21,664 research outputs found
On the extra phase correction to the semiclassical spin coherent-state propagator
The problem of an origin of the Solary-Kochetov extra-phase contribution to
the naive semiclassical form of a generalized phase-space propagator is
addressed with the special reference to the su(2) spin case which is the most
important in applications. While the extra-phase correction to a flat
phase-space propagator can straightforwardly be shown to appear as a difference
between the principal and the Weyl symbols of a Hamiltonian in the
next-to-leading order expansion in the semiclassical parameter, the same
statement for the semiclassical spin coherent-state propagator holds provided
the Holstein-Primakoff representation of the su(2) algebra generators is
employed.Comment: 19 pages, no figures; a more general treatment is presented, some
references are added, title is slightly changed; submitted to JM
Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion
We analyze the interference between tunneling paths that occurs for a spin
system with both fourth-order and second-order transverse anisotropy. Using an
instanton approach, we find that as the strength of the second-order transverse
anisotropy is increased, the tunnel splitting is modulated, with zeros
occurring periodically. This effect results from the interference of four
tunneling paths connecting easy-axis spin orientations and occurs in the
absence of any magnetic field.Comment: 6 pages, 5 eps figures. Version published in EPL. Expanded from v1:
Appendix added, references added, 1 figure added, others modified
cosmeticall
The Giant Monopole Resonance in Pb isotopes
The extraction of the nuclear incompressibility from the isoscalar giant
monopole resonance (GMR) measurements is analysed. Both pairing and mutually
enhanced magicity (MEM) effects play a role in the shift of the GMR energy
between the doubly closed shell Pb nucleus and other Pb isotopes.
Pairing effects are microscopically predicted whereas the MEM effect is
phenomenologically evaluated. Accurate measurements of the GMR in open-shell Pb
isotopes are called for.Comment: 4 page
Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons
Spin coherent state path integrals with discontinuous semiclassical paths are
investigated with special reference to a realistic model for the magnetic
degrees of freedom in the Fe8 molecular solid. It is shown that such paths are
essential to a proper understanding of the phenomenon of quenched spin
tunneling in these molecules. In the Fe8 problem, such paths are shown to arise
as soon as a fourth order anisotropy term in the energy is turned on, making
this term a singular perturbation from the semiclassical point of view. The
instanton approximation is shown to quantitatively explain the magnetic field
dependence of the tunnel splitting, as well as agree with general rules for the
number of quenching points allowed for a given value of spin. An accurate
approximate formula for the spacing between quenching points is derived
Quantum phase interference (Berry phase) in single-molecule magnets of Mn12
Magnetization measurements of a molecular clusters Mn12 with a spin ground
state of S = 10 show resonance tunneling at avoided energy level crossings. The
observed oscillations of the tunnel probability as a function of the magnetic
field applied along the hard anisotropy axis are due to topological quantum
phase interference of two tunnel paths of opposite windings. Mn12 is therefore
the second molecular clusters presenting quantum phase interference.Comment: 3 pages, 4 figures, MMM'01 conference (12-16 Nov.
Greedy Algorithms for Steiner Forest
In the Steiner Forest problem, we are given terminal pairs ,
and need to find the cheapest subgraph which connects each of the terminal
pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson
gave primal-dual constant-factor approximation algorithms for this problem;
until now, the only constant-factor approximations we know are via linear
programming relaxations.
We consider the following greedy algorithm: Given terminal pairs in a metric
space, call a terminal "active" if its distance to its partner is non-zero.
Pick the two closest active terminals (say ), set the distance
between them to zero, and buy a path connecting them. Recompute the metric, and
repeat. Our main result is that this algorithm is a constant-factor
approximation.
We also use this algorithm to give new, simpler constructions of cost-sharing
schemes for Steiner forest. In particular, the first "group-strict" cost-shares
for this problem implies a very simple combinatorial sampling-based algorithm
for stochastic Steiner forest
Bounds on Slow Roll at the Boundary of the Landscape
We present strong evidence that the tree level slow roll bounds of
arXiv:1807.05193 and arXiv:1810.05506 are valid, even when the tachyon has
overlap with the volume of the cycle wrapped by the orientifold. This extends
our previous results in the volume-dilaton subspace to a semi-universal
modulus. Emboldened by this and other observations, we investigate what it
means to have a bound on (generalized) slow roll in a multi-field landscape. We
argue that for point in an -dimensional field space with
, there exists a path of monotonically decreasing potential
energy to a point within a path length , such
that . The
previous de Sitter swampland bounds are specific ways to realize this stringent
non-local constraint on field space, but we show that it also incorporates (for
example) the scenario where both slow roll parameters are intermediate-valued
and the Universe undergoes a small number of e-folds, as in the Type IIA set up
of arXiv:1310.8300. Our observations are in the context of tree level
constructions, so we take the conservative viewpoint that it is a
characterization of the classical "boundary" of the string landscape. To
emphasize this, we argue that these bounds can be viewed as a type of
Dine-Seiberg statement.Comment: v4: one more referenc
Energy Efficient Service Delivery in Clouds in Compliance with the Kyoto Protocol
Cloud computing is revolutionizing the ICT landscape by providing scalable
and efficient computing resources on demand. The ICT industry - especially data
centers, are responsible for considerable amounts of CO2 emissions and will
very soon be faced with legislative restrictions, such as the Kyoto protocol,
defining caps at different organizational levels (country, industry branch
etc.) A lot has been done around energy efficient data centers, yet there is
very little work done in defining flexible models considering CO2. In this
paper we present a first attempt of modeling data centers in compliance with
the Kyoto protocol. We discuss a novel approach for trading credits for
emission reductions across data centers to comply with their constraints. CO2
caps can be integrated with Service Level Agreements and juxtaposed to other
computing commodities (e.g. computational power, storage), setting a foundation
for implementing next-generation schedulers and pricing models that support
Kyoto-compliant CO2 trading schemes
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