564 research outputs found
Fluctuations for the Ginzburg-Landau Interface Model on a Bounded Domain
We study the massless field on , where is a bounded domain with smooth boundary, with Hamiltonian
\CH(h) = \sum_{x \sim y} \CV(h(x) - h(y)). The interaction \CV is assumed
to be symmetric and uniformly convex. This is a general model for a
-dimensional effective interface where represents the height. We
take our boundary conditions to be a continuous perturbation of a macroscopic
tilt: for , , and
continuous. We prove that the fluctuations of linear
functionals of about the tilt converge in the limit to a Gaussian free
field on , the standard Gaussian with respect to the weighted Dirichlet
inner product for some explicit . In a subsequent article,
we will employ the tools developed here to resolve a conjecture of Sheffield
that the zero contour lines of are asymptotically described by , a
conformally invariant random curve.Comment: 58 page
Isoscalar monopole excitations in O: -cluster states at low energy and mean-field-type states at higher energy
Isoscalar monopole strength function in O up to MeV is
discussed. We found that the fine structures at the low energy region up to
MeV in the experimental monopole strength function obtained
by the O reaction can be rather satisfactorily
reproduced within the framework of the cluster model, while the gross
three bump structures observed at the higher energy region ( MeV) look likely to be approximately reconciled by the mean-field
calculations such as RPA and QRPA. In this paper, it is emphasized that two
different types of monopole excitations exist in O; one is the monopole
excitation to cluster states which is dominant in the lower energy part ( MeV), and the other is the monopole excitation of the mean-field
type such as one-particle one-hole () which {is attributed} mainly to the
higher energy part ( MeV). It is found that this
character of the monopole excitations originates from the fact that the ground
state of O with the dominant doubly closed shell structure has a duality
of the mean-field-type {as well as} -clustering {character}. This dual
nature of the ground state seems to be a common feature in light nuclei.Comment: 35 pages, 5 figure
Concepts of alpha-particle condensation
Certain aspects of the recently proposed antisymmetrised alpha particle
product state wave function, or THSR alpha cluster wave function, for the
description of the ground state in 8Be, the Hoyle state in 12C, and analogous
states in heavier nuclei, are elaborated in detail. For instance, the influence
of antisymmetrisation in the Hoyle state on the bosonic character of the alpha
particles is studied carefully. It is shown to be weak, so that bosonic aspects
are predominant. The de Broglie wave length of alpha particles in the Hoyle
state is shown to be much larger than the inter-alpha distance. It is pointed
out that the bosonic features of low density alpha gas states have measurable
consequences, one of which, that is enhanced multi-alpha decay properties,
likely already have been detected. Consistent with experiment, the width of the
proposed analogue to the Hoyle state in 16O at the excitation energy of
E_x=15.1 MeV is estimated to be very small (34 keV), lending credit to the
existence of heavier Hoyle-like states. The intrinsic single boson density
matrix of a self-bound Bose system can, under physically desirable boundary
conditions, be defined unambiguously. One eigenvalue then separates out, being
close to the number of alpha's in the system. Differences between Brink and
THSR alpha cluster wave functions are worked out. No cluster model of the Brink
type can describe the Hoyle state with a single configuration. On the contrary,
many superpositions of the Brink type are necessary, implying delocalisation
towards an alpha product state. It is shown that single alpha particle orbits
in condensates of different nuclei are almost the same. It is thus argued that
alpha particle antisymmetrised product states of the THSR type are a very
promising novel and useful concept in nuclear physics.Comment: 16 pages, 14 figures, to appear in PR
Dilute Multi Alpha Cluster States in Nuclei
Dilute multi cluster condensed states with spherical and axially
deformed shapes are studied with the Gross-Pitaevskii equation and Hill-Wheeler
equation, where the cluster is treated as a structureless boson.
