59 research outputs found
Internal dynamics around static-deformation FEM states
Constant velocity or constant force FEM solutions are static-deformation states, where the elastic deformation is stationary. These are the typical operation conditions. Time-dependence, or fluctuations, of the static-deformation states are treated as perturbations, leading to a fast-converging expansion, for typical operation conditions, in which the time-scale of the input force is slower than the internal dynamics
Coherent bubble-sum approximation for coupled-channel resonance scattering
For coupled-channel resonance scattering we derive a model with a closed form
solution for the -matrix that satisfies unitarity and analyticity. The
two-channel case is handled explicitly for an arbitrary number of resonances.
The method focuses on the expansion of the transition matrix elements,
, in known analytical functions. The appropriate hadronic form
factors and the related energy shifts can be determined from the scattering
data. The differences between this method and the -matrix and the
Breit-Wigner approximation are illustrated in the case of the
resonances and .Comment: 8 pages, 1 figure, code available from
http://www.phyast.pitt.edu/~norbertl/bubblegum2
Towards a coupled-cluster treatment of SU(N) lattice gauge field theory
A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU(N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional
Quantum Phase Transitions and the Extended Coupled Cluster Method
We discuss the application of an extended version of the coupled cluster
method to systems exhibiting a quantum phase transition. We use the lattice
O(4) non-linear sigma model in (1+1)- and (3+1)-dimensions as an example. We
show how simple predictions get modified, leading to the absence of a phase
transition in (1+1) dimensions, and strong indications for a phase transition
in (3+1) dimensions
Why pair production cures covariance in the light-front?
We show that the light-front vaccum is not trivial, and the Fock space for
positive energy quanta solutions is not complete. As an example of this non
triviality we have calculated the electromagnetic current for scalar bosons in
the background field method were the covariance is restored through considering
the complete Fock space of solutions. We also show thus that the method of
"dislocating the integration pole" is nothing more than a particular case of
this, so that such an "ad hoc" prescription can be dispensed altogether if we
deal with the whole Fock space. In this work we construct the electromagnetic
current operator for a system composed of two free bosons. The technique
employed to deduce these operators is through the definition of global
propagators in the light front when a background electromagnetic field acts on
one of the particles.Comment: 11 pages, 2 figure
Phase transition in the transverse Ising model using the extended coupled-cluster method
The phase transition present in the linear-chain and square-lattice cases of
the transverse Ising model is examined. The extended coupled cluster method
(ECCM) can describe both sides of the phase transition with a unified approach.
The correlation length and the excitation energy are determined. We demonstrate
the ability of the ECCM to use both the weak- and the strong-coupling starting
state in a unified approach for the study of critical behavior.Comment: 10 pages, 7 eps-figure
A Coupled-Cluster Formulation of Hamiltonian Lattice Field Theory: The Non-Linear Sigma Model
We apply the coupled cluster method (CCM) to the Hamiltonian version of the
latticised O(4) non-linear sigma model. The method, which was initially
developed for the accurate description of quantum many-body systems, gives rise
to two distinct approximation schemes. These approaches are compared with each
other as well as with some other Hamiltonian approaches. Our study of both the
ground state and collective excitations leads to indications of a possible
chiral phase transition as the lattice spacing is varied.Comment: 44 Pages, 14 figures. Uses Latex2e, graphicx, amstex and geometry
package
The Coupled Cluster Method in Hamiltonian Lattice Field Theory: SU(2) Glueballs
The glueball spectrum within the Hamiltonian formulation of lattice gauge
theory (without fermions) is calculated for the gauge group SU(2) and for two
spatial dimensions.
The Hilbert space of gauge-invariant functions of the gauge field is
generated by its parallel-transporters on closed paths along the links of the
spatial lattice. The coupled cluster method is used to determine the spectrum
of the Kogut-Susskind Hamiltonian in a truncated basis. The quality of the
description is studied by computing results from various truncations, lattice
regularisations and with an improved Hamiltonian.
We find consistency for the mass ratio predictions within a scaling region
where we obtain good agreement with standard lattice Monte Carlo results.Comment: 13 pages, 7 figure
The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets
The spin-half XXZ model on the linear chain and the square lattice are
examined with the extended coupled cluster method (ECCM) of quantum many-body
theory. We are able to describe both the Ising-Heisenberg phase and the
XY-Heisenberg phase, starting from known wave functions in the Ising limit and
at the phase transition point between the XY-Heisenberg and ferromagnetic
phases, respectively, and by systematically incorporating correlations on top
of them. The ECCM yields good numerical results via a diagrammatic approach,
which makes the numerical implementation of higher-order truncation schemes
feasible. In particular, the best non-extrapolated coupled cluster result for
the sublattice magnetization is obtained, which indicates the employment of an
improved wave function. Furthermore, the ECCM finds the expected qualitatively
different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure
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