39,360 research outputs found
Exact Bethe Ansatz solution for chains with non- invariant open boundary conditions
The Nested Bethe Ansatz is generalized to open and independent boundary
conditions depending on two continuous and two discrete free parameters. This
is used to find the exact eigenvectors and eigenvalues of the vertex
models and spin chains with such boundary conditions. The solution is
found for all diagonal families of solutions to the reflection equations in all
possible combinations. The Bethe ansatz equations are used to find de first
order finite size correction.Comment: Two references adde
Combinatorics of lattice paths with and without spikes
We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.Comment: Latex. 25 page
Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics
Implementations of solid-state quantum optics provide us with devices where qubits are placed at fixed positions in photonic or plasmonic one-dimensional waveguides. We show that solely by controlling the position ofthe qubits and withthe help of a coherent driving, collective spontaneous decay may be engineered to yield an entangled mesoscopic steady state. Our scheme relies on the realization of pure superradiant Dicke models by a destructive interference that cancels dipole-dipole interactions in one dimension
Evidence of several dipolar quasi-invariants in Liquid Crystals
In a closed quantum system of N coupled spins with magnetic quantum number I,
there are about (2I + 1)^N constants of motion. However, the possibility of
observing such quasi-invariant (QI) states in solid-like spin systems in
Nuclear Magnetic Resonance (NMR) is not a strictly exact prediction. The aim of
this work is to provide experimental evidence of several QI, in the proton NMR
of small spin clusters, besides those already known Zeeman, and dipolar orders
(strong and weak). We explore the spin states prepared with the
Jeener-Broekaert pulse sequence by analyzing the time-domain signals yielded by
this sequence as a function of the preparation times, in a variety of dipolar
networks. We observe that the signals can be explained with two dipolar QIs
only within a range of short preparation times. At longer times the time-domain
signals have an echo-like behaviour. We study their multiple quantum coherence
content on a basis orthogonal to the z-basis and see that such states involve a
significant number of correlated spins. Then we show that the whole preparation
time-scale can only be reconstructed by assuming the occurrence of multiple QI
which we isolate experimentally
Large N reduction on a twisted torus
We consider SU(N) lattice gauge theory at infinite N defined on a torus with
a CP invariant twist. Massless fermions are incorporated in an elegant way,
while keeping them quenched. We present some numerical results which suggest
that twisting can make numerical simulations of planar QCD more efficient.Comment: 14 pages, 2 figures, 1 tabl
A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks
We introduce an alternative formulation of the exact stochastic simulation
algorithm (SSA) for sampling trajectories of the chemical master equation for a
well-stirred system of coupled chemical reactions. Our formulation is based on
factored-out, partial reaction propensities. This novel exact SSA, called the
partial propensity direct method (PDM), is highly efficient and has a
computational cost that scales at most linearly with the number of chemical
species, irrespective of the degree of coupling of the reaction network. In
addition, we propose a sorting variant, SPDM, which is especially efficient for
multiscale reaction networks.Comment: 23 pages, 3 figures, 4 tables; accepted by J. Chem. Phy
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