7,504 research outputs found
Theta dependence of SU(N) gauge theories in the presence of a topological term
We review results concerning the theta dependence of 4D SU(N) gauge theories
and QCD, where theta is the coefficient of the CP-violating topological term in
the Lagrangian. In particular, we discuss theta dependence in the large-N
limit.
Most results have been obtained within the lattice formulation of the theory
via numerical simulations, which allow to investigate the theta dependence of
the ground-state energy and the spectrum around theta=0 by determining the
moments of the topological charge distribution, and their correlations with
other observables. We discuss the various methods which have been employed to
determine the topological susceptibility, and higher-order terms of the theta
expansion. We review results at zero and finite temperature. We show that the
results support the scenario obtained by general large-N scaling arguments, and
in particular the Witten-Veneziano mechanism to explain the U(1)_A problem. We
also compare with results obtained by other approaches, especially in the
large-N limit, where the issue has been also addressed using, for example, the
AdS/CFT correspondence.
We discuss issues related to theta dependence in full QCD: the neutron
electric dipole moment, the dependence of the topological susceptibility on the
quark masses, the U(1)_A symmetry breaking at finite temperature.
We also consider the 2D CP(N) model, which is an interesting theoretical
laboratory to study issues related to topology. We review analytical results in
the large-N limit, and numerical results within its lattice formulation.
Finally, we discuss the main features of the two-point correlation function
of the topological charge density.Comment: A typo in Eq. (3.9) has been corrected. An additional subsection
(5.2) has been inserted to demonstrate the nonrenormalizability of the
relevant theta parameter in the presence of massive fermions, which implies
that the continuum (a -> 0) limit must be taken keeping theta fixe
Effect of correlations on network controllability
A dynamical system is controllable if by imposing appropriate external
signals on a subset of its nodes, it can be driven from any initial state to
any desired state in finite time. Here we study the impact of various network
characteristics on the minimal number of driver nodes required to control a
network. We find that clustering and modularity have no discernible impact, but
the symmetries of the underlying matching problem can produce linear, quadratic
or no dependence on degree correlation coefficients, depending on the nature of
the underlying correlations. The results are supported by numerical simulations
and help narrow the observed gap between the predicted and the observed number
of driver nodes in real networks
Chaotic scattering in solitary wave interactions: A singular iterated-map description
We derive a family of singular iterated maps--closely related to Poincare
maps--that describe chaotic interactions between colliding solitary waves. The
chaotic behavior of such solitary wave collisions depends on the transfer of
energy to a secondary mode of oscillation, often an internal mode of the pulse.
Unlike previous analyses, this map allows one to understand the interactions in
the case when this mode is excited prior to the first collision. The map is
derived using Melnikov integrals and matched asymptotic expansions and
generalizes a ``multi-pulse'' Melnikov integral and allows one to find not only
multipulse heteroclinic orbits, but exotic periodic orbits. The family of maps
derived exhibits singular behavior, including regions of infinite winding. This
problem is shown to be a singular version of the conservative Ikeda map from
laser physics and connections are made with problems from celestial mechanics
and fluid mechanics.Comment: 29 pages, 17 figures, submitted to Chaos, higher-resolution figures
available at author's website: http://m.njit.edu/goodman/publication
Forbidden ordinal patterns in higher dimensional dynamics
Forbidden ordinal patterns are ordinal patterns (or `rank blocks') that
cannot appear in the orbits generated by a map taking values on a linearly
ordered space, in which case we say that the map has forbidden patterns. Once a
map has a forbidden pattern of a given length , it has forbidden
patterns of any length and their number grows superexponentially
with . Using recent results on topological permutation entropy, we study in
this paper the existence and some basic properties of forbidden ordinal
patterns for self maps on n-dimensional intervals. Our most applicable
conclusion is that expansive interval maps with finite topological entropy have
necessarily forbidden patterns, although we conjecture that this is also the
case under more general conditions. The theoretical results are nicely
illustrated for n=2 both using the naive counting estimator for forbidden
patterns and Chao's estimator for the number of classes in a population. The
robustness of forbidden ordinal patterns against observational white noise is
also illustrated.Comment: 19 pages, 6 figure
Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
The largest eigenvalue of a network's adjacency matrix and its associated
principal eigenvector are key elements for determining the topological
structure and the properties of dynamical processes mediated by it. We present
a physically grounded expression relating the value of the largest eigenvalue
of a given network to the largest eigenvalue of two network subgraphs,
considered as isolated: The hub with its immediate neighbors and the densely
connected set of nodes with maximum -core index. We validate this formula
showing that it predicts with good accuracy the largest eigenvalue of a large
set of synthetic and real-world topologies. We also present evidence of the
consequences of these findings for broad classes of dynamics taking place on
the networks. As a byproduct, we reveal that the spectral properties of
heterogeneous networks built according to the linear preferential attachment
model are qualitatively different from those of their static counterparts.Comment: 18 pages, 13 figure
Deconfined quantum critical points: symmetries and dualities
The deconfined quantum critical point (QCP), separating the N\'eel and
valence bond solid phases in a 2D antiferromagnet, was proposed as an example
of D criticality fundamentally different from standard
Landau-Ginzburg-Wilson-Fisher {criticality}. In this work we present multiple
equivalent descriptions of deconfined QCPs, and use these to address the
possibility of enlarged emergent symmetries in the low energy limit. The
easy-plane deconfined QCP, besides its previously discussed self-duality, is
dual to fermionic quantum electrodynamics (QED), which has its own
self-duality and hence may have an O(4) symmetry. We propose
several dualities for the deconfined QCP with spin symmetry
which together make natural the emergence of a previously suggested
symmetry rotating the N\'eel and VBS orders. These emergent symmetries are
implemented anomalously. The associated infra-red theories can also be viewed
as surface descriptions of 3+1D topological paramagnets, giving further insight
into the dualities. We describe a number of numerical tests of these dualities.
We also discuss the possibility of "pseudocritical" behavior for deconfined
critical points, and the meaning of the dualities and emergent symmetries in
such a scenario.Comment: Published version, 44 pages + references, 4 figures. A summary of
main results in p7-
Microscopic activity patterns in the Naming Game
The models of statistical physics used to study collective phenomena in some
interdisciplinary contexts, such as social dynamics and opinion spreading, do
not consider the effects of the memory on individual decision processes. On the
contrary, in the Naming Game, a recently proposed model of Language formation,
each agent chooses a particular state, or opinion, by means of a memory-based
negotiation process, during which a variable number of states is collected and
kept in memory. In this perspective, the statistical features of the number of
states collected by the agents becomes a relevant quantity to understand the
dynamics of the model, and the influence of topological properties on
memory-based models. By means of a master equation approach, we analyze the
internal agent dynamics of Naming Game in populations embedded on networks,
finding that it strongly depends on very general topological properties of the
system (e.g. average and fluctuations of the degree). However, the influence of
topological properties on the microscopic individual dynamics is a general
phenomenon that should characterize all those social interactions that can be
modeled by memory-based negotiation processes.Comment: submitted to J. Phys.
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