291 research outputs found
Chiral crystals in strong-coupling lattice QCD at nonzero chemical potential
We study the effective action for strong-coupling lattice QCD with
one-component staggered fermions in the case of nonzero chemical potential and
zero temperature. The structure of this action suggests that at large chemical
potentials its ground state is a crystalline `chiral density wave' that
spontaneously breaks chiral symmetry and translation invariance. In mean-field
theory, on the other hand, we find that this state is unstable. We show that
lattice artifacts are partly responsible for this, and suggest that if this
phase exists in QCD, then finding it in Monte-Carlo simulations would require
simulating on relatively fine lattices. In particular, the baryon mass in
lattice units, m_B, should be considerably smaller than its strong-coupling
limit of m_B~3.Comment: 33 pages, 8 figure
Phase Transitions from Saddles of the Potential Energy Landscape
The relation between saddle points of the potential of a classical
many-particle system and the analyticity properties of its thermodynamic
functions is studied. For finite systems, each saddle point is found to cause a
nonanalyticity in the Boltzmann entropy, and the functional form of this
nonanalytic term is derived. For large systems, the order of the nonanalytic
term increases unboundedly, leading to an increasing differentiability of the
entropy. Analyzing the contribution of the saddle points to the density of
states in the thermodynamic limit, our results provide an explanation of how,
and under which circumstances, saddle points of the potential energy landscape
may (or may not) be at the origin of a phase transition in the thermodynamic
limit. As an application, the puzzling observations by Risau-Gusman et al. on
topological signatures of the spherical model are elucidated.Comment: 5 pages, no figure
Phase transitions induced by saddle points of vanishing curvature
Based on the study of saddle points of the potential energy landscapes of
generic classical many-particle systems, we present a necessary criterion for
the occurrence of a thermodynamic phase transition. Remarkably, this criterion
imposes conditions on microscopic properties, namely curvatures at the saddle
points of the potential, and links them to the macroscopic phenomenon of a
phase transition. We apply our result to two exactly solvable models,
corroborating that the criterion derived is not only valid, but also sharp and
useful: For both models studied, the criterion excludes the occurrence of a
phase transition for all values of the potential energy but the transition
energy. This result adds a geometrical ingredient to an established topological
condition for the occurrence of a phase transition, thereby providing an answer
to the long standing question of which topology changes in configuration space
can induce a phase transition.Comment: 5 page
Enzymatic Synthesis of M1Gâ Deoxyribose
Adducts formed between electrophiles and nucleic acid bases are believed to play a key role in chemically induced mutations and cancer. M1Gâ dR is an endogenous exocyclic DNA adduct formed by the reaction of the dicarbonyl compound malondialdehyde with a dG residue in DNA. It is an intermediate in the synthesis of a class of modified oligodeoxyribonucleotides that are used to study the mutagenicity and repair of M1G. This unit presents methods for synthesizing M1Gâ dR by enzymatic coupling.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143678/1/cpnc0102.pd
Rise and diversification of chondrichthyans in the Paleozoic
The Paleozoic represents a key time interval in the origins and early diversification of chondrichthyans (cartilaginous fishes), but their diversity and macroevolution are largely obscured by heterogenous spatial and temporal sampling. The predominantly cartilaginous skeletons of chondrichthyans pose an additional limitation on their preservation potential and hence on the quality of their fossil record. Here, we use a newly compiled genus-level dataset and the application of sampling standardization methods to analyze global total-chondrichthyan diversity dynamics through time from their first appearance in the Ordovician through to the end of the Permian. Subsampled estimates of chondrichthyan genus richness were initially low in the Ordovician and Silurian but increased substantially in the Early Devonian. Richness reached its maximum in the middle Carboniferous before dropping across the Carboniferous/Permian boundary and gradually decreasing throughout the Permian. Sampling is higher in both the Devonian and Carboniferous compared with the Silurian and most of the Permian stages. Shark-like scales from the Ordovician are too limited to allow for some of the subsampling techniques. Our results detect two Paleozoic radiations in chondrichthyan diversity: the first in the earliest Devonian, led by acanthodians (stem-group chondrichthyans), which then decline rapidly by the Late Devonian, and the second in the earliest Carboniferous, led by holocephalans, which increase greatly in richness across the Devonian/Carboniferous boundary. Dispersal of chondrichthyans, specifically holocephalans, into deeper-water environments may reflect a niche expansion following the faunal displacement in the aftermath of the Hangenberg extinction event at the end of the Devonian
Chiral Modulations in Curved Space I: Formalism
The goal of this paper is to present a formalism that allows to handle
four-fermion effective theories at finite temperature and density in curved
space. The formalism is based on the use of the effective action and zeta
function regularization, supports the inclusion of inhomogeneous and
anisotropic phases. One of the key points of the method is the use of a
non-perturbative ansatz for the heat-kernel that returns the effective action
in partially resummed form, providing a way to go beyond the approximations
based on the Ginzburg-Landau expansion for the partition function. The
effective action for the case of ultra-static Riemannian spacetimes with
compact spatial section is discussed in general and a series representation,
valid when the chemical potential satisfies a certain constraint, is derived.
