589 research outputs found
Fragility of String Orders
One-dimensional gapped systems are often characterized by a 'hidden'
non-local order parameter, the so-called string order. Due to the gap,
thermodynamic properties are robust against a weak higher-dimensional coupling
between such chains or ladders. To the contrary, we find that the string order
is not stable and decays for arbitrary weak inter-chain or inter-ladder
coupling. We investigate the vanishing of the order for three different
systems: spin-one Haldane chains, band insulators, and the transverse-field
Ising model. Using perturbation theory and bosonization, we show that the
fragility of the string order arises from non-local commutation relations
between the non-local order parameter and the perturbation.Comment: 7 pages, 3 figures. Published versio
Nonaffine Correlations in Random Elastic Media
Materials characterized by spatially homogeneous elastic moduli undergo
affine distortions when subjected to external stress at their boundaries, i.e.,
their displacements \uv (\xv) from a uniform reference state grow linearly
with position \xv, and their strains are spatially constant. Many materials,
including all macroscopically isotropic amorphous ones, have elastic moduli
that vary randomly with position, and they necessarily undergo nonaffine
distortions in response to external stress. We study general aspects of
nonaffine response and correlation using analytic calculations and numerical
simulations. We define nonaffine displacements \uv' (\xv) as the difference
between \uv (\xv) and affine displacements, and we investigate the
nonaffinity correlation function
and related functions. We introduce four model random systems with random
elastic moduli induced by locally random spring constants, by random
coordination number, by random stress, or by any combination of these. We show
analytically and numerically that scales as A |\xv|^{-(d-2)}
where the amplitude is proportional to the variance of local elastic moduli
regardless of the origin of their randomness. We show that the driving force
for nonaffine displacements is a spatial derivative of the random elastic
constant tensor times the constant affine strain. Random stress by itself does
not drive nonaffine response, though the randomness in elastic moduli it may
generate does. We study models with both short and long-range correlations in
random elastic moduli.Comment: 22 Pages, 18 figures, RevTeX
Competition between Vortex Unbinding and Tunneling in an Optical Lattice
We study a system of two-dimensional Bose gases trapped in minima of a deep
one-dimensional optical lattice potential. Increasing the tunneling amplitude
between adjacent gases drives a deconfinement transition to a phase where
coherence is established between neighboring two-dimensional gases. We compute
the signature of this transition in the interference pattern of the system as
well as in its rotational response, which provides a direct measurement of the
superfluidity in the system.Comment: 4+ pages, 1 figur
The Smectic - Phase Transition in Biaxial Disordered Environments
We study the smectic - phase transition in biaxial disordered
environments, e.g. fully anisotropic aerogel. We find that both the and
phases belong to the universality class of the "XY Bragg glass", and therefore
have quasi-long-ranged translational smectic order. The phase transition itself
belongs to a new universality class, which we study using an
expansion. We find a stable fixed point, which implies a continuous transition,
the critical exponents of which we calculate
Concentration of rare earth elements (Sc, y, la, ce, nd, sm) in bauxite residue (red mud) obtained by water and alkali leaching of bauxite sintering dust
One of the potential sources of rare-earth elements (REE) is the industrial waste known as red mud (bauxite residue), in which the majority of REE from the initial bauxite are concentrated via the Bayer process. Therefore, the studies of the subject, both in Russia and outside, focus almost exclusively on red mud processing. This article looks into the possibility of REE concentration into red mud by leaching an intermediate product of the bauxite sintering process at Russian alumina refineries, namely electrostatic precipitator (ESP) dust. The experimental works were performed by X-ray diffraction (XRD)and electron probe microanalysis (EPMA) of the sinter and sinter dust. The determination of major and rare-earth elements in the sinter from the rotary kilns and in the ESP dust before and after leaching was carried out by X-ray fluorescence (XRF) and plasma mass spectrometry (ICP-MS). The study showed that it is possible to obtain red mud that contains three times more REE than traditional waste red mud after two-stage leaching ESP dust in the water at 95◦ C followed by leaching in an alkaline-aluminate liquor at 240◦ C. The shrinking core model was used to study the kinetics of leaching of the original ESP dust and water-treated dust in alkaline-aluminate liquor. The study showed the change in the limiting stage of the alkaline leaching process after water treatment, with the activation energy growing from 24.98 to 33.19 kJ/mol. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Russian Science Foundation, RSF: 18-19-00186Funding: The research was funded by the Russian Science Foundation, grant number 18-19-00186
Phase separation in fluids exposed to spatially periodic external fields
We consider the liquid-vapor type phase transition for fluids confined within
spatially periodic external fields. For a fluid in d=3 dimensions, the periodic
field induces an additional phase, characterized by large density modulations
along the field direction. At the triple point, all three phases (modulated,
vapor, and liquid) coexist. At temperatures slightly above the triple point and
for low (high) values of the chemical potential, two-phase coexistence between
the modulated phase and the vapor (liquid) is observed. We study this
phenomenon using computer simulations and mean-field theory for the Ising
model. The theory shows that, in order for the modulated phase to arise, the
field wavelength must exceed a threshold value. We also find an extremely low
tension of the interface between the modulated phase and the vapor/liquid
phases. The tension is of the order 10^{-4} kB T per squared lattice spacing,
where kB is the Boltzmann constant, and T the temperature. In order to detect
such low tensions, a new simulation method is proposed. We also consider the
case of d=2 dimensions. The modulated phase then does not survive, leading to a
radically different phase diagram.Comment: 11 pages, 14 figure
Cross-correlations in scaling analyses of phase transitions
Thermal or finite-size scaling analyses of importance sampling Monte Carlo
time series in the vicinity of phase transition points often combine different
estimates for the same quantity, such as a critical exponent, with the intent
to reduce statistical fluctuations. We point out that the origin of such
estimates in the same time series results in often pronounced
cross-correlations which are usually ignored even in high-precision studies,
generically leading to significant underestimation of statistical fluctuations.