Applications to self-conjugate nuclei show that the dilute
states of C to Ca with appear in the energy region
from threshold up to about 20 MeV, and the critical number of bosons
that the dilute system can sustain as a self-bound nucleus is
estimated roughly to be . We discuss the characteristics of the
dilute states with emphasis on the dependence of their energies
and rms radii.Comment: 44 pages, 8 figure
The Enskog Process
The existence of a weak solution to a McKean-Vlasov type stochastic
differential system corresponding to the Enskog equation of the kinetic theory
of gases is established under natural conditions. The distribution of any
solution to the system at each fixed time is shown to be unique. The existence
of a probability density for the time-marginals of the velocity is verified in
the case where the initial condition is Gaussian, and is shown to be the
density of an invariant measure.Comment: 38 page
On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics
We present a lattice gas model that without fine tuning of parameters is
expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ)
universality class. To this end, we review briefly how non-linear fluctuating
hydrodynamics in one dimension predicts that all dynamical universality classes
in its range of applicability belong to an infinite discrete family which we
call Fibonacci family since their dynamical exponents are the Kepler ratios
of neighbouring Fibonacci numbers , including
diffusion (), KPZ (), and the limiting ratio which is the
golden mean . Then we revisit the case of two
conservation laws to which the modified KPZ model belongs. We also derive
criteria on the macroscopic currents to lead to other non-KPZ universality
classes.Comment: 17 page
On the exclusion of intra-cluster plasma from AGN-blown bubbles
Simple arguments suggest that magnetic fields should be aligned tangentially
to the surface of an AGN-blown bubble. If this is the case, charged particles
from the fully ionised intra-cluster medium (ICM) will be prevented,
ordinarily, from crossing the boundary by the Lorentz force. However, recent
observations indicate that thermal material may occupy up to 50% of the volume
of some bubbles. Given the effect of the Lorentz force, the thermal content
must then be attributed to one, or a combination, of the following processes:
i) the entrainment of thermal gas into the AGN outflow that inflated the
bubble; ii) rapid diffusion across the magnetic field lines at the ICM/bubble
interface; iii) magnetic reconnection events which transfer thermal material
across the ICM/bubble boundary. Unless the AGN outflow behaves as a magnetic
tower jet, entrainment may be significant and could explain the observed
thermal content of bubbles. Alternatively, the cross-field diffusion
coefficient required for the ICM to fill a typical bubble is roughly 10^16 cm^2
s^-1, which is anomalously high compared to predictions from turbulent
diffusion models. Finally, the mass transfer rate due to magnetic reconnection
is uncertain, but significant for plausible reconnection rates. We conclude
that entrainment into the outflow and mass transfer due to magnetic
reconnection events are probably the most significant sources of thermal
content in AGN-blown bubbles.Comment: Accepted for publication in MNRAS, 8 pages, 1 figur
Consistent alpha-cluster description of the 12C (0^+_2) resonance
The near-threshold 12C (0^+_2) resonance provides unique possibility for fast
helium burning in stars, as predicted by Hoyle to explain the observed
abundance of elements in the Universe. Properties of this resonance are
calculated within the framework of the alpha-cluster model whose two-body and
three-body effective potentials are tuned to describe the alpha - alpha
scattering data, the energies of the 0^+_1 and 0^+_2 states, and the
0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2
state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition
radius are found in remarkable agreement with the experimental data. The
0^+_2-state structure is described as a system of three alpha-particles
oscillating between the ground-state-like configuration and the elongated chain
configuration whose probability exceeds 0.9
Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
The rigorous microscopic theory of equilibrium crystal shapes has made
enormous progress during the last decade. We review here the main results which
have been obtained, both in two and higher dimensions. In particular, we
describe how the phenomenological Wulff and Winterbottom constructions can be
derived from the microscopic description provided by the equilibrium
statistical mechanics of lattice gases. We focus on the main conceptual issues
and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical
Physics on Probabilistic Methods in Statistical Physic
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