569 Emergent States of Matter

Term essays Spring 2018

These essays were written by students taking Physics 569 Emergent States of Matter, Spring 2018, 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: James Allen

Title: Dynamics of an Exciton-Polariton Condensate

Abstract: This essay describes the condensation of special exciton-polariton quasiparticles in a semiconductor optical cavity, and the hydrodynamical properties of the resulting superfluid, paying special attention to why polariton condensates are a powerful tool for studying more conventional quantum fluids.

Author: Gilbert Arias

Title: Traffic Jams as Emergent Behavior

Abstract:The flow of traffic can be thought of having phase transitions where macroscopic flow can be free, jammed or in an intermediate state between the two. Said transition can be seen to be first order. There are several models that describe the behavior of traffic ranging from the microscopic to macroscopic regime. One may even explain the system with the Ginzberg-Landau approach. Linear stability analysis reveals backwards propagating collective waves in many models of the system.

Author: Dmytro Bandak

Title: Spin Glasses: Emergent Behavior of Systems with Quenched Disorder and Frustration


In this essay, we will consider the interplay of quenched disorder with frustration and how it gives rise to emergent behavior. The field was experimentally motivated by an observed phase transition and properties of structural and spin glass phases. The latter provides a natural setup for our discussion and we will focus on Edwards-Anderson and Sherrington-Kirkpatrick models originally suggested to describe spin glasses. In the process, we will get acquainted with replica theory, the concept of replica symmetry breaking and discuss its physical meaning.

Author: Katie Bolan

Title: Patterns of Collective Behaviour in Ballroom Dance


On a typical ballroom dance floor, there are many couples on the floor, moving according to the prescribed rules of the dance. Though each couple typically has their own sequence of steps that they try to dance, their motion is constantly being affected by that of the other couples on the floor. Due to these interactions and the characteristics of a given dance, patterns of collective motion arise from the various individual routines. These types of patterns are not unique to competitive ballroom dance floors, but can also be observed in the motion of other groups of individuals. The mathematical and computer models describing these other systems can therefore also be useful in describing the collective motion of couples on a ballroom dance floor.

Name: Brandon Buncher

Title: The Emergence of an Arrow of Time from Microscopic Principles


The arrow of time, or an asymmetry in the allowed direction of travel through time, is a fundamental property that differentiates space from time; however, its mechanism of existence is poorly understood. This work will detail explanations for the arrow of time arising from quantum/statistical mechanics and thermodynamics, identifying their pitfalls and describing experimental tests.

Title: Dark Matter as an Emergent Phenomenon of Entanglement

Author: Fikret Ali Ceyhan


Velocity profile of the outer regions of galaxies tend to stay constant instead of following the expected Kepplerian one over square root law. Modified versions of Newtonian gravity, while being in agreement with the observational results, fail to ascribe a self-consistent microscopic origin to this bizarre phenomenon. Another explanation for the observed profile is Dark Matter, existence of an unseen additional mass that could provide an anchor for the motion of the stellar mass to give rise to the constant velocity behavior. In this essay, we will describe Verlinde's proposition that dark matter or modification to Newtonian gravity comes from a competition between area and volume-law variation of entanglement entropy in de Sitter Space, where non-Newtonian behavior manifests as an elastic response due to entropy displacement. We will also explore the strengths and shortcomings of Verlinde's theory, its regime of validity, and how it matches the observational evidence.

Author: Yueqing Chang

Title: Symmetry of pairing states in cuprate superconductors


Ever since the discovery of the high-Tc cuprate superconductors in 1986, physicists have been endeavoring to understand the pairing mechanism of these unconventional superconducting materials. Non-phase-sensitive and phase-sensitive experiments show strong evidences for the d-wave pairing in cuprates, either via measurement of the penetration depth in low temperature regime, and determination of the modulation pattern of critical currents with respect to external field. In this essay, we include a discussion about the symmetry of the unconventional pairing states in cuprates and review the early experimental efforts in establishing their d-wave symmetry.

Author: Yidong Chen

Title: Models of Complex Networks

Abstract: In this essay, we will discuss various models of real world networks, including random graph theory (Erdos-Renyi), percolation theory, small-world networks (Watts-Strogatz), and scale-free networks.

Author: Jin Chen

Title: Experimental evidence of pseudogap and its emergence


Energy gap is necessary in superconductor phase transition, as physicists widely agree with. Unconventional superconductors, especially cuprates, among other novel properties, has been believed to exist a so-called pseudogap state, where only wave vectors oriented in copper oxide bond are allowed, within a temperature range, while higher than Tc. Experiments on underdoped superconductors such as BSCCO reveal its close relationship with preformed cooper pairs. The recently observed pair density wave is possible to correspond with its spatial distribution. However, the origin of pseudogap is still under debate. Here we mainly present a review of the experiment evidence. We will also briefly introduce several theoretical progress on its emergence.

