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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Abstract: This essay present the basics of Bose-Einstein condensation
in trapped alkali gases, both experiments and theories are covered.
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.
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.
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.
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.
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.
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.
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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