Department of Physics

University of Illinois at Urbana-Champaign

**Title:**Is Gravity Emergent?

**Abstract:**The purpose of this paper is to discuss the consequences of regarding gravity as emergent and how is this approach beneficial in solving long-standing problems like information loss in black holes, the entropy paradox, and the cosmological constant problem. Contrary to common belief, one can perform experiments to test the validity of these proposals. The microscopics of the effective theory will only be briefly discussed because there isn't any complete microscopic theory at present from which space-time is emergent.

**Vamsi Akkineni**Quantum Phase Transitions of Correlated Electrons in Two Dimensions: Connections to Cuprate Superconductivity

**Title:**Quantum Phase Transitions of Correlated Electrons in Two Dimensions: Connections to Cuprate Superconductivity

**Abstract:**This essay describes the Quantum Phase Transitions in the ground state and the nature of excitations above the ground state of the coupled ladder antiferromagnet model. It is then shown that the quantum phase transitions in the correlated two dimensional electronic system in the cuprate superconductors have similar universal properties as the above model.

**Soon Yong Chang**Spontaneous symmetry breaking and Goldstone bosons - Applications in a broad range of physical systems

**Title:**Spontaneous symmetry breaking and Goldstone bosons - Applications in a broad range of physical systems

**Abstract:**The concept of Goldstone bosons that arises as consequence of the breaking of continuous symmetry was born in the high energy physics and found interesting applications in other fields of physics such as solid state. This is a review assay of the reference articles where a summary of basic theory and some interesting applications are outlined

**Title:**Quantum Criticality as a possible theory for High Tc Superconductivity

**Abstract:**Recent neutron scattering, nuclear magnetic rersonance, and scanningtunneling microscopy experiments have revealed the coexistence of chargeand spin density waves and superconductivity in the cupratesuperconductors and have yielded valuable new information on the interplaybetween these distinct orders. They suggest that the theory for a High Tcsuperconductor can perhaps be built out of a theory of competing groundstates and quantum orders.

**Jordi Cohen**The Blue Phase of Cholesteric Liquid Crystals

**Title:**The Blue Phase of Cholesteric Liquid Crystals

**Abstract:**In a 1K interval between the cholesteric and isotropic phases of chiral liquid crystals, a triplet of very colorful phases are sometimes observed. Although they are liquid (in that they can be poured, etc.), they have a 3D crystalline orientational structure with a periodicity in the 100nm range. This is accompanied by other crystal-like properties such as a finite static shear modulus, an extremely high viscosity and the observation that they can be grown into crystals with very well-defined facets (floating in the isotropic phase). The blue phases have a complex structure composed of long "tubes" of very stable regions patched together by a periodic network of connected line defects between them.

**Madalina Colci**The Superconducting Phases of UPt3

**Title:**The Superconducting Phases of UPt3

**Abstract:**In this essay I present the experiments that provide clues about the order parameter and indicate a coupling between antiferromagnetism and superconductivity in the heavy fermion superconducting UPt3 compound. I also mention the leading theoretical models that aim to explain the multicomponent phase diagram and identify the superconducting phases, although up to now no single theoretical scenario is completely consistent with all of the data.

**Kevin P. Esler Jr.**Exotic Phases of DNA-Lipid Complexes

**Title:**Exotic Phases of DNA-Lipid Complexes**Abstract:**It was found in 1997 that mixing DNA and lipid vesicles in water results in the formation of complexes comprised of bilipid layers with aligned DNA strands intercalated between the layers. In addition to having useful applications in gene therapy, these complexes exhibit unique physical properties and manifest phases that had been previously only of theoretical interest. In particular, these systems have an approximate expression of the 2D smectic phase. This paper provides a brief summary of the progress in both the theoretical and experimental study of these complexes.

**Dimitrios Galanakis**Vortices In Trapped Alkali BECs

**Title:**Vortices In Trapped Alkali BECs**Abstract:**This essay presents a very brief review of the theory of the Bose-Einstein condensation in alkali gases concentrating more in the description of vortices and vortex lattices and also in their recent experimental observation.