Title: Role of phonon coupling in cuprates

Author: Chad Germany


High temperature superconductors promises to usher in major technological advances.  Cuprates in particular are an interesting called such because they are a class of compounds containing copper and oxygen that exhibit superconductivity. During the discovery of the cuprates theorist tried to use BCS theory to explain the pairing mechanism of the cooper pairs. They found that phonon-electron interactions do not entirely explain why cooper pairs form and additional studies need to be made to fully understand these superconductors outside a BCS model.  Although this is not to say that phonons do not play any part in the formation of the cooper pairs in cuprates.  In this article will explain what role the phonons have by examining ARPES and STM data.

Author: Udit Gupta

Title: Emergent Spacetime


There have been recent theoretical hints that spacetime should not be thought of as a fundamental concept but rather as an emergent property of an underlying microscopic theory. In this paper we give an overview of proposed microscopic models that suggest that of spacetime should emerge as an effective description.

Author: Weizhen Jia

Title: Phase Transitions and the Inflationary Cosmological Models


In this paper, we review how the idea of a delayed first-order phase transition was used in the inflationary cosmological model and how it solves, or at least relieves, the problems from the standard cosmological model that are contradicted by the CMB observation. We also discuss the problems of the original inflationary model, and how it was improved by other inflationary models.

Author: Thomas Johnson

Title: Basics of Quantum Spin Liquids

Abstract: A quantum spin liquid is a state of matter in which the spins are highly entangled and don't order, even at T = 0. They are predicted to exhibit fractional particle excitations and emergent gauge fields. In this essay, I introduce the basics of quantum spin liquids with an emphasis on their universal features, and cover some experiments done on ZnCu3(OH)6Cl2.

Author: Abid Khan

Title: Emergent Behavior in Neural Networks


The main objective of machine learning is to extract important features from data. Similarly, the main goal of studying emergent phenomenon is to take a high-dimensional system and explain it on a higher level with fewer dimensions. In this report, we show that neural networks exhibit emergent behavior and can be explained with the tools of condensed matter physics. We also show how neural networks can be used to extract emergent phenomenon in physical systems.

Name: Lazar Kish

Title: Skyrmions in Chiral Magnets


Skyrmions are topological solitons originally invented by Tony Skyrme as a model for the nucleon, but which have since been realized in a broad range of other physical contexts. In magnetic materials, two dimensional versions of these skyrmions appear both in the bulk or in thin films as topologically stable, 'vortex-like' spin configurations that result from chiral interactions. This paper reviews the properties of magnetic skyrmions, beginning with their topological properties, moving to a theoretical description using a Landau free energy, and then experimental observations of their behavior in a variety of systems.

Author: Ryan Levy

Title: Kondo, Kondo, everywhere, but what is going on in the bulk: Kondo insulators and strong correlations?


A class of materials has been found where quasiparticle excitations have an enormous effective mass, known as heavy fermion materials. Examples of such materials are Kondo insulators, in which this behavior is driven by spin-orbit coupling and the presence of localized f orbitals. Coupling between free electrons and localized spins produces interesting physics, namely a large effective mass, through screening and hybridization. In this paper, we discuss a toy model realizing the physics of these materials, the Kondo Lattice Model, and its connection to experiment. Finally, we investigate some of the properties of SmB6, a potential topological Kondo insulator.

Name: Yao Li

Title: Superconductivity in Fe-Chalcogenide


Shortly after the discovery of iron-based superconductor(FeSC) in early 2008, iron-chalcogenide FeX (X=Se,Te,S) emerged as a promising group of compounds for studying the mechanism of iron-based superconductivity. In this term paper, the physical and chemical properties of iron-chalcogenide(FeCh) superconductor are reviewed, progresses in the study of its pairing mechanism are discussed and some of the recent experimental results are summarized.

Author: Sungsoo Lim

Title: Spatial pattern formation during morphogenesis


Various biological systems and processes are understood to be emergent properties of the collective interactions of networks. Morphogenesis, the organized spatial distribution of cells to establish different body parts during an organism's development, is an interesting example. Several of general structural and dynamical properties of biological networks have been established, with which the molecular details of spatial pattern formation during morphogenesis can be understood. To this end, this essay describes some of the general properties of biological networks. The reaction-diffusion model is also introduced, and in this context, the left-right asymmetry and the segmentation of embryos are discussed.

