926 research outputs found
Geometric phases in astigmatic optical modes of arbitrary order
The transverse spatial structure of a paraxial beam of light is fully
characterized by a set of parameters that vary only slowly under free
propagation. They specify bosonic ladder operators that connect modes of
different order, in analogy to the ladder operators connecting
harmonic-oscillator wave functions. The parameter spaces underlying sets of
higher-order modes are isomorphic to the parameter space of the ladder
operators. We study the geometry of this space and the geometric phase that
arises from it. This phase constitutes the ultimate generalization of the Gouy
phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the
geometric phase of non-astigmatic optical modes with orbital angular momentum
states in limiting cases. We briefly discuss the well-known analogy between
geometric phases and the Aharonov-Bohm effect, which provides some
complementary insights in the geometric nature and origin of the generalized
Gouy phase shift. Our method also applies to the quantum-mechanical description
of wave packets. It allows for obtaining complete sets of normalized solutions
of the Schr\"odinger equation. Cyclic transformations of such wave packets give
rise to a phase shift, which has a geometric interpretation in terms of the
other degrees of freedom involved.Comment: final versio
Naming the Terrorist in Our Midst: Park51 and the Politics of Injustice
Given the role that “far-right Christianism” plays in fomenting suspicion and prejudice against non-Christians, this article argues that feminist and liberation theologies are critical for effective theory. Theoretical analysis is more robust when combined with critical feminist and liberation theological analyses for three reasons. First, religion is often appealed to as the moral underpinning of many positions in public debates when in fact it is being used to reinforce dominant systems of power. Second, without critical feminist and liberation theologians and ethicists taking a part in public debates, often the loudest or only religious voice heard in public debates has been that of a few conservative Christian groups with enormous power to define what counts as “Christian” for everyone else. Finally, perhaps the most critical potential contribution of critical feminist and liberation theologies and ethics is in the motivation they bring as many freedom struggles have been inspired by religious faith. This article utilizes these theories to critique the ad called “Kill the Ground Zero Mosque” developed by the National Republican Trust PAC and to expose its xenophobic and racist message
Geometric criticality between plaquette phases in integer-spin kagome XXZ antiferromagnets
The phase diagram of the uniaxially anisotropic antiferromagnet on the
kagom\'e lattice includes a critical line exactly described by the classical
three-color model. This line is distinct from the standard geometric classical
criticality that appears in the classical limit () of the 2D XY
model; the geometric T=0 critical line separates two unconventional
plaquette-ordered phases that survive to nonzero temperature. The
experimentally important correlations at finite temperature and the nature of
the transitions into these ordered phases are obtained using the mapping to the
three-color model and a combination of perturbation theory and a variational
ansatz for the ordered phases. The ordered phases show sixfold symmetry
breaking and are similar to phases proposed for the honeycomb lattice dimer
model and model. The same mapping and phase transition can be
realized also for integer spins but then require strong on-site
anisotropy in the Hamiltonian.Comment: 5 pages, 2 figure
Dutch fruiting vegetable growers prepare themselves for future demands of foreign retailers: British retailers in particular expect co-operation in supply chain May 2001
Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
General local spin ground states, described by a Valence Bond Solid (VBS)
on a two dimensional lattice are studied. The norm of these ground states is
mapped to a classical O(3) model on the same lattice. Using this
quantum-to-classical mapping we obtain the partial density matrix
associated with a subsystem of the original ground state. We show that
the entanglement spectrum of in a translation invariant lattice
is given by the spectrum of a quantum spin chain at the boundary of region ,
with local Heisenberg type interactions between spin 1/2 particles.Comment: 8 pages, 4 figures, one section and references adde
Diffraction and trapping in circular lattices
When a single two-level atom interacts with a pair of Laguerre-Gaussian beams
with opposite helicity, this leads to an efficient exchange of angular momentum
between the light field and the atom. When the radial motion is trapped by an
additional potential, the wave function of a single localized atom can be split
into components that rotate in opposite direction. This suggests a novel scheme
for atom interferometry without mirror pulses. Also atoms in this configuration
can be bound into a circular lattice
A constrained Potts antiferromagnet model with an interface representation
We define a four-state Potts model ensemble on the square lattice, with the
constraints that neighboring spins must have different values, and that no
plaquette may contain all four states. The spin configurations may be mapped
into those of a 2-dimensional interface in a 2+5 dimensional space. If this
interface is in a Gaussian rough phase (as is the case for most other models
with such a mapping), then the spin correlations are critical and their
exponents can be related to the stiffness governing the interface fluctuations.
Results of our Monte Carlo simulations show height fluctuations with an
anomalous dependence on wavevector, intermediate between the behaviors expected
in a rough phase and in a smooth phase; we argue that the smooth phase (which
would imply long-range spin order) is the best interpretation.Comment: 61 pages, LaTeX. Submitted to J. Phys.
Kondo lattice on the edge of a two-dimensional topological insulator
We revisit the problem of a single quantum impurity on the edge of a
two-dimensional time-reversal invariant topological insulator and show that the
zero temperature phase diagram contains a large local moment region for
antiferromagnetic Kondo coupling which was missed by previous poor man's
scaling treatments. The combination of an exact solution at the so-called
decoupling point and a renormalization group analysis \`a la
Anderson-Yuval-Hamann allows us to access the regime of strong
electron-electron interactions on the edge and strong Kondo coupling. We apply
similar methods to the problem of a regular one-dimensional array of quantum
impurities interacting with the edge liquid. When the edge electrons are at
half-filling with respect to the impurity lattice, the system remains gapless
unless the Luttinger parameter of the edge is less than 1/2, in which case
two-particle backscattering effects drive the system to a gapped phase with
long-range Ising antiferromagnetic order. This is in marked contrast with the
gapped disordered ground state of the ordinary half-filled one-dimensional
Kondo lattice.Comment: 18 pages, 3 figures; fixed typos, updated reference
Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective
We analyze the problem of a quantum computer in a correlated environment
protected from decoherence by QEC using a perturbative renormalization group
approach. The scaling equation obtained reflects the competition between the
dimension of the computer and the scaling dimension of the correlations. For an
irrelevant flow, the error probability is reduced to a stochastic form for long
time and/or large number of qubits; thus, the traditional derivation of the
threshold theorem holds for these error models. In this way, the ``threshold
theorem'' of quantum computing is rephrased as a dimensional criterion.Comment: 4.1 pages, minor correction and an improved discussion of Eqs. (4)
and (14
- …