7,861 research outputs found
On Matrix Product States for Periodic Boundary Conditions
The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.Comment: 7 pages, late
Isospin-breaking two-nucleon force with explicit Delta-excitations
We study the leading isospin-breaking contributions to the two-nucleon
two-pion exchange potential due to explicit Delta degrees of freedom in chiral
effective field theory. In particular, we find important contributions due to
the delta mass splittings to the charge symmetry breaking potential that act
opposite to the effects induced by the nucleon mass splitting.Comment: 10 pages, 4 figure
On-shell consistency of the Rarita-Schwinger field formulation
We prove that any bilinear coupling of a massive spin-3/2 field can be
brought into a gauge invariant form suggested by Pascalutsa by means of a
non-linear field redefinition. The corresponding field transformation is given
explicitly in a closed form and the implications for chiral effective field
theory with explicit Delta (1232) isobar degrees of freedom are discussed.Comment: 9 pages, 1 figur
Reconciling threshold and subthreshold expansions for pion-nucleon scattering
Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating
the pion-nucleon amplitude in the physical region and for subthreshold
kinematics due to loop effects enhanced by large low-energy constants. Studying
the chiral convergence of threshold and subthreshold parameters up to fourth
order in the small-scale expansion, we address the question to what extent this
tension can be mitigated by including the as an explicit degree
of freedom and/or using a covariant formulation of baryon ChPT. We find that
the inclusion of the indeed reduces the low-energy constants to more
natural values and thereby improves consistency between threshold and
subthreshold kinematics. In addition, even in the -less theory the
resummation of corrections in the covariant scheme improves the results
markedly over the heavy-baryon formulation, in line with previous observations
in the single-baryon sector of ChPT that so far have evaded a profound
theoretical explanation.Comment: 10 pages, 4 tables, Mathematica notebook with the analytic
expressions for threshold and subthreshold parameters included as
supplementary material; journal versio
Exactly solvable models through the empty interval method, for more-than-two-site interactions
Single-species reaction-diffusion systems on a one-dimensional lattice are
considered, in them more than two neighboring sites interact. Constraints on
the interaction rates are obtained, that guarantee the closedness of the time
evolution equation for 's, the probability that consecutive sites
are empty at time . The general method of solving the time evolution
equation is discussed. As an example, a system with next-nearest-neighbor
interaction is studied.Comment: 19 pages, LaTeX2
Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances
We present the results of a third order calculation of the pion-nucleon
scattering amplitude in a chiral effective field theory with pions, nucleons
and delta resonances as explicit degrees of freedom. We work in a manifestly
Lorentz invariant formulation of baryon chiral perturbation theory using
dimensional regularization and the extended on-mass-shell renormalization
scheme. In the delta resonance sector, the on mass-shell renormalization is
realized as a complex-mass scheme. By fitting the low-energy constants of the
effective Lagrangian to the - and -partial waves a satisfactory
description of the phase shifts from the analysis of the Roy-Steiner equations
is obtained. We predict the phase shifts for the and waves and compare
them with the results of the analysis of the George Washington University
group. The threshold parameters are calculated both in the delta-less and
delta-full cases. Based on the determined low-energy constants, we discuss the
pion-nucleon sigma term. Additionally, in order to determine the strangeness
content of the nucleon, we calculate the octet baryon masses in the presence of
decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral
perturbation theory. The octet baryon sigma terms are predicted as a byproduct
of this calculation.Comment: 41 pages, 12 figures, 7 table
EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS
Time-dependent correlation functions of (unstable) particles undergoing
biased or unbiased diffusion, coagulation and annihilation are calculated. This
is achieved by similarity transformations between different stochastic models
and between stochastic and soluble {\em non-stochastic} models. The results
agree with experiments on one-dimensional annihilation-coagulation processes.Comment: 15 pages, Latex. Some corrections made and an appendix adde
Spin Glass and ferromagnetism in disordered Cerium compounds
The competition between spin glass, ferromagnetism and Kondo effect is
analysed here in a Kondo lattice model with an inter-site random coupling
between the localized magnetic moments given by a generalization of
the Mattis model which represents an interpolation between ferromagnetism and a
highly disordered spin glass. Functional integral techniques with Grassmann
fields have been used to obtain the partition function. The static
approximation and the replica symmetric ansatz have also been used. The
solution of the problem is presented as a phase diagram giving {\it
versus} where is the temperature, and are the
strengths of the intrasite Kondo and the intersite random couplings,
respectively. If is small, when temperature is decreased, there is a
second order transition from a paramagnetic to a spin glass phase. For lower
, a first order transition appears between the spin glass phase and a
region where there are Mattis states which are thermodynamically equivalent to
the ferromagnetism. For very low , the Mattis states become stable. On
the other hand, it is found as solution a Kondo state for large
values. These results can improve the theoretical description of the well known
experimental phase diagram of .Comment: 17 pages, 5 figures, accepted Phys. Rev.
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