Name: Zhiru Liu

Title: Turbulence in Active Matter


The presence of active particles in fluid often results in complex collective patterns and dynamics. In this essay, we focus on a particular non-equilibrium phase that resembles turbulence in classical fluid dynamics. We review both the experimental setups and the candidates of modeling this phenomenon. Power laws in the energy spectrum have been found in both experiments and simulations, but controversy exists.

Author: Orlando Melchor-Alonso

Title: The emergence of the human brain through bottom-up and top-down procedures


The emergent properties of the human brain such as learning and memorization are explored. First, one discusses the short comings of representing the brain using artificial neural networks. Then one proceeds to outline one of the first bottom-up methods used to describe the emergent phenomena of the brain known as the Hopfield network. One then discusses why top-down procedures are more successful in describing the emergent states of the brain. Lastly, one outlines the advantages of top-down methods and potential advances in these methods for the future.

Author: Tim Miller

Title: Formation and Behavior of Traffic Jams


This essay will discuss how traffic jams can emerge from free traffic on highways and how these traffic jams behave. This discussion will include an introduction to a few models of traffic flow as well as comparison with experimental data.

Name: Viviana Nguyen

Title: Fractional fermi fluid as a model to understand the pseudogap in high temperature cuprate superconductors


At low temperatures, atoms form Cooper pairs in the superconducting state. Because it takes energy to break these pairs, there is no way to remove a single particle without adding energy to the system. This leads to a gap in the single-particle energy spectrum. When temperature is increased such that , remnants of this gap, where certain energy ranges have few states associated with them, remain. These have been termed pseudogaps. This pseudogap behavior has been found to exist in under-doped cuprates and is temperature and doping dependent. This paper aims to review the pseudogap regime of cuprate superconductors and to discuss the experimental observations of this pseudogap. Then it will introduce the fractional fermi liquid model as an explanation for this pseudogap.

Author: Junseok Oh

Title: Synchronization of Josephson Junctions


Synchronization is a common yet interesting emergent phenomenon observed in various parts of nature, such as condensed matter systems and biological coupled oscillators. How does a synchronization arise in a given system? This essay introduces a mathematical explanation to the emergence of synchronization and describes emergence of partially and completely synchronized phases in a series of current biased Josephson junctions.

Author: Jorge Olivares Rodriguez

Title: Dynamics of Epidemic Spreading in Complex Networks


Several mathematical models, mostly based on graph theory, have been developed over the past decades to predict and explain the behavior within complex interconnected dynamical systems. Here we present an introduction to the current theoretical models on epidemic spreading mechanisms in complex networks.  We show using several mathematical models how the topology of the network determines the behavior of the epidemic. An analysis of the strengths and weaknesses of each model presented is also included.  The study of the patterns emerging from epidemic spreading in complex networks can not only help prevent and contain the spread of computer viruses or biological epidemics, but may also help understand similar phenomena in other areas such as social media.

Author: Pin-Yi Li

Title: Emergence of polarity in early C. elegans embryo


The establishment of cell polarity during embryogenesis is a crucial process. The molecular basis for polarity in C. elegans embryos involves a set of partitioning-defective (PAR) polarity proteins that segregates into anterior and posterior domains to form the basis of a stable front-back axis. While experimental evidence suggested that external signals trigger an anterior-directed cortical flow to transport the anterior PAR proteins, it has also been shown that a reaction-diffusion system without coupling to advective flow is sufficient to generate stable partitioning. In this report, I will try to summarize some models that explains the spontaneous emergence of cell polarity by reaction-diffusion patterns. I will also try to discuss the effect of coupling cortical flow to the reaction-diffusion models.

Author: Pranjal Ralegankar

Title: Understanding Emergence of Cooperation using Tools from Thermodynamics


Understanding how cooperation emerged in evolutionary biological systems is a long studied problem. To mathematically understand this phenomenon, simplified models of game theory are constructed and then analysed usually with the help of simulations. Closed form solutions of when cooperation emerges even in such simplified models are hard to come by. This study will be primarily focusing on possible ways the problem of emergence of cooperation could be framed in thermodynamic language. Such a bridge will allow us to mine the extensive literature on critical dynamics in statistical mechanical systems, many of which have exact closed form solutions, for the purpose of understanding emergence of cooperation.

Author: Brendan Rhyno

Title: Magnons: Spin-Waves in Magnetic Materials


The purpose of this essay is to develop the notion of emergent magnon excitations which appear in magnetic materials. In particular, we will discuss the so-called Holstein-Primakoff boson and Schwinger boson representations of spin-operators. This technique is powerful in that we can utilize the second quantization formalism discussed in class; however, we will find this approach places a constraint on the Hilbert space of the operators. With the preceding formalism established, we will apply it to the Heisenberg model (a minimal model of a ferromagnet) and show that the low-energy quasiparticle excitations describing such a system are spin-waves. We will conclude with a discussion of potential technologies which can exploit spin-wave physics --- a field known as magnonics.

