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Theory of Coherent Van der Waals Matter
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
457.41582%
#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics#Condensed Matter - Strongly Correlated Electrons
We explain in depth the previously proposed theory of the coherent Van der
Waals(cVdW) interaction - the counterpart of Van der Waals (VdW) force -
emerging in spatially coherently fluctuating electromagnetic fields. We show
that cVdW driven matter is dominated by many body interactions, which are
significantly stronger than those found in standard Van der Waals (VdW)
systems. Remarkably, the leading 2- and 3-body interactions are of the same
order with respect to the distance $(\propto R^{-6})$, in contrast to the
usually weak VdW 3-body effects ($\propto R^{-9}$). From a microscopic theory
we show that the anisotropic cVdW many body interactions drive the formation of
low-dimensional structures such as chains, membranes and vesicles with very
unusual, non-local properties. In particular, cVdW chains display a
logarithmically growing stiffness with the chain length, while cVdW membranes
have a bending modulus growing linearly with their size. We argue that the cVdW
anisotropic many body forces cause local cohesion but also a negative effective
"surface tension". We conclude by deriving the equation of state for cVdW
materials and propose new experiments to test the theory, in particular the
unusual 3-body nature of cVdW.; Comment: 26 pages...
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Self Assembly of Soft Matter Quasicrystals and Their Approximants
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
457.00207%
#Condensed Matter - Soft Condensed Matter#Condensed Matter - Mesoscale and Nanoscale Physics#Condensed Matter - Materials Science
The surprising recent discoveries of quasicrystals and their approximants in
soft matter systems poses the intriguing possibility that these structures can
be realized in a broad range of nano- and micro-scale assemblies. It has been
theorized that soft matter quasicrystals and approximants are largely
entropically stabilized, but the thermodynamic mechanism underlying their
formation remains elusive. Here, we use computer simulation and free energy
calculations to demonstrate a simple design heuristic for assembling
quasicrystals and approximants in soft matter systems. Our study builds on
previous simulation studies of the self-assembly of dodecagonal quasicrystals
and approximants in minimal systems of spherical particles with complex,
highly-specific interaction potentials. We demonstrate an alternative
entropy-based approach for assembling dodecagonal quasicrystals and
approximants based solely on particle functionalization and shape, thereby
recasting the interaction-potential-based assembly strategy in terms of
simpler-to-achieve bonded and excluded-volume interactions. Here, spherical
building blocks are functionalized with mobile surface entities to encourage
the formation of structures with low surface contact area, including
non-close-packed and polytetrahedral structures. The building blocks also
possess shape polydispersity...
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Dynamics of Symmetry Breaking Out of Equilibrium: From Condensed Matter to QCD and the Early Universe
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/09/1999
Relevância na Pesquisa
455.86555%
The dynamics of symmetry breaking during out of equilibrium phase transitions
is a topic of great importance in many disciplines, from condensed matter to
particle physics and early Universe cosmology with definite experimental
impact. In these notes we provide a summary of the relevant aspects of the
dynamics of symmetry breaking in many different fields with emphasis on the
experimental realizations. In condensed matter we address the dynamics of phase
ordering, the emergence of condensates, coarsening and dynamical scaling. In
QCD the possibility of disoriented chiral condensates of pions emerging during
a strongly out of equilibrium phase transition is discussed. We elaborate on
the dynamics of phase ordering in phase transitions in the Early Universe, in
particular the emergence of condensates and scaling in FRW cosmologies. We
mention some experimental efforts in different fields that study this wide
ranging phenomena and offer a quantitative theoretical description both at the
phenomenological level in condensed matter, introducing the scaling hypothesis
as well as at a microscopic level in quantum field theories. The emergence of
semiclassical condensates and a dynamical length scale is shown in detail, in
quantum field theory this length scale is constrained by causality. The large N
limit provides a natural bridge to compare the solutions in different settings
and to establish similarities and differences.; Comment: 35 pages...
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Cold Rydberg atoms for quantum simulation of exotic condensed matter interactions
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/10/2013
Relevância na Pesquisa
457.72773%
#Condensed Matter - Strongly Correlated Electrons#Condensed Matter - Superconductivity#Physics - Atomic Physics
Quantum simulators could provide an alternative to numerical simulations for
understanding minimal models of condensed matter systems in a controlled way.
