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 $^{208}$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.

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 $any$ point $\phi_0$ in an $N$-dimensional field space with $V(\phi_0) > 0$, there exists a path of monotonically decreasing potential energy to a point $\phi_1$ within a path length $\lesssim {\cal O}(1)$, such that $\sqrt{N}\ln \frac{V(\phi_1)}{V(\phi_0)} \lesssim - {\cal O} (1)$. 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

Greedy Algorithms for Steiner Forest

In the Steiner Forest problem, we are given terminal pairs $\{s_i, t_i\}$, 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 $s_i, t_j$), 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

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