**Evan Graves**Formation of Two-Dimensional DNA Smectics Layered between Lipid Membranes

**Title:**Formation of Two-Dimensional DNA Smectics Layered between Lipid Membranes**Abstract:**This essay describes a novel biological structure that self assembles an experimentally rare 2D smectic. Experimental results are from x-ray diffraction and some theoretical models are briefly addressed.

**Parag Ghosh**Superfluid to Mott insulator transition on an Optical Lattice

**Title:**Superfluid to Mott insulator transition on an Optical Lattice**Abstract:**Quantum phase transition is studied in a Bose-Einstein condensate held in a three dimensional optical lattice potential. The system shows a superfluid to Mott insulator transition as the lattice potential is increased. But unlike the unconfined case, this system shows a Mott insulator phase even at incommensurate densities. Experimental results along with Quantum Monte Carlo studies indicate a remarkable situation where there are locally confined Mott domains in the condensate. This new feature is an outcome of translational symmetry breaking in presence of harmonic confinement. Nevertheless, the system exhibits most of the essential features of a superfluid-Mott insulator transtion observed in unconfined lattice bosons.

**S.A.Gifford**The Quark-Gluon Plasma

**Title:**The Quark-Gluon Plasma**Abstract:**The quark-gluon plasma is an exotic state of matter that occurs at high density and temperature. I describe the basic theory of the quark-gluon plasma and its formation in terms of simple ideal models. I describe current experiments that are attempting to produce and observe the quark-gluon plamsa and discuss some of their results.

**T. Siegfried Ip**Critical Dynamics of Superconductor Transition

**Title:**Critical Dynamics of Superconductor Transition**Abstract:**This paper aims to be a brief survey to recent development on critical dynamics on high temperature superconductor made by cuprate oxide. Instead of looking at the normal-superconducting phase transition, focus is on the antiferromagnetic-superconducting phase. The AF-SC phase leads to the formulation of the SO(5) theory, which seems to be quite popular amount many research institute overseas.

**Evan Jeffrey**Superfluid-Insulator Transition in a Lattice Boson Gas

**Title:**Superfluid-Insulator Transition in a Lattice Boson Gas**Abstract:**Atoms in a Bose-Einstein Condensate can, under the influence of a periodic potential, make a quantum phase transition from the more usual superfluid (SF) phase to an insulating phase known as a Mott Insulator (MI). This transition is characterized by the destruction of long range phase coherence and number squeezing arising, so that each lattice site has a well defined number of atoms. The MI phase is being investigated to better understand the behavior of ultra-cold atoms, and to implement fine control over atomic systems for possible uses including quantum computers.

**Francoise Kidwingira**Phase diagram of cupprate superconductors: evidence of universal properties?

**Title:**Phase diagram of cupprate superconductors: evidence of universal properties?**Abstract:**In this essay, the phase diagram of cuprates superconductors is reviewed. Doping and magnetic field induced transitions are studied at finite temperature and at zero temperature. Scaling predictions are compared with experimental results.

**Hyejung Kim**Quasiparticle localization transition in dirty superconductors

**Title:**Quasiparticle localization transition in dirty superconductors**Abstract:**This paper describes the quasiparticle localization transition within a superconducting state by field-theoretical and numerical approaches. Starting with the Bogoliubov deGennes Hamiltonian and setting models for numeric calculation, some critical properties including the localization length exponent are obtained.

### Laura Kolb Superconductivity in C-60

**Title:**Superconductivity in C-60**Abstract:**Recently, a superconducting transition temperature of 117 K has been reported for lattice expanded hole-doped C$_{60}$ single crystals, and evidence suggests that C$_{60}$ compounds could soon overtake the cuprates as the highest temperature superconducting materials \cite{Sc01}. In this paper, I will review the history of investigations of the superconductivity of C$_{60}$, overviewing experimental observations and attempts at theoretical explanations of this phenomena, as well as summarizing some of the open questions.

