15,772 research outputs found
Resonances, Unstable Systems and Irreversibility: Matter Meets Mind
The fundamental time-reversal invariance of dynamical systems can be broken
in various ways. One way is based on the presence of resonances and their
interactions giving rise to unstable dynamical systems, leading to well-defined
time arrows. Associated with these time arrows are semigroups bearing time
orientations. Usually, when time symmetry is broken, two time-oriented
semigroups result, one directed toward the future and one directed toward the
past. If time-reversed states and evolutions are excluded due to resonances,
then the status of these states and their associated backwards-in-time oriented
semigroups is open to question. One possible role for these latter states and
semigroups is as an abstract representation of mental systems as opposed to
material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum
Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior
Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting,
7-22 July 2004, University of Denver. Accepted for publication in the
Internation Journal of Theoretical Physic
Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method
We outline how the coupled cluster method of microscopic quantum many-body
theory can be utilized in practice to give highly accurate results for the
ground-state properties of a wide variety of highly frustrated and strongly
correlated spin-lattice models of interest in quantum magnetism, including
their quantum phase transitions. The method itself is described, and it is
shown how it may be implemented in practice to high orders in a systematically
improvable hierarchy of (so-called LSUB) approximations, by the use of
computer-algebraic techniques. The method works from the outset in the
thermodynamic limit of an infinite lattice at all levels of approximation, and
it is shown both how the "raw" LSUB results are themselves generally
excellent in the sense that they converge rapidly, and how they may accurately
be extrapolated to the exact limit, , of the truncation
index , which denotes the {\it only} approximation made. All of this is
illustrated via a specific application to a two-dimensional, frustrated,
spin-half -- model on a honeycomb lattice with
nearest-neighbor and next-nearest-neighbor interactions with exchange couplings
and , respectively, where both
interactions are of the same anisotropic type. We show how the method can
be used to determine the entire zero-temperature ground-state phase diagram of
the model in the range of the frustration parameter and
of the spin-space anisotropy parameter. In particular,
we identify a candidate quantum spin-liquid region in the phase space
Spin-1/2 - Heisenberg model on a cross-striped square lattice
Using the coupled cluster method (CCM) we study the full (zero-temperature)
ground-state (GS) phase diagram of a spin-half () -
Heisenberg model on a cross-striped square lattice. Each site of the square
lattice has 4 nearest-neighbour exchange bonds of strength and 2
next-nearest-neighbour (diagonal) bonds of strength . The bonds
are arranged so that the basic square plaquettes in alternating columns have
either both or no bonds included. The classical () version of the model has 4 collinear phases when and
can take either sign. Three phases are antiferromagnetic (AFM), showing
so-called N\'{e}el, double N\'{e}el and double columnar striped order
respectively, while the fourth is ferromagnetic. For the quantum model
we use the 3 classical AFM phases as CCM reference states, on top of which the
multispin-flip configurations arising from quantum fluctuations are
incorporated in a systematic truncation hierarchy. Calculations of the
corresponding GS energy, magnetic order parameter and the susceptibilities of
the states to various forms of valence-bond crystalline (VBC) order are thus
carried out numerically to high orders of approximation and then extrapolated
to the (exact) physical limit. We find that the model has 5 phases,
which correspond to the four classical phases plus a new quantum phase with
plaquette VBC order. The positions of the 5 quantum critical points are
determined with high accuracy. While all 4 phase transitions in the classical
model are first order, we find strong evidence that 3 of the 5 quantum phase
transitions in the model are of continuous deconfined type
A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice
The coupled cluster method (CCM) is used to study the zero-temperature
properties of a frustrated spin-half () -- Heisenberg
antiferromagnet (HAF) on a 2D chevron-square lattice. Each site on an
underlying square lattice has 4 nearest-neighbor exchange bonds of strength
and 2 next-nearest-neighbor (diagonal) bonds of strength , with each square plaquette having only one diagonal bond.