Title: Emergent Electrodynamics in a Skyrmion Lattice

Author: Marcus Rosales


When an electron travels through a non-uniform magnetic structure, it constantly experiences forces which attempt to orient it with the local magnetization. An emergent electrodynamics can be used to describe the net effect of these re-orientations. This essay focuses on Skyrmion lattices, topological quantum numbers and how topological properties of our lattice is inherited by the emergent fields. There is a discussion on the Quantum Hall Effect to motivate topological quantum numbers and the experiment also uses the Hall Effect as a means of data collection.

Author: Tyler Salners

Title: Long Period Phase Oscillations Emerge from Connectivity Symmetry Breaking in the Brain

Abstract: None given.

Author: Varsha Subramanyan

Title: Double Trouble: Memory Formation as Emergence in the Brain


This essay lays out arguments in favour of considering functions of the brain as emergent phenomena arising out of neuronal interactions. The brain is modeled as a non linear, dynamical, many body, open quantum system that is constantly interacting with its environment by means of external stimuli. The phenomenon of memory formation is described by means of this model by employing quantum many body theories. Finally, experimental evidence in support of employing a quantum model of the brain, and the dissipation model in particular are laid out.

Author: Xueying Wang

Title: Quantum Turbulence, and How it is Related to Classical Turbulence


Since the discovery of turbulence in superfluid, great attention has been paid in finding out and understanding its properties. One way to understand quantum turbulence is by comparing it to classical turbulence. In recent researches, some similarities and differences between the properties of quantum turbulence and classical turbulence have been found. In this essay, analytical models, experimental and numerical results on turbulence in He II will be discussed and compared to the properties of classical turbulence. I will focus on the similarity and difference in energy spectrum of He II turbulence and classical turbulence. The cause of the similarity and difference will also be addressed briefly. Finally, ongoing research problems concerning quantum turbulence and its relationship with classical turbulence will be briefly discussed at the end of this essay.

Author: Jimmy Yuan

Title: Fractional Excitations and the Quantum Hall Effect


The fractional quantum Hall effect explains the fractional quantization of transverse conductance in the presence of a magnetic field. This effect has become of interest due to the presence of fractional excitations and other exotic emergent phenomena. In this essay, we introduce the motivation for the variational wavefunction first proposed by Laughlin, which predicts the existence of quasi-particles with fractional charge and fractional statistics, and also explains several values of the Hall quantization. We finally construct a top-down Chern-Simons theory for the FQHE in the spirit of a Landau-Ginzburg functional, and reproduce some of the phenomenology.

Author: Xiaoyu Zhang

Title: Understanding of Spin Glass from Susceptibility Measurement


Materials that are consist of disordered and frustrated magnetic spin alignment with complicated energy landscape are called spin glasses. This kind of magnetic material is first realized in susceptibility measurement. In this paper, I will discuss about three important magnetic behaviors observed in different susceptibility experiments and the unique properties we learn from these experiment. Then some theory models that used to describe spin glass will be mentioned as followed.

Author: Mengdi Zhao

Title: Emergence of Anyons with Novel Statistics in 2-dimensional Systems

Abstract: In certain two-dimensional systems, due to the interactions between electrons or atoms, a neither fermionic nor bosonic kind of quasi-particles can emerge. They are called anyons. In this essay, I will review the Abelian and non-Abelian statistics of anyons, and explain the quantum Hall effect which offers possible systems for anyons to exist. Experimental techniques to detect anyons and some evidence will also be mentioned. The identification of non-Abelian anyonic states will be a crucial step in topological quantum computation.

Author: Penghao Zhu

Title: Cooper pairs in Superfluid He3


In this paper, I will talk about why the Cooper pairs in superfluid He3 is spin triplet pairing and P-wave. I mainly argue from the aspect that how the theory match with the experiment data on spin susceptibility. 

Author: Minhui Zhu

Title: Activator-inhibitor model for seashell pattern formation


Seashells exhibit diversified types of pigmentation patterns on their surfaces. While pattern formation is a ubiquitous phenomena in many different systems, seashells are a rare type of system that can record the formation and time evolution of the spatial pattern through calcium deposition.  This essay mainly reviews the activator-inhibitor model for seashell pattern formation, where spatial variation arises from diffusion. We derive the instability condition for a uniform state, which initiates the pattern formation, through linear stability analysis. Based on this model, computer simulations are performed and the results match well with observation in nature, which are shown in several examples.  Furthermore, we review the application of the activator-inhibitor model to many other systems. Though extensive literature can be found on this topic, many features of seashell patterns and their molecular basis remain unexplained while some others are still in debate.

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