**Amit P. Mehta**Dynamic Hysteresis and Spontaneous Symmetry Breaking in Magnets

**Title:**Dynamic Hysteresis and Spontaneous Symmetry Breaking in Magnets**Abstract:**When a many-body interacting system, such as a magnet, is driven by a time-varying external field it exhibits new and intriguing physics. In particular, when a magnet is driven by a periodically varying field h(t) = h_osin(wt) it exhibits dynamic hysteresis, that is, hysteresis that is not present in the adiabatic limit with thermal fluctuations present. Under certain conditions a dynamic trasition to a spontaneously broken state occurs, where the time average of the magnetization becomes nonzero. We present both theoretical and experimental studies of dynamic hysteresis and transitions in magnets.

**Swagatam Mukhopadhyay**Bits and pieces of spin glass physics

**Title:**Bits and pieces of spin glass physics**Abstract:**Spin glasses, an emergent phase of matter in random magnetic systems, is briefly discussed with an aim of understanding Replica Field theory, a tool to tackle quenched disorder in general. The physics of spin-glasses plays a pivotal role in our understanding of quenched disordered sytems. The Replica symmetric solution of the SK model is discussed in affordable detail and the necessity of Replica Symmetry Breaking (RSB) is argued. The TAP equation is introduced as an alternative to RSB. The experimental scenario is briefly dicussed, where aging, a peculiarity of spin-glass is introduced.

**Michelle Nahas**Luttinger Liquids

**Title:**Luttinger Liquids**Abstract:**Luttinger liquids are paramagnetic one-dimensional metals that do not exhibit the quasi-particle excitations of Fermi liquid theory. Rather Luttinger liquids will be seen to have strong responses to any perturbation no matter how small. Bosonization will be used to expand the Fermi fields in terms of boson operators, allowing almost all physical properties to be calculated. It will be seen that the correlation function exhibits power law behaviour which leads to the experimental prediction of power law conductance for tunnelling into Luttinger liquids. The results of experiments that measure the tunneling conductance of by electrostatic force microscopy (ESM) on single walled carbon nanotubes will then be discussed and compared to these predictions.

**Brian W. O'Shea**The Quark-Hadron Transition and its Effect on Primordial Nucleosynthesis

**Title:**The Quark-Hadron Transition and its Effect on Primordial Nucleosynthesis**Abstract:**In this paper, I discuss the quark-hadron transition in the early universe and analyze how possible inhomogeneities resulting from this phase transition can impact big bang nucleosynthesis. I describe how a possible phase transition could cause inhomogeneities to develop and, after providing a brief description of standard BBN, describe how these inhomogeneities can affect primordial light element abundances. I will then describe how the physics during and after the transition can be constrained by observations.

**Rahul Roy**The Superfluid phases of Helium 3

**Title:**The Superfluid phases of Helium 3**Abstract:**The BCS theory of superconductivity is generalised to triplet pairing states is used to study the phases of liquid Helium 3. Expressions for the spin susceptibility and specific heat are derived and compared with experiment.

**Olena Rudko**Liquid crystalline polymers. Uniaxial-biaxial nematic phase transition.

**Title:**Liquid crystalline polymers. Uniaxial-biaxial nematic phase transition.**Abstract:**A brief introduction to the field of Liquid Crystalline Polymer (LCP) physics is provided in this paper. The focus of the manuscript is on contrasting high molecular weight LCP and low molecular weight LCP (frequently named simply as liquid crystals). We discuss theoretical models describing LCP and experimental techniques that are used to determine their properties. As an example of contrast between liquid crystalline monomers and polymers we provide short description of studies of the uniaxial-biaxial nematic phase transition.

**Kan Shen**Bose-Einstein Condensation in Trapped Gases---A Review of Experiments and Theories

**Title:**Bose-Einstein Condensation in Trapped Gases---A Review of Experiments and Theories**Abstract:**This essay present the basics of Bose-Einstein condensation in trapped alkali gases, both experiments and theories are covered.