The diagonal bonds form a chevron pattern, and the model thus interpolates
smoothly between 2D HAFs on the square () and triangular () lattices,
and also extrapolates to disconnected 1D HAF chains (). The
classical () version of the model has N\'{e}el order for and a form of spiral order for , where
. For the model we use both these classical
states, as well as other collinear states not realized as classical
ground-state (GS) phases, as CCM reference states, on top of which the
multispin-flip configurations resulting from quantum fluctuations are
incorporated in a systematic truncation scheme, which we carry out to high
orders and extrapolate to the physical limit. We calculate the GS energy, GS
magnetic order parameter, and the susceptibilities of the states to various
forms of valence-bond crystalline (VBC) order, including plaquette and two
different dimer forms. We find that the model has two quantum
critical points, at and ,
with N\'{e}el order for , a form of spiral order for
that includes the correct three-sublattice
spin ordering for the triangular-lattice HAF at , and
parallel-dimer VBC order for
Effects of harvesting methods on sustainability of a bay scallop fishery: dredging uproots seagrass and displaces recruits
Fishing is widely recognized to have profound effects on estuarine and marine ecosystems (Hammer and Jansson, 1993; Dayton et al., 1995). Intense commercial and recreational
harvest of valuable species can result in population collapses of target and nontarget species (Botsford et al.,
1997; Pauly et al., 1998; Collie et al. 2000; Jackson et al., 2001). Fishing gear, such as trawls and dredges, that
are dragged over the seafloor inflict damage to the benthic habitat (Dayton et al., 1995; Engel and Kvitek, 1995;
Jennings and Kaiser, 1998; Watling and Norse, 1998). As the growing human population, over-capitalization, and increasing government subsidies of fishing place increasing pressures on marine resources (Myers, 1997), a clear understanding of the mechanisms by which fishing affects coastal systems is required to craft sustainable fisheries management
Phase Transitions in the Spin-Half J_1--J_2 Model
The coupled cluster method (CCM) is a well-known method of quantum many-body
theory, and here we present an application of the CCM to the spin-half J_1--J_2
quantum spin model with nearest- and next-nearest-neighbour interactions on the
linear chain and the square lattice. We present new results for ground-state
expectation values of such quantities as the energy and the sublattice
magnetisation. The presence of critical points in the solution of the CCM
equations, which are associated with phase transitions in the real system, is
investigated. Completely distinct from the investigation of the critical
points, we also make a link between the expansion coefficients of the
ground-state wave function in terms of an Ising basis and the CCM ket-state
correlation coefficients. We are thus able to present evidence of the
breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which
is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any
bipartite lattice. For the square lattice, our best estimates of the points at
which the sign rule breaks down and at which the phase transition from the
antiferromagnetic phase to the frustrated phase occurs are, respectively, given
(to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure
General relativistic null-cone evolutions with a high-order scheme
We present a high-order scheme for solving the full non-linear Einstein
equations on characteristic null hypersurfaces using the framework established
by Bondi and Sachs. This formalism allows asymptotically flat spaces to be
represented on a finite, compactified grid, and is thus ideal for far-field
studies of gravitational radiation. We have designed an algorithm based on
4th-order radial integration and finite differencing, and a spectral
representation of angular components. The scheme can offer significantly more
accuracy with relatively low computational cost compared to previous methods as
a result of the higher-order discretization. Based on a newly implemented code,
we show that the new numerical scheme remains stable and is convergent at the
expected order of accuracy.Comment: 24 pages, 3 figure
Theory of Bubble Nucleation and Cooperativity in DNA Melting
The onset of intermediate states (denaturation bubbles) and their role during
the melting transition of DNA are studied using the Peyrard-Bishop-Daxuois
model by Monte Carlo simulations with no adjustable parameters. Comparison is
made with previously published experimental results finding excellent
agreement. Melting curves, critical DNA segment length for stability of bubbles
and the possibility of a two states transition are studied.Comment: 4 figures. Accepted for publication in Physical Review Letter
Comment on "Can one predict DNA Transcription Start Sites by Studying Bubbles?"
Comment on T.S. van Erp, S. Cuesta-Lopez, J.-G. Hagmann, and M. Peyrard,
Phys. Rev. Lett. 95, 218104 (2005) [arXiv: physics/0508094]
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