Bound States and Universality in Layers of Cold Polar Molecules

The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multi-layer systems.Comment: 6 pages, 5 figures. Revised version to be publishe

Weakly bound states of polar molecules in bilayers

We investigate a system of two polarized molecules in a layered trap. The molecules reside in adjacent layers and interact purely via the dipole-dipole interaction. We determine the properties of the ground state of the system as a function of the dipole moment and polarization angle. A bound state is always present in the system and in the weak binding limit the bound state extends to a very large distance and shows universal behavior.Comment: Presented at the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, 30 August - 3 September 201

Bound states of Dipolar Bosons in One-dimensional Systems

We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole-dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three, four, and five-body problems in two or more tubes. Our results indicate that in the weakly-coupled limit the inter-tube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.Comment: 22 pages, 7 figures, revised versio

Systematization of tensor mesons and the determination of the 2++2^{++} glueball

It is shown that new data on the $(J^{PC}=2^{++})$-resonances in the mass range $M\sim1700-2400$MeV support the linearity of the $(n,M^2)$-trajectories, where $n$ is the radial quantum number of quark--antiquark state. In this way all vacancies for the isoscalar tensor $q\bar q$-mesons in the range up to 2450 MeV are filled in. This allows one to fix the broad $f_2$-state with $M=2000\pm30$MeV and $\Gamma=530\pm40$MeV as the lowest tensor glueball. PACS numbers: 14.40.-n, 12.38.-t, 12.39.-MkComment: 10 pages, 1 figur

Generation of continuous-wave THz radiation by use of quantum interference

We propose a scheme for generation of continuous-wave THz radiation. The scheme requires a medium where three discrete states in a $\Lambda$ configuration can be selected, with the THz-frequency transition between the two lower metastable states. We consider the propagation of three-frequency continuous-wave electromagnetic (e.m.) radiation through a $\Lambda$ medium. Under resonant excitation, the medium absorption can be strongly reduced due to quantum interference of transitions, while the nonlinear susceptibility is enhanced. This leads to very efficient energy transfer between the e.m. waves providing a possibility for THz generation. We demonstrate that the photon conversion efficiency is approaching unity in this technique.Comment: 18 pages, 4 figure

A randomised feasibility study of serial magnetic resonance imaging to reduce treatment times in Charcot neuroarthropathy in people with diabetes (CADOM): A protocol

Background Charcot neuroarthropathy is a complication of peripheral neuropathy associated with diabetes which most frequently affects the lower limb. It can cause fractures and dislocations within the foot, which may progress to deformity and ulceration. Recommended treatment is immobilisation and offloading, with a below knee non-removable cast or boot. Duration of treatment varies from six months to more than one year. Small observational studies suggest that repeated assessment with Magnetic Resonance Imaging improves decision making about when to stop treatment, but this has not been tested in clinical trials. This study aims to explore the feasibility of using serial Magnetic Resonance Imaging without contrast in the monitoring of Charcot neuroarthropathy to reduce duration of immobilisation of the foot. A nested qualitative study aims to explore participants’ lived experience of Charcot neuroarthropathy and of taking part in the feasibility study. Methods We will undertake a two arm, open study, and randomise 60 people with a suspected or confirmed diagnosis of Charcot neuroarthropathy from five NHS, secondary care multidisciplinary Diabetic Foot Clinics across England. Participants will be randomised 1:1 to receive Magnetic Resonance Imaging at baseline and remission up to 12 months, with repeated foot temperature measurements and x-rays (standard care plus), or standard care plus with additional three-monthly Magnetic Resonance Imaging until remission up to 12 months (intervention). Time to confirmed remission of Charcot neuroarthropathy with off-loading treatment (days) and its variance will be used to inform sample size in a full-scale trial. We will look for opportunities to improve the protocols for monitoring techniques and the clinical, patient centred, and health economic measures used in a future study. For the nested qualitative study, we will invite a purposive sample of 10-14 people able to offer maximally varying experiences from the feasibility study to take part in semi-structured interviews to be analysed using thematic analysis. Discussion The study will inform the decision whether to proceed to a full-scale trial. It will also allow deeper understanding of the lived experience of Charcot neuroarthropathy, and factors that contribute to engagement in management and contribute to the development of more effective patient centred strategies. Trial registration ISRCTN, ISRCTN, 74101606. Registered on 6 November 2017, http://www.isrctn.com/ISRCTN74101606?q=CADom&filters=&sort=&offset=1&totalResults=1&page=1&pageSize=10&searchType=basic-searc

Generating random density matrices

We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transformations are introduced. To analyze statistical properties of quantum entanglement in bi-partite systems we analyze the distribution of Schmidt coefficients of random pure states. Such a distribution is derived in the case of a superposition of k random maximally entangled states. For another ensemble, obtained by performing selective measurements in a maximally entangled basis on a multi--partite system, we show that this distribution is given by the Fuss-Catalan law and find the average entanglement entropy. A more general class of structured ensembles proposed, containing also the case of Bures, forms an extension of the standard ensemble of structureless random pure states, described asymptotically, as N \to \infty, by the Marchenko-Pastur distribution.Comment: 13 pages in latex with 8 figures include