Typically, cold atom systems are used to simulate e.g. Hubbard models. In this
paper, we discuss a range of exotic interactions that can be formed when cold
Rydberg atoms are loaded into optical lattices with unconventional geometries;
such as long-range electron-phonon interactions and extended Coulomb like
interactions. We show how these can lead to proposals for quantum simulators
for complex condensed matter systems such as superconductors. Continuous time
quantum Monte Carlo is used to compare the proposed schemes with the physics
found in traditional condensed matter Hamiltonians for systems such as high
temperature superconductors.
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The Onset of Phase Transitions in Condensed Matter and Relativistic QFT
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/01/2000
Relevância na Pesquisa
457.72773%
Kibble and Zurek have provided a unifying causal picture for the appearance
of topological defects like cosmic strings or vortices at the onset of phase
transitions in relativistic QFT and condensed matter systems respectively.
There is no direct experimental evidence in QFT, but in condensed matter the
predictions are largely, but not wholly, supported in superfluid experiments on
liquid helium. We provide an alternative picture for the initial appearance of
strings/vortices that is commensurate with all the experimental evidence from
condensed matter and consider some of its implications for QFT.; Comment: 37 pages, to be published in Condensed Matter Physics, 2000
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Local structure of supercritical matter
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/05/2014
Relevância na Pesquisa
457.9382%
#Condensed Matter - Statistical Mechanics#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Materials Science#Condensed Matter - Soft Condensed Matter
The supercritical state is currently viewed as uniform on the
pressure-temperature phase diagram. Supercritical fluids have the dynamic
motions of a gas but are able to dissolve materials like a liquid. They have
started to be deployed in many important industrial applications stimulating
fundamental theoretical work and development of experimental techniques. Here,
we have studied local structure of supercritical matter by calculating static
structure factor, mean force potential, self-diffusion, first coordination
shell number and pair distribution function within very wide temperature
ranges. Our results show a monotonic disappearance of medium-range order
correlations at elevated temperatures providing direct evidence for structural
crossover in the reciprocal and real spaces. Importantly, the discovered
structural crossover in the reciprocal space is fundamentally inter-related to
structural crossover in the real space, granting new unexpected interlinks
between operating system properties in the supercritical state. Finally, we
discuss an evolution analysis of the local structure and important implications
for an experimental detection of structural monotonic transitions in the
supercritical matter.; Comment: 4 pages, 3 figures
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Visibility of the Amplitude (Higgs) Mode in Condensed Matter
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
457.72773%
#Condensed Matter - Superconductivity#Condensed Matter - Quantum Gases#Condensed Matter - Statistical Mechanics#Condensed Matter - Strongly Correlated Electrons
The amplitude mode is a ubiquitous collective excitation in condensed matter
systems with broken continuous symmetry. It is expected in antiferromagnets,
short coherence length superconductors, charge density waves, and lattice Bose
condensates. Its detection is a valuable test of the corresponding field
theory, and its mass gap measures the proximity to a quantum critical point.
However, since the amplitude mode can decay into low-energy Goldstone modes,
its experimental visibility has been questioned. Here we show that the
visibility depends on the symmetry of the measured susceptibility. The
longitudinal susceptibility diverges at low frequency as \chi_{\sigma\sigma} ~
i/\omega (d=2) or log(1/|\omega|) (d=3), which can completely obscure the
amplitude peak. In contrast, the scalar susceptibility is suppressed by four
extra powers of frequency, exposing the amplitude peak throughout the ordered
phase. We discuss experimental setups for measuring the scalar susceptibility.
The conductivity of the O(2) theory (relativistic superfluid) is a scalar
response and therefore exhibits suppressed absorption below the Higgs mass
threshold, \sigma ~ \omega^{2d+1}. In layered, short coherence length
superconductors, (relevant e.g. to cuprates) this threshold is raised by the
interlayer plasma frequency.; Comment: 17 pages...
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What can gauge-gravity duality teach us about condensed matter physics?
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
456.05973%
I discuss the impact of gauge-gravity duality on our understanding of two
classes of systems: conformal quantum matter and compressible quantum matter.
The first conformal class includes systems, such as the boson Hubbard model
in two spatial dimensions, which display quantum critical points described by
conformal field theories. Questions associated with non-zero temperature
dynamics and transport are difficult to answer using conventional field
theoretic methods. I argue that many of these can be addressed systematically
using gauge-gravity duality, and discuss the prospects for reliable computation
of low frequency correlations.
