389 research outputs found
Pattern orientation in finite domains without boundaries
We investigate the orientation of nonlinear stripe patterns in finite
domains. Motivated by recent experiments, we introduce a control parameter drop
from supercritical inside a domain to subcritical outside without boundary
conditions at the domain border. As a result, stripes align perpendicular to
shallow control parameter drops. For steeper drops, non-adiabatic effects lead
to a surprising orientational transition to parallel stripes with respect to
the borders. We demonstrate this effect in terms of the Brusselator model and
generic amplitude equations
Trionic phase of ultracold fermions in an optical lattice: A variational study
To investigate ultracold fermionic atoms of three internal states (colors) in
an optical lattice, subject to strong attractive interaction, we study the
attractive three-color Hubbard model in infinite dimensions by using a
variational approach. We find a quantum phase transition between a
weak-coupling superconducting phase and a strong-coupling trionic phase where
groups of three atoms are bound to a composite fermion. We show how the
Gutzwiller variational theory can be reformulated in terms of an effective
field theory with three-body interactions and how this effective field theory
can be solved exactly in infinite dimensions by using the methods of dynamical
mean field theory.Comment: 14 PRB pages, 8 figure
Color Superfluidity and "Baryon" Formation in Ultracold Fermions
We study fermionic atoms of three different internal quantum states (colors)
in an optical lattice, which are interacting through attractive on site
interactions, U<0. Using a variational calculation for equal color densities
and small couplings, |U| < |U_C|, a color superfluid state emerges with a
tendency to domain formation. For |U| > |U_C|, triplets of atoms with different
colors form singlet fermions (trions). These phases are the analogies of the
color superconducting and baryonic phases in QCD. In ultracold fermions, this
transition is found to be of second order. Our results demonstrate that quantum
simulations with ultracold gases may shed light on outstanding problems in
quantum field theory.Comment: 4 PRL pages, 1 figur
Systematic extension of the Cahn-Hilliard model for motility-induced phase separation
We consider a continuum model for motility-induced phase separation (MIPS) of
active Brownian particles [J. Chem. Phys. 142, 224149 (2015)]. Using a recently
introduced perturbative analysis [Phys. Rev. E 98, 020604(R) (2018)], we show
that this continuum model reduces to the classic Cahn-Hilliard (CH) model near
the onset of MIPS. This makes MIPS another example of the so-called active
phase separation. We further introduce a generalization of the perturbative
analysis to the next higher order. This results in a generic higher order
extension of the CH model for active phase separation. Our analysis establishes
the mathematical link between the basic mean-field MIPS model on the one hand,
and the leading order and extended CH models on the other hand. Comparing
numerical simulations of the three models, we find that the leading order CH
model agrees nearly perfectly with the full continuum model near the onset of
MIPS. We also give estimates of the control parameter beyond which the higher
order corrections become relevant and compare the extended CH model to recent
phenomenological models.Comment: 10 pages, 5 figure
Periodic patterns displace active phase separation
In this work we identify and investigate a novel bifurcation in conserved
systems. This secondary bifurcation stops active phase separation in its
nonlinear regime. It is then either replaced by an extended, system-filling,
spatially periodic pattern or, in a complementary parameter region, by a novel
hybrid state with spatially alternating homogeneous and periodic states. The
transition from phase separation to extended spatially periodic patterns is
hysteretic. We show that the resulting patterns are multistable, as they show
stability beyond the bifurcation for different wavenumbers belonging to a
wavenumber band. The transition from active phase separation to the hybrid
states is continuous. Both transition scenarios are systems-spanning phenomena
in particle conserving systems. They are predicted with a generic dissipative
model introduced in this work. Candidates for specific systems, in which these
generic secondary transitions are likely to occur, are, for example,
generalized models for motility-induced phase separation in active Brownian
particles, models for cell division or chemotactic systems with conserved
particle dynamics.Comment: 17 pages, 7 figure
Vector meson masses in hot nuclear matter : the effect of quantum corrections
The medium modification of vector meson masses is studied taking into account
the quantum correction effects for the hot and dense hadronic matter. In the
framework of Quantum Hadrodynamics, the quantum corrections from the baryon and
scalar meson sectors were earlier computed using a nonperturbative variational
approach through a realignment of the ground state with baryon-antibaryon and
sigma meson condensates. The effect of such corrections was seen to lead to a
softer equation of state giving rise to a lower value for the compressibility
and, an increase in the in-medium baryonic masses than would be reached when
such quantum effects are not taken into account. These quantum corrections
arising from the scalar meson sector result in an increase in the masses of the
vector mesons in the hot and dense matter, as compared to the situation when
only the vacuum polarisation effects from the baryonic sector are taken into
account.Comment: 13 pages revtex file, 6 figure
Strange Stars with a Density-Dependent Bag Parameter
We have studied strange quark stars in the framework of the MIT bag model,
allowing the bag parameter B to depend on the density of the medium. We have
also studied the effect of Cooper pairing among quarks, on the stellar
structure. Comparison of these two effects shows that the former is generally
more significant. We studied the resulting equation of state of the quark
matter, stellar mass-radius relation, mass-central-density relation,
radius-central-density relation, and the variation of the density as a function
of the distance from the centre of the star. We found that the
density-dependent B allows stars with larger masses and radii, due to
stiffening of the equation of state. Interestingly, certain stellar
configurations are found to be possible only if B depends on the density. We
have also studied the effect of variation of the superconducting gap parameter
on our results.Comment: 23 pages, 8 figs; v2: 25 pages, 9 figs, version to be published in
Phys. Rev. (D
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