569 Emergent States of Matter

Term essays Fall 2012

These essays were written by students taking Physics 569 Emergent States of Matter, Fall 2012, 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: Jiawen Liu

Title: Cosmic strings and other Topological defects


In this review article, we point out spontaneous symmetry breaking is closely related to the emergence of the topological defects. Basic de finitions and dynamics of the domain walls are introduced in the second section. Finally, we worked out an example of the spherical domain wall by using semi-classical approach.

Author: John Jeffrey Damasco

Title: Gravity as an Emergent Phenomenon


While general relativity explains gravitational interactions well, it only answers the question of the nature of gravity by telling us that the geometry of space-time is gravity. Some physicists theorize that gravity is not fundamental, but emergent. Two of the theories that this paper will examine propose gravity as an emergent phenomenon rely on entropy as the origin of gravity or propose that it is a result of examining a quantum field theory on a Lorentz manifold. While these new theories of gravity are certainly attractive, experimental results refute some theories of emergent gravity, and there exist theoretical arguments against the general idea of emergent gravity.

Author: Brian Wolin

Title: Studying Collective Phenomena Using Ultracold Atoms in Optical Cavities


The extreme precision and tunability of ultracold atom experiments allows condensed matter problems that are often intractable to the traditional condensed matter physicist to be studied in the laboratory. Atoms in optical cavities display emergent self-organizing behavior, opening the door toward studying problems such as crystal dynamics and supersolidity, which cannot be simulated with externally determined lattice potentials. These systems exhibit spontaneous symmetry breaking of both discrete and continuous natures. Both single-mode and multi-mode cavities have been studied, with rich applications of the latter to the study of defects, frustration, and glassiness.

Author: Yizhi Fang

Title: Mysterious hidden order, superconductivity and magnetism of URu_2Si_2


The term "Hidden Order" (HO), brought up ten years ago, has been used to describe unknown ordered state whose origin could not explained by conventional solid state probes and is able to prove superconductivity at lower temperature (Tc ~ 1.5 K). This essay reviews the 25 year efforts to understand the continuous (second-order) and mean-field-like phase transition occurring at 17.5 K in URu_2Si_2 , known as HO, mainly through experimental phenomena, in particular, construction of the Fermi Surface (FS) and destroying HO via large magnetic field and Rh doping. Recent theoretical models will also be discussed at the end.

Author: Progna Banerjee

Title: Emergence of Majorana Fermions as quasiparticles in superconductors


This essay describes the need to study and search for Majorana fermions in condensed matter systems, the concept of Majorana fermions as emergent quasiparticle excitations in 2+1 dimensions, the method of obtaining them in superconductors, detection using suitable spectroscopic measurements and ultimately application in topological quantum computing.

Author: Yichen Hu

Title: Swarm intelligence


Swarm intelligence is an important concept in artificial intelligence and computer science with emergent properties. The essential idea of swarm intelligence algorithms is to employ many simple agents applying almost no rule which in turn leads to an emergent global behavior. In this paper, we will introduce some of the most famous bio-mimicry algorithms and discuss their applications as well as metaheuristics inspired from the collective behaviors of nature.

Author: Moonjip Park

Title: Three phase traffic theory


In the three phase theory, the traffic phenomena are explained by three phase theory: free flow, synchronized flow, and moving jam. Here, this paper introduces the concept of each phase. Moreover, the paper explains the process of the phase transition. The three phase traffic theory offers qualitative explanation of real traffic.

Author: Vatsal Dwivedi

Title: Condensates in Neutron Star Interiors


The pulsars, now identified as neutron stars, are one of the most fascinating astronomical objects studied so far. The detailed observation of various pulsars over the past 50 years presents clues to the understanding of its internal structure, esp the study of cooling rates and ‘glitches'. Theoretically, various kinds of condensates are expected in the interior of neutron stars, including neutrons in a superfluid state, protons in a superconducting state and other exotic states like pion and kaon condensates. This essay focuses on various emergent states in the interior of a neutron stars in presence of a strongly interacting fermion system and their effects on the dynamics of the neutron star.

Author: John Henry Hinnefeld

Title: Morality as an Emergent Property of Human Interaction


Altruism directed towards non-related individuals has long presented an evolutionary puzzle: why would the intensely competitive process of natural selection favor individuals who helped their genetic rivals, occasionally disadvantaging themselves in the process? For many years, the prevailing answer in the scientific community was that altruism somehow directly benefited the altruist; that apparent displays of selflessness were in fact subtly self-interested. This belief stemmed from a reductionist approach to evolutionary biology, epitomized by Richard Dawkins' 1976 book ``The Selfish Gene," which posited that all evolutionary analyses should be conducted at the level of the gene. Recently, however, a view based on a different level of description has been gaining acceptance. First suggested by Darwin himself in 1871, the idea of `group selection', wherein natural selection happens at the level of groups, as well as individuals and genes, has recently found support in a variety of experiments. One of the most interesting implications of these experiments is that the morality underlying cooperation and non-kin altruism may be a result of group-level natural selection. When applied to questions of morality, these `Multi-Level Selection Theories' imply that morality arises from interactions between humans within a group; that is, morality is emergent in collective human behavior. In this paper I will present the experimental evidence for this conclusion, as well as a historical summary of morality theories, from the reductionist theories prevalent in the past to current emergent models.