**Davit Sivil**Pattern Formation in Chemical Reactions

**Title:**Pattern Formation in Chemical Reactions**Abstract:**In this term paper, I will make a survey of pattern formation in chemical reactions. I will use the chlorine dioxide-iodine-malonic acid(CIMA1)[1] and chlorite-iodine-malonic acid(CIMA2)[10] reactions to explain two types of mechanism that lead to pattern formation. These are the Hopf bifurcation and the Turing instability respectively. This topic is important and interesting because it can shed light on the biological pattern formation problems.

**William Tucker**Magnetic Monopoles from 1931 to 2002

**Title:**Magnetic Monopoles from 1931 to 2002**Abstract:**The physics of magnetic monopoles is described as introduced by Dirac and later 't Hooft and Polyakov. Experimental searches for monopoles are described. Monopoles are introduces as possible "confiners" in the dual superconductor model and the phenomena of abelian dominance and monopole dominance are explained. Confinement in examined in U(1) Lattice Gauge Theory (LGT). The techniques are generalized to SU(2) LGT. Complications arising in extension to SU(3) LGT are discussed along with a prospects for future research.

**Aaron VanDevender**Ferroelectric Switching in Liquid Crystals

**Title:**Ferroelectric Switching in Liquid Crystals**Abstract:**The ferroelectric modes of liquid crystals which allow for easy reorientation of the direction of polarization make liquid crystals an attractive element to use for applications such as optical storage, and optical switching. Three schemes for achieving ferroelectricity are discussed: chiral smectic alignment, achiral ``banana-shaped'' smectic alignment, and the nematic phase that comes from strong dipole interactions. We also examine how ferroelectric liquid crystals can be used for thresholdless switching and optical storage.

**Kalin Vetsigian**Chern-Simons Theory of Fractional Quantum Hall Effect

**Title:**Chern-Simons Theory of Fractional Quantum Hall Effect**Abstract:**The Fractional Quantum Hall effect is reviewed from the perspective of Chern-Simons field theory.The interacting 2D electron gas in magnetic field problem is exactly mapped to a bosonic problem in which the bosons couple to a new gauge field in addition to the electromagnetic field. It is shown that mean field analysis in the new formulation is sufficient to explain all basic features of the fractional quantum Hall effect.

**Tzu-Chieh Wei**Superconducting states as quantum bits

**Title:**Superconducting states as quantum bits**Abstract:**There are two basic types of proposals of superconductors used to implement quantum bits (qubits): flux qubits and charge qubits. These two designs are based on Josephson junction but are operated at two extreme regimes: phase dominated and charge dominated regimes respectively. In both limits, the system behaves approximately as a two-level quantum-mechanical system, which serves as a basic requirement of quantum bits. There is a recent hybrid design, which can operate at the intermediate regime under appropriate control. In this paper, we focus on discussions of these designs of qubits and experiments demonstrating coherent superpositions of two levels and coherent control of some systems, with the problems regarding decoherence and measurement briefly mentioned in the concluding remarks.

**Paul B. Welander**Josephson Effects and a Pi-State in Superfluid Helium

**Title:**Josephson Effects and a Pi-State in Superfluid Helium**Abstract:**In this paper, I shall discuss the recent discovery of a metastable pi-state in a He-3 Josephson junction. This state is characterized by low frequency current oscillations and a nearly constant cross-junction phase difference of pi. The pi-state occupies a local minimum in the junction's free energy, and decays with an average lifetime on the order of a minute. Whether or not this state is an intrinsic one or systematic one is debated. For background, a brief review of the Josephson effects is included.

**Guojun Zhu**Quantum Phase Transition

**Title:**Quantum Phase Transition**Abstract:**A quantum system can undergo a continuous phase transition (QPT) at the absolute zero of temperature as some parameters entering its Hamiltonian are varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. In this essay, 1 dimensional Ising chain is studied as an example for QPTs. Then I briefly described QPTs in quantum hall effects and high Tc superconductors.

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