502 research outputs found
Sine-Gordon Model - Renormalization Group Solutions and Applications
The sine-Gordon model is discussed and analyzed within the framework of the
renormalization group theory. A perturbative renormalization group procedure is
carried out through a decomposition of the sine-Gordon field in slow and fast
modes. An effective slow modes's theory is derived and re-scaled to obtain the
model's flow equations. The resulting Kosterlitz-Thouless phase diagram is
obtained and discussed in detail. The theory's gap is estimated in terms of the
sine-Gordon model paramaters. The mapping between the sine-Gordon model and
models for interacting electrons in one dimension, such as the g-ology model
and Hubbard model, is discussed and the previous renormalization group results,
obtained for the sine-Gordon model, are thus borrowed to describe different
aspects of Luttinger liquid systems, such as the nature of its excitations and
phase transitions. The calculations are carried out in a thorough and
pedagogical manner, aiming the reader with no previous experience with the
sine-Gordon model or the renormalization group approach.Comment: 44 pages, 7 figure
Nonlinear Elasticity in Biological Gels
Unlike most synthetic materials, biological materials often stiffen as they
are deformed. This nonlinear elastic response, critical for the physiological
function of some tissues, has been documented since at least the 19th century,
but the molecular structure and the design principles responsible for it are
unknown. Current models for this response require geometrically complex ordered
structures unique to each material. In this Article we show that a much simpler
molecular theory accounts for strain stiffening in a wide range of molecularly
distinct biopolymer gels formed from purified cytoskeletal and extracellular
proteins. This theory shows that systems of semi-flexible chains such as
filamentous proteins arranged in an open crosslinked meshwork invariably
stiffen at low strains without the need for a specific architecture or multiple
elements with different intrinsic stiffnesses.Comment: 23 pages, 5 figures, submitted to Natur
Fluid dynamics - Turbulence without inertia
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62901/1/405027a0.pd
Chaos and Quantum Thermalization
We show that a bounded, isolated quantum system of many particles in a
specific initial state will approach thermal equilibrium if the energy
eigenfunctions which are superposed to form that state obey {\it Berry's
conjecture}. Berry's conjecture is expected to hold only if the corresponding
classical system is chaotic, and essentially states that the energy
eigenfunctions behave as if they were gaussian random variables. We review the
existing evidence, and show that previously neglected effects substantially
strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas
as an explicit example of a many-body system which is known to be classically
chaotic, and show that an energy eigenstate which obeys Berry's conjecture
predicts a Maxwell--Boltzmann, Bose--Einstein, or Fermi--Dirac distribution for
the momentum of each constituent particle, depending on whether the wave
functions are taken to be nonsymmetric, completely symmetric, or completely
antisymmetric functions of the positions of the particles. We call this
phenomenon {\it eigenstate thermalization}. We show that a generic initial
state will approach thermal equilibrium at least as fast as
, where is the uncertainty in the total energy
of the gas. This result holds for an individual initial state; in contrast to
the classical theory, no averaging over an ensemble of initial states is
needed. We argue that these results constitute a new foundation for quantum
statistical mechanics.Comment: 28 pages in Plain TeX plus 2 uuencoded PS figures (included); minor
corrections only, this version will be published in Phys. Rev. E;
UCSB-TH-94-1
Rapidly Rotating Atomic Gases
This article reviews developments in the theory of rapidly rotating
degenerate atomic gases. The main focus is on the equilibrium properties of a
single component atomic Bose gas, which (at least at rest) forms a
Bose-Einstein condensate. Rotation leads to the formation of quantized vortices
which order into a vortex array, in close analogy with the behaviour of
superfluid helium. Under conditions of rapid rotation, when the vortex density
becomes large, atomic Bose gases offer the possibility to explore the physics
of quantized vortices in novel parameter regimes. First, there is an
interesting regime in which the vortices become sufficiently dense that their
cores -- as set by the healing length -- start to overlap. In this regime, the
theoretical description simplifies, allowing a reduction to single particle
states in the lowest Landau level. Second, one can envisage entering a regime
of very high vortex density, when the number of vortices becomes comparable to
the number of particles in the gas. In this regime, theory predicts the
appearance of a series of strongly correlated phases, which can be viewed as
{\it bosonic} versions of fractional quantum Hall states. This article
describes the equilibrium properties of rapidly rotating atomic Bose gases in
both the mean-field and the strongly correlated regimes, and related
theoretical developments for Bose gases in lattices, for multi-component Bose
gases, and for atomic Fermi gases. The current experimental situation and
outlook for the future are discussed in the light of these theoretical
developments.Comment: Published version + minor correction
Protocol for the saMS trial (supportive adjustment for multiple sclerosis): a randomized controlled trial comparing cognitive behavioral therapy to supportive listening for adjustment to multiple sclerosis
