2,280 research outputs found
Quantum mechanics on manifolds and topological effects
A unique classification of the topological effects associated to quantum
mechanics on manifolds is obtained on the basis of the invariance under
diffeomorphisms and the realization of the Lie-Rinehart relations between the
generators of the diffeomorphism group and the algebra of infinitely
differentiable functions on the manifold. This leads to a unique
("Lie-Rinehart") C* algebra as observable algebra; its regular representations
are shown to be locally Schroedinger and in one to one correspondence with the
unitary representations of the fundamental group of the manifold. Therefore, in
the absence of spin degrees of freedom and external fields, the first homotopy
group of the manifold appears as the only source of topological effects.Comment: A few comments have been added to the Introduction, together with
related references; a few words have been changed in the Abstract and a Note
added to the Titl
Refined Algebraic Quantization in the oscillator representation of SL(2,R)
We investigate Refined Algebraic Quantization (RAQ) with group averaging in a
constrained Hamiltonian system with unreduced phase space T^*R^4 and gauge
group SL(2,R). The reduced phase space M is connected and contains four
mutually disconnected `regular' sectors with topology R x S^1, but these
sectors are connected to each other through an exceptional set where M is not a
manifold and where M has non-Hausdorff topology. The RAQ physical Hilbert space
H_{phys} decomposes as H_{phys} = (direct sum of) H_i, where the four subspaces
H_i naturally correspond to the four regular sectors of M. The RAQ observable
algebra A_{obs}, represented on H_{phys}, contains natural subalgebras
represented on each H_i. The group averaging takes place in the oscillator
representation of SL(2,R) on L^2(R^{2,2}), and ensuring convergence requires a
subtle choice for the test state space: the classical analogue of this choice
is to excise from M the exceptional set while nevertheless retaining
information about the connections between the regular sectors. A quantum theory
with the Hilbert space H_{phys} and a finitely-generated observable subalgebra
of A_{obs} is recovered through both Ashtekar's Algebraic Quantization and
Isham's group theoretic quantization.Comment: 30 pages, REVTeX v3.1 with amsfonts. (v4: Published version.
Developing a Framework for Child Welfare Supervision
The roles of the child welfare supervisor in guiding practice and in retaining child welfare workers are well established in the literature. In this article, we discuss a framework for child welfare supervision that was developed and implemented in the state of Iowa with support from the Children’s Bureau through a five-year grant to improve recruitment and retention in public child welfare. The framework supports family centered practice through a parallel process of supervision reflecting these guiding principles: strength-based, competency-based, culturally competent, reflective, individualized to workers’ learning styles and stages of development, and aimed at enhancing worker skill, autonomy, teamwork, and commitment to the organization. We present key elements of the framework, an overview of implementation, and evaluation results regarding knowledge gain, use of skills, and rates of worker retention
Complete chaotic synchronization in mutually coupled time-delay systems
Complete chaotic synchronization of end lasers has been observed in a line of
mutually coupled, time-delayed system of three lasers, with no direct
communication between the end lasers. The present paper uses ideas from
generalized synchronization to explain the complete synchronization in the
presence of long coupling delays, applied to a model of mutually coupled
semiconductor lasers in a line. These ideas significantly simplify the analysis
by casting the stability in terms of the local dynamics of each laser. The
variational equations near the synchronization manifold are analyzed, and used
to derive the synchronization condition that is a function of the parameters.
The results explain and predict the dependence of synchronization on various
parameters, such as time-delays, strength of coupling and dissipation. The
ideas can be applied to understand complete synchronization in other chaotic
systems with coupling delays and no direct communication between synchronized
sub-systems.Comment: 22 pages, 6 figure
Theory for all-optical responses in topological materials: The velocity gauge picture
High-order harmonic generation (HHG), which has been widely studied in atomic gas, has recently been expanded to solids to study the highly nonlinear electronic response in condensed matter and produce coherent high-frequency radiation. Recently, attention has turned to topological materials and the use of HHG to characterize topological bands and invariants. However, the theoretical interpretation of the nonlinear electronic response in topological materials presents many challenges. In particular, the Bloch wavefunction phase of topological materials has undefined points in the Brillouin zone. This leads to singularities in the calculation of the interband and intraband transition dipole matrix elements of the semiconductor Bloch equations (SBEs). Here, we use the laser-electromagnetic velocity gauge p⋅A(t) to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra with better numerical efficiency and more straightforward implementation. We used a prototype of Chern insulators (CIs), the Haldane model, to demonstrate our approach. The validity of the velocity gauge approach is demonstrated in the following way: for topologically trivial materials such as MoS2, qualitative agreement is achieved with the results of the length gauge approach and the time-dependent density functional theory. For the application of the velocity gauge approach to topological materials, Chern insulator is taken, using the two-band Haldane model. We found a good qualitative agreement between the velocity gauge and the length gauge approach in view of (i) the selection rules, (ii) the linear cutoff law scaling, and (iii) anomalous circular dichroism. We conclude that the velocity-gauge approach for HHG provides a theoretical tool to investigate topological materials
Group averaging in the (p,q) oscillator representation of SL(2,R)
We investigate refined algebraic quantisation with group averaging in a
finite-dimensional constrained Hamiltonian system that provides a simplified
model of general relativity. The classical theory has gauge group SL(2,R) and a
distinguished o(p,q) observable algebra. The gauge group of the quantum theory
is the double cover of SL(2,R), and its representation on the auxiliary Hilbert
space is isomorphic to the (p,q) oscillator representation. When p>1, q>1 and
p+q == 0 (mod 2), we obtain a physical Hilbert space with a nontrivial
representation of the o(p,q) quantum observable algebra. For p=q=1, the system
provides the first example known to us where group averaging converges to an
indefinite sesquilinear form.Comment: 34 pages. LaTeX with amsfonts, amsmath, amssymb. (References added;
minor typos corrected.
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