Compressible quantum matter is characterized by the smooth dependence of the
charge density, associated with a global U(1) symmetry, upon a chemical
potential. Familiar examples are solids, superfluids, and Fermi liquids, but
there are more exotic possibilities involving deconfined phases of gauge fields
in the presence of Fermi surfaces. I survey the compressible systems studied
using gauge-gravity duality, and discuss their relationship to the condensed
matter classification of such states. The gravity methods offer hope of a
deeper understanding of exotic and strongly-coupled compressible quantum
states.; Comment: 34 pages...
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Thermodynamic QED Coherence in Condensed Matter: Microscopic Basis of Thermal Superradiance
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/09/2002
Relevância na Pesquisa
457.72773%
Electromagnetic superradiant field coherence exists in a condensed matter
system if the electromagnetic field oscillators undergo a mean displacement.
Transitions into thermal states with ordered superradiant phases have been
shown to theoretically exist in Dicke-Preparata models. The theoretical
validity of these models for condensed matter has been called into question due
to non-relativistic diamagnetic terms in the electronic Hamiltonian. The
microscopic bases of Dicke-Preparata thermal superradiance for realistic
macroscopic systems are explored in this work. The impossibility of diaelectric
correlations in condensed matter systems (via the Landau-Lifshitz theorem)
provides a strong theoretical basis for understanding the physical reality of
condensed matter thermodynamic superradiant phases.; Comment: 11 pages, no figures, LaTeX format
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Finite temperature effects in Bose-Einstein Condensed dark matter halos
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
457.9382%
#Astrophysics - Astrophysics of Galaxies#Condensed Matter - Quantum Gases#General Relativity and Quantum Cosmology
Once the critical temperature of a cosmological boson gas is less than the
critical temperature, a Bose-Einstein Condensation process can always take
place during the cosmic history of the universe. Zero temperature condensed
dark matter can be described as a non-relativistic, Newtonian gravitational
condensate, whose density and pressure are related by a barotropic equation of
state, with barotropic index equal to one. In the present paper we analyze the
effects of the finite dark matter temperature on the properties of the
Bose-Einstein Condensed dark matter halos. We formulate the basic equations
describing the finite temperature condensate, representing a generalized
Gross-Pitaevskii equation that takes into account the presence of the thermal
cloud. The static condensate and thermal cloud in thermodynamic equilibrium is
analyzed in detail, by using the Hartree-Fock-Bogoliubov and Thomas-Fermi
approximations. The condensed dark matter and thermal cloud density and mass
profiles at finite temperatures are explicitly obtained. Our results show that
when the temperature of the condensate and of the thermal cloud are much
smaller than the critical Bose-Einstein transition temperature, the zero
temperature density and mass profiles give an excellent description of the dark
matter halos. However...
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Spin-polarized muons in condensed matter physics
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/07/2002
Relevância na Pesquisa
457.72773%
#Condensed Matter - Strongly Correlated Electrons#Condensed Matter - Materials Science#Condensed Matter - Superconductivity
A positive muon is a spin-1/2 particle. Beams of muons with all their spins
polarized can be prepared and subsequently implanted in various types of
condensed matter. The subsequent precession and relaxation of their spins can
then be used to investigate a variety of static and dynamic effects in a sample
and hence to deduce properties concerning magnetism, superconductivity and
molecular dynamics. Though strictly a lepton, and behaving essentially like a
heavy electron, it is convenient to think of a muon as a light proton, and it
is often found with a captured electron in a hydrogen-like atom known as
muonium. This article outlines the principles of various experimental
techniques which involve implanted muons and describes some recent
applications. The use of muons in condensed matter physics has shed new light
on subjects as diverse as passivation in semiconductors, frustrated spin
systems, vortex lattice melting, and quantum diffusion of light particles.; Comment: 17 pages, 21 figures, review article
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The Fermi Gases and Superfluids: Short Review of Experiment and Theory for Condensed Matter Physicists
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/02/2012
Relevância na Pesquisa
456.84492%
The study of ultracold atomic Fermi gases is a rapidly exploding subject
which is defining new directions in condensed matter and atomic physics. Quite
generally what makes these gases so important is their remarkable tunability
and controllability. Using a Feshbach resonance one can tune the attractive
two-body interactions from weak to strong and thereby make a smooth crossover
from a BCS superfluid of Cooper pairs to a Bose-Einstein condensed superfluid.
