Quantum Entangled Dark Solitons Formed by Ultracold Atoms in Optical Lattices

Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in our analysis, including von Neumann and generalized quantum entropies, quantum depletion, and the pair correlation function. We find that quantum effects cause the soliton to fill in. Moreover, soliton-soliton collisions become inelastic, in strong contrast to the predictions of mean-field theory. These features show that the lifetime and collision properties of dark solitons in optical lattices provide clear signals of quantum effects.Comment: 4 pages, 4 figures; version appearing in PRL, only minor changes from v

Option pricing in affine generalized Merton models

In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in [Belomestny et al., J. Func. Anal., 2009]. We conclude with some numerical examples

Growth of primordial black holes in a universe containing a massless scalar field

The evolution of primordial black holes in a flat Friedmann universe with a massless scalar field is investigated in fully general relativistic numerical relativity. A primordial black hole is expected to form with a scale comparable to the cosmological apparent horizon, in which case it may go through an initial phase with significant accretion. However, if it is very close to the cosmological apparent horizon size, the accretion is suppressed due to general relativistic effects. In any case, it soon gets smaller than the cosmological horizon and thereafter it can be approximated as an isolated vacuum solution with decaying mass accretion. In this situation the dynamical and inhomogeneous scalar field is typically equivalent to a perfect fluid with a stiff equation of state $p=\rho$. The black hole mass never increases by more than a factor of two, despite recent claims that primordial black holes might grow substantially through accreting quintessence. It is found that the gravitational memory scenario, proposed for primordial black holes in Brans-Dicke and scalar-tensor theories of gravity, is highly unphysical.Comment: 24 pages, accepted for publication in Physical Review

Dynamical Realization of Macroscopic Superposition States of Cold Bosons in a Tilted Double Well

We present exact expressions for the quantum sloshing of Bose-Einstein condensates in a tilted two-well potential. Tunneling is suppressed by a small potential difference between wells, or tilt. However, tunneling resonances occur for critical values of the tilt when the barrier is high. At resonance, tunneling times on the order of 10-100 ms are possible. Furthermore, such tilted resonances lead to a dynamical scheme for creating few-body NOON-like macroscopic superposition states which are protected by the many body wavefunction against potential fluctuations.Comment: 6 pages, 5 figures, final version, only minor changes from previous arXiv versio

Intermediate inflation in light of the three-year WMAP observations

The three-year observations from the Wilkinson Microwave Anisotropy Probe have been hailed as giving the first clear indication of a spectral index n_s<1. We point out that the data are equally well explained by retaining the assumption n_s=1 and allowing the tensor-to-scalar ratio r to be non-zero. The combination n_s=1 and r>0 is given (within the slow-roll approximation) by a version of the intermediate inflation model with expansion rate H(t) \propto t^{-1/3}. We assess the status of this model in light of the WMAP3 data.Comment: 4 pages RevTeX4 with one figure. Minor changes to match PRD accepted versio

An overview of tea research in Tanzania - with special reference to the Southern Highlands.

The history of tea development in Tanzania from the early part of this century to the present is summarised. Average yields of made tea from well managed estates in the Mufindi district have increased from around 600 kg ha-1 in the late 1950s to 3000 kg ha-1 at the present time: by comparison, yields from smallholder farms have remained much lower, averaging only 400-500 kg ha-1. There have been a large number of technical, economic and other changes over the last 30 to 40 years. The removal of shade trees, the use of herbicides, the application of NPK compound fertilisers, the introduction of irrigation (on some estates) and changes in harvesting policy have all contributed to the increases in yield. Financial and infrastructural problems have contributed to the low yields from many smallholders and others, and have limited the uptake of new technology. The contribution of research is reviewed, from the start of the Tea Research Institute of East Africa in Kenya in 1951, through to the development of the Marikitanda Tea Research Centre in Amani in 1967; the Ngwazi Tea Research Unit in Mufindi (1967 to 1970, and from 1986), and lastly the Kifyulilo Tea Research Station, also in Mufindi in 1986. The yield potential of well fertilized and irrigated clonal tea, grown at an altitude of 1800 m, is around 6000 kg ha-1. This potential is reduced by drought, lack of fertilizer, bush vacancies and inefficient harvesting practices. The corresponding potential yields at high (2200 m) and low (1200 m) altitude sites range from 3000-3500 kg ha-1 up to 9000-10000 kg ha-1 and are largely a function of temperature. The opportunities for increasing yields of existing tea, smallholder and estate, are enormous. Tea production in the Southern Highlands of Tanzania is about to expand rapidly. Good, appropriate research is needed to sustain this development over the long term, and suggestions on how best this is done in order to assist the large scale producers as well as the smallholders, are discussed

Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design

R. Lavy and C. Swamy (FOCS 2005, J. ACM 2011) introduced a general method for obtaining truthful-in-expectation mechanisms from linear programming based approximation algorithms. Due to the use of the Ellipsoid method, a direct implementation of the method is unlikely to be efficient in practice. We propose to use the much simpler and usually faster multiplicative weights update method instead. The simplification comes at the cost of slightly weaker approximation and truthfulness guarantees