To see the formalism at work, we consider the case of static Einstein spaces at
zero chemical potential. Although in this case we expect inhomogeneous phases
to occur only as meta-stable states, the problem is complex enough and allows
to illustrate how to implement numerical studies of inhomogeneous phases in
curved space. Finally, we extend the formalism to include arbitrary chemical
potentials and obtain the analytical continuation of the effective action in
curved space.Comment: 22 pages, 3 figures; version to appear in JHE
Generating Functions for Coherent Intertwiners
We study generating functions for the scalar products of SU(2) coherent
intertwiners, which can be interpreted as coherent spin network evaluations on
a 2-vertex graph. We show that these generating functions are exactly summable
for different choices of combinatorial weights. Moreover, we identify one
choice of weight distinguished thanks to its geometric interpretation. As an
example of dynamics, we consider the simple case of SU(2) flatness and describe
the corresponding Hamiltonian constraint whose quantization on coherent
intertwiners leads to partial differential equations that we solve.
Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2)
flatness on coherent spin networks for arbitrary graphs.Comment: 31 page
From Euler's play with infinite series to the anomalous magnetic moment
During a first St. Petersburg period Leonhard Euler, in his early twenties,
became interested in the Basel problem: summing the series of inverse squares
(posed by Pietro Mengoli in mid 17th century). In the words of Andre Weil
(1989) "as with most questions that ever attracted his attention, he never
abandoned it". Euler introduced on the way the alternating "phi-series", the
better converging companion of the zeta function, the first example of a
polylogarithm at a root of unity. He realized - empirically! - that odd zeta
values appear to be new (transcendental?) numbers. It is amazing to see how, a
quarter of a millennium later, the numbers Euler played with, "however
repugnant" this game might have seemed to his contemporary lovers of the
"higher kind of calculus", reappeared in the analytic calculation of the
anomalous magnetic moment of the electron, the most precisely calculated and
measured physical quantity. Mathematicians, inspired by ideas of Grothendieck,
are reviving the dream of Galois of uncovering a group structure in the ring of
periods (that includes the multiple zeta values) - applied to the study of
Feynman amplitudes.Comment: v.2: minor corrections, references adde
On the mean-field spherical model
Exact solutions are obtained for the mean-field spherical model, with or
without an external magnetic field, for any finite or infinite number N of
degrees of freedom, both in the microcanonical and in the canonical ensemble.
The canonical result allows for an exact discussion of the loci of the Fisher
zeros of the canonical partition function. The microcanonical entropy is found
to be nonanalytic for arbitrary finite N. The mean-field spherical model of
finite size N is shown to be equivalent to a mixed isovector/isotensor
sigma-model on a lattice of two sites. Partial equivalence of statistical
ensembles is observed for the mean-field spherical model in the thermodynamic
limit. A discussion of the topology of certain state space submanifolds yields
insights into the relation of these topological quantities to the thermodynamic
behavior of the system in the presence of ensemble nonequivalence.Comment: 21 pages, 5 figure
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