BackgroundMultiple Sclerosis (MS) is an incurable, chronic, potentially progressive and unpredictable disease of the central nervous system. The disease produces a range of unpleasant and debilitating symptoms, which can have a profound impact including disrupting activities of daily living, employment, income, relationships, social and leisure activities, and life goals. Adjusting to the illness is therefore particularly challenging. This trial tests the effectiveness of a cognitive behavioural intervention compared to supportive listening to assist adjustment in the early stages of MS.MethodsThis is a two arm randomized multi-centre parallel group controlled trial. 122 consenting participants who meet eligibility criteria will be randomly allocated to receive either Cognitive Behavioral Therapy or Supportive Listening. Eight one hour sessions of therapy (delivered over a period of 10 weeks) will be delivered by general nurses trained in both treatments. Self-report questionnaire data will be collected at baseline (0 weeks), mid-therapy (week 5 of therapy), post-therapy (15 weeks) and at six months (26 weeks) and twelve months (52 weeks) follow-up. Primary outcomes are distress and MS-related social and role impairment at twelve month follow-up. Analysis will also consider predictors and mechanisms of change during therapy. In-depth interviews to examine participants’ experiences of the interventions will be conducted with a purposively sampled sub-set of the trial participants. An economic analysis will also take place. DiscussionThis trial is distinctive in its aims in that it aids adjustment to MS in a broad sense. It is not a treatment specifically for depression. Use of nurses as therapists makes the interventions potentially viable in terms of being rolled out in the NHS. The trial benefits from incorporating patient input in the development and evaluation stages. The trial will provide important information about the efficacy, cost-effectiveness and acceptability of the interventions as well as mechanisms of psychosocial adjustment.Trial registrationCurrent Controlled Trials ISRCTN91377356<br/
Quantum Point Contacts and Coherent Electron Focusing
I. Introduction
II. Electrons at the Fermi level
III. Conductance quantization of a quantum point contact
IV. Optical analogue of the conductance quantization
V. Classical electron focusing
VI. Electron focusing as a transmission problem
VII. Coherent electron focusing (Experiment, Skipping orbits and magnetic
edge states, Mode-interference and coherent electron focusing)
VIII. Other mode-interference phenomenaComment: #3 of a series of 4 legacy reviews on QPC'
Imbibition in Disordered Media
The physics of liquids in porous media gives rise to many interesting
phenomena, including imbibition where a viscous fluid displaces a less viscous
one. Here we discuss the theoretical and experimental progress made in recent
years in this field. The emphasis is on an interfacial description, akin to the
focus of a statistical physics approach. Coarse-grained equations of motion
have been recently presented in the literature. These contain terms that take
into account the pertinent features of imbibition: non-locality and the
quenched noise that arises from the random environment, fluctuations of the
fluid flow and capillary forces. The theoretical progress has highlighted the
presence of intrinsic length-scales that invalidate scale invariance often
assumed to be present in kinetic roughening processes such as that of a
two-phase boundary in liquid penetration. Another important fact is that the
macroscopic fluid flow, the kinetic roughening properties, and the effective
noise in the problem are all coupled. Many possible deviations from simple
scaling behaviour exist, and we outline the experimental evidence. Finally,
prospects for further work, both theoretical and experimental, are discussed.Comment: Review article, to appear in Advances in Physics, 53 pages LaTe
On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
We propose a first implementation of the integrand-reduction method for
two-loop scattering amplitudes. We show that the residues of the amplitudes on
multi-particle cuts are polynomials in the irreducible scalar products
involving the loop momenta, and that the reduction of the amplitudes in terms
of master integrals can be realized through polynomial fitting of the
integrand, without any apriori knowledge of the integral basis. We discuss how
the polynomial shapes of the residues determine the basis of master integrals
appearing in the final result. We present a four-dimensional constructive
algorithm that we apply to planar and non-planar contributions to the 4- and
5-point MHV amplitudes in N=4 SYM. The technique hereby discussed extends the
well-established analogous method holding for one-loop amplitudes, and can be
considered a preliminary study towards the systematic reduction at the
integrand-level of two-loop amplitudes in any gauge theory, suitable for their
automated semianalytic evaluation.Comment: 26 pages, 11 figure
Physics of Neutron Star Crusts
The physics of neutron star crusts is vast, involving many different research
fields, from nuclear and condensed matter physics to general relativity. This
review summarizes the progress, which has been achieved over the last few
years, in modeling neutron star crusts, both at the microscopic and macroscopic
levels. The confrontation of these theoretical models with observations is also
briefly discussed.Comment: 182 pages, published version available at
<http://www.livingreviews.org/lrr-2008-10
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