Author: Han Zhao

Title: FFLO State in Heavy Fermion Superconductors


The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can arise in superconductors in large magnetic field, characterized by cooper pairs with non-zero total momentum and a spatially non-uniform order parameter. For the FFLO state to appear, Pauli pair breaking is required to be the mechanism to suppress superconductivity, which is not the case for conventional superconductors whose orbital pair breaking is stronger. On the other hand, in heavy-fermion superconductor, the f-electrons of the rare earth or actinide atoms hybridize with the normal conduction electrons leading to quasiparticles with enhanced masses, which suppress orbital pair breaking. Recent studies on the heavy fermion superconductors have shown evidence of the FFLO states. In this paper, we will present the theoretical backgrounds and experimental progress of the FFLO state in heavy fermion superconductors. In particular, we will address the recently discovered quasi-two-dimensional superconductor CeCoIn5, which is a strong candidate for the formation of the FFLO state.

Author: Xiongjie Yu

Title: Vortices in type-II superconductors


Vortices in type-II superconductor arise when the magnetic field starts to penetrate the materials in the form of quantized flux. The vortices interact with each, and can form different phases under the influence of the magnetic field, thermal fluctuations, and the pinning effect of disorder and defects. As the usual theoretical methods towards vortex matter, the London model is briefly introduced while the Ginzburg-Landau models are discussed at length for their capability of describing more interesting phases of the vortices. Some experimental techniques of measuring the vortices are also mentioned at the end of the term essay.

Author: Erik Huemiller

Title: The Emergence of Polarization in Flocks of Starlings


Society is very familiar with the concept of a flock or herd moving in one direction. This paper seeks to introduce the reader to the fundamental models and observations that are present in the community. These models describe the organization of the flock in the normalized average velocity or polarization of the members of the flock. The polarization of the flock can be treated as the order parameter that describes the organization of the flock. Models are presented that show the dependence of the polarization on bird density and the random noise added to the interaction between birds.

Author: Pei-Wen Tsai

Title: Spontaneous genetic clustering in populations of competing organisms


One of the fundamental question in evolution is why species are dramatically different from each other? Through analyzing the simple mathematical models, the authors identify the sufficient and necessary conditions for this phenomenon. The species defined here is the cluster formed by similar organisms and organism is characterized by its genome sequence. Different from the previous work which treat the entire population as a whole in evolution, the authors introduce stochas- tics to each species. They analyze the stability of the fixed points in the limit of infinite populations, which correspond to a deterministic result. The effect of individual stochastics to the formation of genome clusters becomes clear when the system is large but finite.

Author: Jason Merritt

Title: Cellular automata as emergent systems and models of physical behavior


Cellular automata provide a basic model for complex systems generated by simplistic rulesets. While each step in a simulation is dominated by local interactions, over time complex macroscopic behavior can emerge. Observation of this long-term emergent behavior due to simple, easily understood and computationally efficient rules has led to attempts to model physical systems within the framework of simple cellular automata. This paper aims to briefly review the behavior and properties of cellular automata, provide some specific examples of CA models for physical systems, and point out the advantages and disadvantages of approaching a problem with a CA-based simulation.

Author: Shu Chen

Title: From Mott insulating to superfluid in optical lattices


This essay introduces the Bose-Hubbard model (BHM), which describes the behavior of bosonic atoms in optical lattices with strong interactions. Then this model is applied to describe two phases: superfluid and Mott insulator. The phase diagram and experiments concerning this are also discussed in this essay.

Author: Chi Xue

Title: Voting, a process of emergence of order


Consensus in a vote is an emergence of order. In this term paper, voter models on lattice and graphs are reviewed, with particular emphasis on dimension and topology underlying the process of approaching consensus. Its found that when individuals are connected to few neighbors, like in 1D and 2D lattice, consensus can always be achieved in both finite and infinite systems; when individuals have many neighbors, like in high dimensional lattice and graphs, consensus can only be reached in finite systems. Time needed for consensus is calculated for each finite system discussed. Numerical experiments are also presented to supplement the theory.