Furthermore, one can tune the population of the two spin states, allowing
observation of exotic spin-polarized superfluids, such as the Fulde Ferrell
Larkin Ovchinnikov (FFLO) phase. A wide array of powerful characterization
tools, which often have direct condensed matter analogues, are available to the
experimenter. In this Chapter, we present a general review of the status of
these Fermi gases with the aim of communicating the excitement and great
potential of the field.; Comment: 34 pages, 15 figures. To appear as a chapter in "Contemporary
Concepts of Condensed Matter Science", Elsevier
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Shock (Blast) Mitigation by "Soft" Condensed Matter
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
458.39523%
It is a common point that "soft" condensed matter (like granular materials or
foams) can reduce damage caused by impact or explosion. It is attributed to
their ability to absorb significant energy. This is certainly the case for a
quasistatic type of deformation at low velocity of impact where such materials
are widely used for packing of fragile devices. At the same time a mitigation
of blast phenomena must take into account shock wave properties of "soft"
matter which very often exhibit highly nonlinear, highly heterogeneous and
dissipative behavior. This paper considers applications of "soft" condensed
matter for blast mitigation using simplified approach, presents analysis of
some anomalous effects and suggestions for future research in this exciting
area.; Comment: 12 pages, 12 figures
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Non-equilibrium phase transitions in condensed matter and cosmology: spinodal decomposition, condensates and defects
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/03/1999
Relevância na Pesquisa
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These lectures address the dynamics of phase ordering out of equilibrium in
condensed matter and in quantum field theory in cosmological settings,
emphasizing their similarities and differences. In condensed matter we describe
the phenomenological approach based on the Time Dependent Ginzburg-Landau
(TDGL) description. After a general discussion of the main experimental and
theoretical features of phase ordering kinetics and the description of linear
(spinodal) instabilities we introduce the scaling hypothesis and show how a
dynamical correlation length emerges in the large N limit in condensed matter
systems. The large N approximation is a powerful tool in quantum field theory
that allows the study of non-perturbative phenomena in a consistent manner. We
study the exact solution to the dynamics after a quench in this limit in
Minkowski space time and in radiation dominated Friedman-Robertson-Walker
Cosmology. There are some remarkable similarities between these very different
settings such as the emergence of a scaling regime and of a dynamical
correlation length at late times that describe the formation and growth of
ordered regions. In quantum field theory and cosmology this length scale is
constrained by causality and its growth in time is also associated with
coarsening and the onset of a condensate. We provide a density matrix
interpretation of the formation of defects and the classicalization of quantum
fluctuations.; Comment: 23 pages (revtex)...
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Microscopic theory of non-adiabatic response in real and imaginary time
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
549.4809%
We present a general approach to describe slowly driven quantum systems both
in real and imaginary time. We highlight many similarities, qualitative and
quantitative, between real and imaginary time evolution. We discuss how the
metric tensor and the Berry curvature can be extracted from both real and
imaginary time simulations as a response of physical observables. For quenches
ending at or near the quantum critical point, we show the utility of the
scaling theory for detecting the location of the quantum critical point by
comparing sweeps at different velocities. We briefly discuss the universal
relaxation to equilibrium of systems after a quench. We finally review recent
developments of quantum Monte Carlo methods for studying imaginary-time
evolution. We illustrate our findings with explicit calculations using the
transverse field Ising model in one dimension.; Comment: 22 pages, 10 figures, revised version, contribution to the special
issue of J. Phys. Condensed Matter: "Condensed matter analogues of
cosmology", edited by T. Kibble and Ajit Srivastava
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The Mechanics and Statistics of Active Matter
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/04/2010
Relevância na Pesquisa
456.05973%
#Condensed Matter - Soft Condensed Matter#Condensed Matter - Statistical Mechanics#Physics - Biological Physics
Active particles contain internal degrees of freedom with the ability to take
in and dissipate energy and, in the process, execute systematic movement.
Examples include all living organisms and their motile constituents such as
molecular motors. This article reviews recent progress in applying the
principles of nonequilibrium statistical mechanics and hydrodynamics to form a
systematic theory of the behaviour of collections of active particles -- active
matter -- with only minimal regard to microscopic details. A unified view of
the many kinds of active matter is presented, encompassing not only living
systems but inanimate analogues. Theory and experiment are discussed side by
side.; Comment: This review is to appear in volume 1 of the Annual Review of
Condensed Matter Physics in July 2010 and is posted here with permission from
that journal
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Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/02/2015
Relevância na Pesquisa
457.41582%
#Condensed Matter - Soft Condensed Matter#Condensed Matter - Mesoscale and Nanoscale Physics#Condensed Matter - Materials Science#Physics - Chemical Physics#Physics - Fluid Dynamics
Spatial confinement in nanoporous media affects the structure, thermodynamics
and mobility of molecular soft matter often markedly. This article reviews
thermodynamic equilibrium phenomena, such as physisorption, capillary
condensation, crystallisation, self-diffusion, and structural phase transitions
as well as selected aspects of the emerging field of spatially confined,
non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow
phenomena, and imbibition front broadening in nanoporous materials. The
observations in the nanoscale systems are related to the corresponding bulk
phenomenologies. The complexity of the confined molecular species is varied
from simple building blocks, like noble gas atoms, normal alkanes and alcohols
to liquid crystals, polymers, ionic liquids, proteins and water. Mostly,
experiments with mesoporous solids of alumina, carbon, gold, silica, and
silicon having pore diameters ranging from a few up to 50 nanometers are
presented. The observed peculiarities of nanopore-confined condensed matter are
also discussed with regard to applications. A particular emphasis is put on
texture formation upon crystallisation in nanoporous media, a topic both of
high fundamental interest and of increasing nanotechnological importance...
