Coherent states for a particle on a sphere

The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J. Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space related with quantum fluctuations. The expectation values of the position and the angular momentum in the coherent states are regarded as the best possible approximation of the classical phase space. The correctness of the introduced coherent states is illustrated by an example of the rotator.Comment: LaTeX, 16 pages, 2 figure

Extended coherent states and modified perturbation theory

An extended coherent state for describing a system of two interacting quanum objects is considered. A modified perturbation theory based on using the extended coherent states is formulated.Comment: LaTex, 7 pages, no figures, minor correction

Developing a Pedagogical Framework for Designing a Multisensory Serious Gaming Environment

The importance of multisensory interaction for learning has increased with improved understanding of children’s sensory development, and a flourishing interest in embodied cognition. The potential to foster new forms of multisensory interaction through various sensor, mobile and haptic technologies is promising in providing new ways for young children to engage with key mathematical concepts. However, designing effective learning environments for real world classrooms is challenging, and requires a pedagogically, rather than technologically, driven approach to design. This paper describes initial work underpinning the development of a pedagogical framework, intended to inform the design of a multisensory serious gaming environment. It identifies the theoretical basis of the framework, illustrates how this informs teaching strategies, and outlines key technology research driven perspectives and considerations important for informing design. An initial table mapping mathematical concepts to design, a framework of considerations for design, and a process model of how the framework will continue to be developed across the design process are provided

Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates

Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.Comment: Phd tutorial, 23 pages, 17 figure

Method of Collective Degrees of Freedom in Spin Coherent State Path Integral

We present a detailed field theoretic description of those collective degrees of freedom (CDF) which are relevant to study macroscopic quantum dynamics of a quasi-one-dimensional ferromagnetic domain wall. We apply spin coherent state path integral (SCSPI) in the proper discrete time formalism (a) to extract the relevant CDF's, namely, the center position and the chirality of the domain wall, which originate from the translation and the rotation invariances of the system in question, and (b) to derive effective action for the CDF's by elimination of environmental zero-modes with the help of the {\it Faddeev-Popov technique}. The resulting effective action turns out to be such that both the center position and the chirality can be formally described by boson coherent state path integral. However, this is only formal; there is a subtle departure from the latter.Comment: 10 pages, 1 figur

Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.Comment: 5 pages, RevTe

f-Oscillators and Nonlinear Coherent States

The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.Comment: Latex, 32 pages, accepted by Physica Script

Semiclassical description of Heisenberg models via spin-coherent states

We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of coherent states. This quantity turns out to have a natural interpretation with respect to time-dependent solutions of the equations of motion and allows for an estimate of quantum fluctuations in a semiclassical regime. The general results are applied to solitons, instantons and vortices in several one- and two-dimensional models.Comment: 14 page