58 research outputs found
An Equation of State of a Carbon-Fibre Epoxy Composite under Shock Loading
An anisotropic equation of state (EOS) is proposed for the accurate
extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic)
states to other thermodynamic (anisotropic and isotropic) states for a shocked
carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a
generalised decomposition of a stress tensor [Int. J. Plasticity \textbf{24},
140 (2008)], represents a mathematical and physical generalisation of the
Mie-Gr\"{u}neisen EOS for isotropic material and reduces to this equation in
the limit of isotropy. Although a linear relation between the generalised
anisotropic bulk shock velocity and particle velocity was
adequate in the through-thickness orientation, damage softening process
produces discontinuities both in value and slope in the -
relation. Therefore, the two-wave structure (non-linear anisotropic and
isotropic elastic waves) that accompanies damage softening process was proposed
for describing CFC behaviour under shock loading. The linear relationship
- over the range of measurements corresponding to non-linear
anisotropic elastic wave shows a value of (the intercept of the
- curve) that is in the range between first and second
generalised anisotropic bulk speed of sound [Eur. Phys. J. B \textbf{64}, 159
(2008)]. An analytical calculation showed that Hugoniot Stress Levels (HELs) in
different directions for a CFC composite subject to the two-wave structure
(non-linear anisotropic elastic and isotropic elastic waves) agree with
experimental measurements at low and at high shock intensities. The results are
presented, discussed and future studies are outlined.Comment: 12 pages, 9 figure
Particle-Field Duality and Form Factors from Vertex Operators
Using a duality between the space of particles and the space of fields, we
show how one can compute form factors directly in the space of fields. This
introduces the notion of vertex operators, and form factors are vacuum
expectation values of such vertex operators in the space of fields. The vertex
operators can be constructed explicitly in radial quantization. Furthermore,
these vertex operators can be exactly bosonized in momentum space. We develop
these ideas by studying the free-fermion point of the sine-Gordon theory, and
use this scheme to compute some form-factors of some non-free fields in the
sine-Gordon theory. This work further clarifies earlier work of one of the
authors, and extends it to include the periodic sector.Comment: 17 pages, 2 figures, CLNS 93/??
Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field
We consider the anisotropic Heisenberg spin-1/2 chain in a transverse
magnetic field at zero temperature. We first determine all components of the
dynamical structure factor by combining exact results with a mean-field
approximation recently proposed by Dmitriev {\it et al}., JETP 95, 538 (2002).
We then turn to the small anisotropy limit, in which we use field theory
methods to obtain exact results. We discuss the relevance of our results to
Neutron scattering experiments on the 1D Heisenberg chain compound .Comment: 13 pages, 14 figure
Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
In one dimension, the exponential position operators introduced in a theory
of polarization are identified with the twisting operators appearing in the
Lieb-Schultz-Mattis argument, and their finite-size expectation values
measure the overlap between the unique ground state and an excited state.
Insulators are characterized by . We identify with
ground-state expectation values of vertex operators in the sine-Gordon model.
This allows an accurate detection of quantum phase transitions in the
universality classes of the Gaussian model. We apply this theory to the
half-filled extended Hubbard model and obtain agreement with the level-crossing
approach.Comment: 4 pages, 3 figure
Quantum criticalities in a two-leg antiferromagnetic S=1/2 ladder induced by a staggered magnetic field
We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a
staggered magnetic field. We consider two parameter regimes: strong (weak)
coupling along the legs and weak (strong) coupling along the rungs. In both
cases, the staggered field drives the Haldane spin-liquid phase of the ladder
towards a Gaussian quantum criticality. In a generalized spin ladder with a
non-Haldane, spontaneously dimerized phase, the staggered magnetic field
induces an Ising quantum critical regime. In the vicinity of the critical
lines, we derive low-energy effective field theories and use these descriptions
to determine the dynamical response functions, the staggered spin
susceptibility and the string order parameter.Comment: 29 pages of revtex, 10 figure
Effects of a magnetic field on the one-dimensional spin-orbital model
We study the effects of a uniform magnetic field on the one-dimensional
spin-orbital model in terms of effective field theories. Two regions are
examined: one around the SU(4) point (J=K/4) and the other with K<<J. We found
that when , the spin and orbital correlation functions exhibit
power-law decay with nonuniversal exponents. In the region with J>K/4, the
excitation spectrum has a gap. When the magnetic field is beyond some critical
value, a quantum phase transition occurs. However, the correlation functions
around the SU(4) point and the region with K<<J exhibit distinct behavior. This
results from different structures of excitation spectra in both regime.Comment: 22 pages, no figure
Gap generation in the XXZ model in a transverse magnetic field
The ground state phase diagram of the 1D XXZ model in transverse magnetic
field is obtained. It consists of the gapped phases with different types of
long range order (LRO) and critical lines at which the gap and the LRO vanish.
Using scaling estimations and a mean-field approach as well as numerical
results we found critical indices of the gap and the LRO in the vicinity of all
critical lines.Comment: 4 pages, 1 figure, Late
SU(N) Evolution of a Frustrated Spin Ladder
Recent studies indicate that the weakly coupled spin-1/2 Heisenberg
antiferromagnet with next nearest neighbor frustration supports massive spinons
when suitably tuned. The straightforward SU(N) generalization of the low energy
ladder Hamiltonian yields two independent SU(N) Thirring models with N-1
multiplets of massive ``spinon'' excitations. We study the evolution of the
complete set of low-energy dynamical structure factors using form factors.
Those corresponding to the smooth (staggered) magnetizations are qualitatively
different (the same) in the N=2 and N>2 cases. The absence of single-particle
peaks preserves the notion of spinons stabilized by frustration. In contrast to
the ladder, we note that the N=infinity limit of the four chain magnet is not a
trivial free theory.Comment: 10 pages, RevTex, 5 figures; SU(N) approach clarifie
The fate of spinons in spontaneously dimerised spin-1/2 ladders
We study a weakly coupled, frustrated two-leg spin-1/2 Heisenberg ladder. For
vanishing coupling between the chains, elementary excitations are deconfined,
gapless spin-1/2 objects called spinons. We investigate the fate of spinons for
the case of a weak interchain interaction. We show that despite a drastic
change in ground state, which becomes spontaneously dimerised, spinons survive
as elementary excitations but acquire a spectral gap. We furthermore determine
the exact dynamical structure factor for several values of momentum transfer.Comment: 8 pages of revtex, 7 figures; discussion of physical picture for
ground state and excitations in the "twistless" ladder expanded, version to
appear in Phys Rev
Magnetization plateaux in dimerized spin ladder arrays
We investigate the ground state magnetization plateaux appearing in spin 1/2
two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and
dimerized zig-zag interchain couplings. Using both Abelian bosonization and
Lanczos methods we find that the system yields rather unusual plateaux and
exhibits massive and massless phases for specific choices or ``tuning'' of
exchange interactions. The relevance of this behavior in the study of
NH_4CuCl_3 is discussed.Comment: 9 pages, RevTeX, 11 postscript figure
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