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Phase Separation in Soft Matter: Concept of Dynamic Asymmetry
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/07/2013
Relevância na Pesquisa
456.05973%
#Condensed Matter - Soft Condensed Matter#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics#Physics - Chemical Physics
Phase separation is a fundamental phenomenon that produces spatially
heterogeneous patterns in soft matter. In this Lecture Note we show that phase
separation in these materials generally belongs to what we call "viscoelastic
phase separation", where the morphology is determined by the mechanical balance
of not only the thermodynamic force (interface tension) but also the
viscoelastic force. The origin of the viscoelastic force is dynamic asymmetry
between the components of a mixture, which can be caused by either a size
disparity or a difference in the glass transition temperature between the
components. We stress that such dynamic asymmetry generally exists in soft
matter. The key is that dynamical asymmetry leads to a non-trivial coupling
between the concentration, velocity, and stress fields. Viscoelastic phase
separation can be explained by viscoelastic relaxation in pattern evolution and
the resulting switching of the relevant order parameter, which are induced by
the competition between the deformation rate of phase separation and the
slowest mechanical relaxation rate of a system. We also discuss an intimate
link of viscoelastic phase separation, where deformation fields are
spontaneously generated by phase separation itself...
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Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
458.39523%
#Condensed Matter - Soft Condensed Matter#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Materials Science#Condensed Matter - Statistical Mechanics
Local structure characterization with the bond-orientational order parameters
q4, q6, ... introduced by Steinhardt et al. has become a standard tool in
condensed matter physics, with applications including glass, jamming, melting
or crystallization transitions and cluster formation. Here we discuss two
fundamental flaws in the definition of these parameters that significantly
affect their interpretation for studies of disordered systems, and offer a
remedy. First, the definition of the bond-orientational order parameters
considers the geometrical arrangement of a set of neighboring spheres NN(p)
around a given central particle p; we show that procedure to select the spheres
constituting the neighborhood NN(p) can have greater influence on both the
numerical values and qualitative trend of ql than a change of the physical
parameters, such as packing fraction. Second, the discrete nature of
neighborhood implies that NN(p) is not a continuous function of the particle
coordinates; this discontinuity, inherited by ql, leads to a lack of robustness
of the ql as structure metrics. Both issues can be avoided by a morphometric
approach leading to the robust Minkowski structure metrics ql'. These ql' are
of a similar mathematical form as the conventional bond-orientational order
parameters and are mathematically equivalent to the recently introduced
Minkowski tensors [Europhys. Lett. 90...
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Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
Fonte: Universidade Cornell
Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
549.4809%
When a second-order phase transition is crossed at fine rate, the evolution
of the system stops being adiabatic as a result of the critical slowing down in
the neighborhood of the critical point. In systems with a topologically
nontrivial vacuum manifold, disparate local choices of the ground state lead to
the formation of topological defects. The universality class of the transition
imprints a signature on the resulting density of topological defects: It obeys
a power law in the quench rate, with an exponent dictated by a combination of
the critical exponents of the transition. In inhomogeneous systems the
situation is more complicated, as the spontaneous symmetry breaking competes
with bias caused by the influence of the nearby regions that already chose the
new vacuum. As a result, the choice of the broken symmetry vacuum may be
inherited from the neighboring regions that have already entered the new phase.
This competition between the inherited and spontaneous symmetry breaking
enhances the role of causality, as the defect formation is restricted to a
fraction of the system where the front velocity surpasses the relevant sound
velocity and phase transition remains effectively homogeneous. As a
consequence, the overall number of topological defects can be substantially
suppressed. When the fraction of the system is small...
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