17,466 research outputs found
Simplifying the spectral analysis of the volume operator
The volume operator plays a central role in both the kinematics and dynamics
of canonical approaches to quantum gravity which are based on algebras of
generalized Wilson loops. We introduce a method for simplifying its spectral
analysis, for quantum states that can be realized on a cubic three-dimensional
lattice. This involves a decomposition of Hilbert space into sectors
transforming according to the irreducible representations of a subgroup of the
cubic group. As an application, we determine the complete spectrum for a class
of states with six-valent intersections.Comment: 19 pages, TeX, to be published in Nucl. Phys.
Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207
The Gd2Sn2O7 pyrochlore Heisenberg antiferromagnet displays a phase
transition to a four sublattice Neel ordered state at a temperature near 1 K.
Despite the seemingly conventional nature of the ordered state, the specific
heat has been found to be described in the temperature range 350-800 mK by an
anomalous T-squared power law. A similar temperature dependence has also been
reported for Gd2Ti2O7, another pyrochlore Heisenberg material. Such anomalous
T-squared behavior in Cv has been argued to be correlated to an unusual
energy-dependence of the density of states which also seemingly manifests
itself in low-temperature spin fluctuations found in muon spin relaxation
experiments. In this paper, we report calculations of Cv that consider spin
wave like excitations out of the Neel order observed in Gd2Sn2O7 and argue that
the parametric T-squared behavior does not reflect the true low-energy
excitations of Gd2Sn2O7. Rather, we find that the low-energy excitations of
this material are antiferromagnetic magnons gapped by single-ion and dipolar
anisotropy effects, and that the lowest temperature of 350 mK considered in
previous specific heat measurements accidentally happens to coincide with a
crossover temperature below which magnons become thermally activated and Cv
takes an exponential form. We argue that further specific heat measurements
that extend down to at least 100 mK are required in order to ascribe an
unconventional description of magnetic excitations out of the ground state of
Gd2Sn2O7 or to invalidate the standard picture of gapped excitations proposed
herein.Comment: 12 pages, 13 figures; shortened introduction and added 1 figur
A double-sum Kronecker-type identity
We prove a double-sum analog of an identity known to Kronecker and then
express it in terms of functions studied by Appell and Kronecker's student
Lerch, in so doing we show that the double-sum analog is of mixed mock modular
form. We also give related symmetric generalizations.Comment: Major revisions. Identities (1.10) and (1.11) are ne
Imposing det E > 0 in discrete quantum gravity
We point out that the inequality det E > 0 distinguishes the kinematical
phase space of canonical connection gravity from that of a gauge field theory,
and characterize the eigenvectors with positive, negative and zero-eigenvalue
of the corresponding quantum operator in a lattice-discretized version of the
theory. The diagonalization of the operator det E is simplified by classifying
its eigenvectors according to the irreducible representations of the octagonal
group.Comment: 10 pages, plain Te
The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond
We consider the spin-1/2 antiferromagnetic Heisenberg model on the
two-dimensional square-kagome lattice with almost dispersionless lowest magnon
band. For a general exchange coupling geometry we elaborate low-energy
effective Hamiltonians which emerge at high magnetic fields. The effective
model to describe the low-energy degrees of freedom of the initial frustrated
quantum spin model is the (unfrustrated) square-lattice spin-1/2 model in
a -aligned magnetic field. For the effective model we perform quantum Monte
Carlo simulations to discuss the low-temperature properties of the
square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We
pay special attention to a magnetic-field driven
Berezinskii-Kosterlitz-Thouless phase transition which occurs at low
temperatures.Comment: 6 figure
Quantum groups, Yang-Baxter maps and quasi-determinants
For any quasi-triangular Hopf algebra, there exists the universal R-matrix,
which satisfies the Yang-Baxter equation. It is known that the adjoint action
of the universal R-matrix on the elements of the tensor square of the algebra
constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic
Yang-Baxter equation. The map has a zero curvature representation among
L-operators defined as images of the universal R-matrix. We find that the zero
curvature representation can be solved by the Gauss decomposition of a product
of L-operators. Thereby obtained a quasi-determinant expression of the quantum
Yang-Baxter map associated with the quantum algebra . Moreover,
the map is identified with products of quasi-Pl\"{u}cker coordinates over a
matrix composed of the L-operators. We also consider the quasi-classical limit,
where the underlying quantum algebra reduces to a Poisson algebra. The
quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios
of determinants, which give a new expression of a classical Yang-Baxter map.Comment: 46 page
Coupling coefficients of SO(n) and integrals over triplets of Jacobi and Gegenbauer polynomials
The expressions of the coupling coefficients (3j-symbols) for the most
degenerate (symmetric) representations of the orthogonal groups SO(n) in a
canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical
or tree bases [with SO(n) restricted to SO(n'})\times SO(n''), n'+n''=n] are
considered, respectively, in context of the integrals involving triplets of the
Gegenbauer and the Jacobi polynomials. Since the directly derived
triple-hypergeometric series do not reveal the apparent triangle conditions of
the 3j-symbols, they are rearranged, using their relation with the
semistretched isofactors of the second kind for the complementary chain
Sp(4)\supset SU(2)\times SU(2) and analogy with the stretched 9j coefficients
of SU(2), into formulae with more rich limits for summation intervals and
obvious triangle conditions. The isofactors of class-one representations of the
orthogonal groups or class-two representations of the unitary groups (and, of
course, the related integrals involving triplets of the Gegenbauer and the
Jacobi polynomials) turn into the double sums in the cases of the canonical
SO(n)\supset SO(n-1) or U(n)\supset U(n-1) and semicanonical SO(n)\supset
SO(n-2)\times SO(2) chains, as well as into the_4F_3(1) series under more
specific conditions. Some ambiguities of the phase choice of the complementary
group approach are adjusted, as well as the problems with alternating sign
parameter of SO(2) representations in the SO(3)\supset SO(2) and SO(n)\supset
SO(n-2)\times SO(2) chains.Comment: 26 pages, corrections of (3.6c) and (3.12); elementary proof of
(3.2e) is adde
Second order dissipative fluid dynamics from kinetic theory
We derive the equations of second order dissipative fluid dynamics from the relativistic Boltzmann equation following the method of W. Israel and J. M. Stewart [1]. We present a frame independent calculation of all first- and second-order terms and their coefficients using a linearised collision integral. Therefore, we restore all terms that were previously neglected in the original papers of W. Israel and J. M. Stewart
Integrable properties of sigma-models with non-symmetric target spaces
It is well-known that sigma-models with symmetric target spaces are
classically integrable. At the example of the model with target space the flag
manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction
of torsion allows to cast the equations of motion in the form of a
zero-curvature condition for a one-parametric family of connections, which can
be a sign of integrability of the theory. We also elaborate on geometric
aspects of the proposed model.Comment: 8 pages, 1 figur
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