Author: William Rose

Title: Emergence of Traffic Jams in High-Density Environments


"Phantom" traffic jams, those that have no apparent cause, can arise as an emergent phenomenon in many models of traffic flow. These jams emerge when the density of traffic is sufficiently high. This survey paper will describe the basic elements of traffic flow that are consistent across all models and will also analyze the differences in predicted states that occur depending on the chosen model, making comparisons to experimental data when possible.

Author: Eric Petersen

Title: Gravitation and the Emergence of Space-time


The concept of space-time is fundamental to the theory of General Relativity. However, when developing theories of gravity which incorporate quantum mechanics, problems arise on the scales of the Planck length and Planck time. Several solutions have been proposed where the classical idea of space-time as the fundamental backdrop upon which the laws of physics guide the evolution of the universe is rejected. Instead, it is argued, space-time is an emergent property of the more fundamental notion of physical interactions or events. Some of these solutions arise from casting gravity as an entropic force. Others involve imposing certain commutation relations on non-commutative geometries or using Monte Carlo methods on a sub-Planck scale grid and solving for the path integral. Some physicists, however, remain unconvinced that an emergent notion of space-time is necessary and their objections will also be noted. The broad idea of emergent gravity cannot, as of yet, be dismissed, however, certain models can be excluded.

Author: Caizhi Xu

Title: Pairing symmetry in iron based superconductors


Iron-based superconductor is a new type of unconventional superconductors. It is similar to cuprates in some ways, but they have many significant differences. The antiferromagnetic spin fluctuations seem to play a very important role in the pairing mechanism. This paper will briefly talk about the theories and experimental findings on the pairing mechanism of this new type of superconductors.

Author: Adithya Kuchibhotla

Title: Emergent Phenomena in the Internet


In this essay, a brief structure of the Internet is first given and then two emergent phenomena that are exhibited by the Internet, viz., the Self-Similar traffic and the Scale-free Topology are studied. Suitable reasoning behind their occurrence and some mathematical modelling is also given. The Barabasi-Albert model that tries to explain the Scale-free Topology of Internet is explained. Finally, criticisms of some of these models are given along with the reasons for necessity to study the Internet phenomena further in the future

Author: Kenneth Schlax

Title: Ornithopter or Concorde? A review of the understanding and imitation of biological neural networks in theoretical and computational approaches.


The emergence of various properties in neural networks (memory, robustness, computation/ processing) is approached through theory and computational methods. Neural networks are found in nature and created artificially in computer systems. Connections can be made between emergence in models of interacting and dynamical systems and interactions between neurons in the neural networks. Computer methods often attempt to replicate the emergent properties found in biological neural networks. This paper will examine and evaluate the study of biological and computational neural networks in the area of emergent behaviors.

Author: Philip Russ

Title: Emergent quantum phases and excitations of bosonic atoms in an optical lattice


Bosonic atoms in an optical lattice are a useful tool for understanding strongly-interacting systems. This paper presents some of the basic theory for this system and calculations have been performed to reveal some of the properties of each phase. To compliment theory, important experimental research is highlighted which pioneered this area of study in AMO physics, including the observation of a quantum phase transition, fundamental properties of each quantum phase and excitations of the system.

Author: Mohammed Sheikh

Title: Markov Chain Monte Carlo and Image Restoration


The primary purpose of this paper is to illustrate the various concepts involved in Markov Chain Monte Carlo (MCMC), specifically the Metropolis algorithm. By using a process similar to annealing in metals and semiconductors, disordered initial states can be brought into the lowest energy con figuration. The hope is that the lowest energy con figuration in an image also lowers random distortions, such as noise, in an MCMC image restoration problem. This is due to the there being a phase transition in the image model as temperature is lowered similar to the transition towards a finite magnetization in the Ising model.

Author: Gilberto de la Peña

Title: Rare region effects in Ising models


The presence of quenched disorder gives rise to significantly different behavior in magnetic spin systems. This paper introduces the idea of rare regions, and analyses the effects of impurities and defects in several Ising systems. I will discuss the the Griffiths phases and their effect on thermodynamic variables and critical phenomena.

Author : Seyyed Mohammad Hassan Halataei

Title : Exotic phases of the superfluid Helium 3


In this term paper I describe the experimental data which led to the discovery of superfluidity in Helium 3 and then discuss mostly the Leggett's theory of the exotic phases in He-3 and how his theory justified the experimental data of nuclear magnetic resonance in He-3. I will discuss that how he used the concept of the spontaneous symmetry breaking and also spin dynamics of the system to find the spin state of the Helium atoms in two different superfluid phases. I will briefly explain the rival theory introduced by Anderson and Brinkman which could do the same job as Legget's did and mention some of the advantages, applications and usefulness of superfluid He-3.

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