We suggest to use a simple extension of the conventional analysis taking
correlation effects into account, which leads to improved estimators with often
substantially reduced statistical fluctuations at almost no extra cost in terms
of computation time.Comment: 4 pages, RevTEX4, 3 tables, 1 figur
Pairing Fluctuations Determine Low Energy Electronic Spectra in Cuprate Superconductors
We describe here a minimal theory of tight binding electrons moving on the
square planar Cu lattice of the hole-doped cuprates and mixed quantum
mechanically with pairs of them (Cooper pairs). Superconductivity occurring at
the transition temperature T_c is the long-range, d-wave symmetry phase
coherence of these Cooper pairs. Fluctuations necessarily associated with
incipient long-range superconducting order have a generic large distance
behaviour near T_c. We calculate the spectral density of electrons coupled to
such Cooper pair fluctuations and show that features observed in Angle Resolved
Photo Emission Spectroscopy (ARPES) experiments on different cuprates above T_c
as a function of doping and temperature emerge naturally in this description.
These include `Fermi arcs' with temperature-dependent length and an antinodal
pseudogap which fills up linearly as the temperature increases towards the
pseudogap temperature. Our results agree quantitatively with experiment. Below
T_c, the effects of nonzero superfluid density and thermal fluctuations are
calculated and compared successfully with some recent ARPES experiments,
especially the observed `bending' or deviation of the superconducting gap from
the canonical d-wave form.Comment: 14 pages, 8 figures (to appear in Phys. Rev. B
Atom-light crystallization of BECs in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration
The self-organization of a Bose-Einstein condensate in a transversely pumped
optical cavity is a process akin to crystallization: when pumped by a laser of
sufficient intensity, the coupled matter and light fields evolve,
spontaneously, into a spatially modulated pattern, or crystal, whose lattice
structure is dictated by the geometry of the cavity. In cavities having
multiple degenerate modes, the quasi-continuum of possible lattice
arrangements, and the continuous symmetry breaking associated with the adoption
of a particular lattice arrangement, give rise to phenomena such as phonons,
defects, and frustration, which have hitherto been unexplored in ultracold
atomic settings involving neutral atoms. The present work develops a
nonequilibrium field-theoretic approach to explore the self-organization of a
BEC in a pumped, lossy optical cavity. We find that the transition is well
described, in the regime of primary interest, by an effective equilibrium
theory. At nonzero temperatures, the self-organization occurs via a
fluctuation-driven first-order phase transition of the Brazovskii class; this
transition persists to zero temperature, and crosses over into a quantum phase
transition of a new universality class. We make further use of our
field-theoretic description to investigate the role of nonequilibrium
fluctuations on the self-organization transition, as well as to explore the
nucleation of ordered-phase droplets, the nature and energetics of topological
defects, supersolidity in the ordered phase, and the possibility of frustration
controlled by the cavity geometry. In addition, we discuss the range of
experimental parameters for which we expect the phenomena described here to be
observable, along with possible schemes for detecting ordering and fluctuations
via either atomic correlations or the correlations of the light emitted from
the cavity.Comment: 34 pages, 13 figures; follow up to Nat. Phys. 5, 845 (2009
Elastic Instability Triggered Pattern Formation
Recent experiments have exploited elastic instabilities in membranes to
create complex patterns. However, the rational design of such structures poses
many challenges, as they are products of nonlinear elastic behavior. We pose a
simple model for determining the orientational order of such patterns using
only linear elasticity theory which correctly predicts the outcomes of several
experiments. Each element of the pattern is modeled by a "dislocation dipole"
located at a point on a lattice, which then interacts elastically with all
other dipoles in the system. We explicitly consider a membrane with a square
lattice of circular holes under uniform compression and examine the changes in
morphology as it is allowed to relax in a specified direction.Comment: 15 pages, 7 figures, the full catastroph
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