2,701 research outputs found
Thermal Quantum Fields without Cut-offs in 1+1 Space-time Dimensions
We construct interacting quantum fields in 1+1 dimensional Minkowski space,
representing neutral scalar bosons at positive temperature. Our work is based
on prior work by Klein and Landau and Hoegh-KrohnComment: 48 page
Alternative Mathematical Technique to Determine LS Spectral Terms
We presented an alternative computational method for determining the
permitted LS spectral terms arising from electronic configurations. This
method makes the direct calculation of LS terms possible. Using only basic
algebra, we derived our theory from LS-coupling scheme and Pauli exclusion
principle. As an application, we have performed the most complete set of
calculations to date of the spectral terms arising from electronic
configurations, and the representative results were shown. As another
application on deducing LS-coupling rules, for two equivalent electrons, we
deduced the famous Even Rule; for three equivalent electrons, we derived a new
simple rule.Comment: Submitted to Phys. Rev.
Multi-layer S=1/2 Heisenberg antiferromagnet
The multi-layer square lattice Heisenberg antiferromagnet with
up to 6 layers is studied via various series expansions. For the systems with
an odd number of coupled planes, the ground-state energy, staggered
magnetization, and triplet excitation spectra are calculated via two different
Ising expansions. The systems are found to have long range N\'eel order and
gapless excitations for all ratios of interlayer to intralayer couplings, as
for the single-layer system. For the systems with an even number of coupled
planes, there is a second order transition point separating the gapless Ne\'el
phase and gapped quantum disordered spin liquid phase, and the critical points
are located via expansions in the interlayer exchange coupling. This transition
point is found to vary about inversely as the number of layers. The triplet
excitation spectra are also computed, and at the critical point the normalized
spectra appear to follow a universal function, independent of number of layers.Comment: 13 pages plus 8 figure
Various series expansions for a Heisenberg antiferromagnet model for SrCu(BO)
We use a variety of series expansion methods at both zero and finite
temperature to study an antiferromagnetic Heisenberg spin model proposed
recently by Miyahara and Ueda for the quasi two-dimensional material
SrCu(BO). We confirm that this model exhibits a first-order quantum
phase transition at T=0 between a gapped dimer phase and a gapless N\'eel phase
when the ratio of nearest and next-nearest neighbour interactions is
varied, and locate the transition at . Using longer series we are
able to give more accurate estimates of the model parameters by fitting to the
high temperature susceptibility data.Comment: RevTeX, 13 figure
Simulation of truncated normal variables
We provide in this paper simulation algorithms for one-sided and two-sided
truncated normal distributions. These algorithms are then used to simulate
multivariate normal variables with restricted parameter space for any
covariance structure.Comment: This 1992 paper appeared in 1995 in Statistics and Computing and the
gist of it is contained in Monte Carlo Statistical Methods (2004), but I
receive weekly requests for reprints so here it is
Three fermions with six single particle states can be entangled in two inequivalent ways
Using a generalization of Cayley's hyperdeterminant as a new measure of
tripartite fermionic entanglement we obtain the SLOCC classification of
three-fermion systems with six single particle states. A special subclass of
such three-fermion systems is shown to have the same properties as the
well-known three-qubit ones. Our results can be presented in a unified way
using Freudenthal triple systems based on cubic Jordan algebras. For systems
with an arbitrary number of fermions and single particle states we propose the
Pl\"ucker relations as a sufficient and necessary condition of separability.Comment: 23 pages LATE
Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model
We analyze the stability of the spontaneously dimerized spin-liquid phase of
the frustrated Heisenberg antiferromagnet - the J1-J2 model. The lowest triplet
excitation, corresponding to breaking of a singlet bond, is found to be stable
in the region 0.38 < J2/J1 < 0.62. In addition we find a stable low-energy
collective singlet mode, which is closely related to the spontaneous violation
of the discrete symmetry. Both modes are gapped in the quantum disordered phase
and become gapless at the transition point to the Neel ordered phase
(J2/J1=0.38). The spontaneous dimerization vanishes at the transition and we
argue that the disappearance of dimer order is related to the vanishing of the
singlet gap. We also present exact diagonalization data on a small (4x4)
cluster which indeed show a structure of the spectrum, consistent with that of
a system with a four-fold degenerate (spontaneously dimerized) ground state.Comment: 4 pages, 4 figures, small changes, published versio
Fast atomic transport without vibrational heating
We use the dynamical invariants associated with the Hamiltonian of an atom in
a one dimensional moving trap to inverse engineer the trap motion and perform
fast atomic transport without final vibrational heating. The atom is driven
non-adiabatically through a shortcut to the result of adiabatic, slow trap
motion. For harmonic potentials this only requires designing appropriate trap
trajectories, whereas perfect transport in anharmonic traps may be achieved by
applying an extra field to compensate the forces in the rest frame of the trap.
The results can be extended to atom stopping or launching. The limitations due
to geometrical constraints, energies and accelerations involved are analyzed,
as well as the relation to previous approaches (based on classical trajectories
or "fast-forward" and "bang-bang" methods) which can be integrated in the
invariant-based framework.Comment: 10 pages, 5 figure
Discrete integrable systems, positivity, and continued fraction rearrangements
In this review article, we present a unified approach to solving discrete,
integrable, possibly non-commutative, dynamical systems, including the - and
-systems based on . The initial data of the systems are seen as cluster
variables in a suitable cluster algebra, and may evolve by local mutations. We
show that the solutions are always expressed as Laurent polynomials of the
initial data with non-negative integer coefficients. This is done by
reformulating the mutations of initial data as local rearrangements of
continued fractions generating some particular solutions, that preserve
manifest positivity. We also show how these techniques apply as well to
non-commutative settings.Comment: 24 pages, 2 figure
Realizations of Causal Manifolds by Quantum Fields
Quantum mechanical operators and quantum fields are interpreted as
realizations of timespace manifolds. Such causal manifolds are parametrized by
the classes of the positive unitary operations in all complex operations, i.e.
by the homogenous spaces \D(n)=\GL(\C^n_\R)/\U(n) with for mechanics
and for relativistic fields. The rank gives the number of both the
discrete and continuous invariants used in the harmonic analysis, i.e. two
characteristic masses in the relativistic case. 'Canonical' field theories with
the familiar divergencies are inappropriate realizations of the real
4-dimensional causal manifold \D(2). Faithful timespace realizations do not
lead to divergencies. In general they are reducible, but nondecomposable - in
addition to representations with eigenvectors (states, particle) they
incorporate principal vectors without a particle (eigenvector) basis as
exemplified by the Coulomb field.Comment: 36 pages, latex, macros include
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