explain the fractional effect. It then discusses the p-wave paired 5/2 state, and its symmetry breaking properties under particle-hole transformations

Author: Chang-Tse Hsieh

Title: Inverse Melting and the Emergence of Reentrant Phase in physical systems


Inverse melting (freeze) is the situation in which a solid melts (a liquid freezes) when the temperature of the system decreases (increases). It also concerns to the emergence of reentrant phase transition of a physical system. Here we overview these concepts and the corresponding phenomena, which usually occur in the condensed matter system.

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