Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a "relativity group" which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inonu contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's Theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the "Eisenhart" or "lightlike" lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.Comment: Typos corrected, references adde

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.Comment: 17 pages, 19 figure

Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy

We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in N=6 Chern-Simons theory. We show that D4-branes wrapped on CP^1 or D8-branes wrapped on CP^3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)_k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on C^2/Z_n.Comment: 36 pages, 6 figures; v2: with an improved derivation of Hall conductivity in section 3.2, typo corrections, and additional references; v3: explanations and comments adde

Well-being, job satisfaction, stress and burnout in speech-language pathologists: A review.

Purpose: The purpose of this review was to evaluate the factors that influence well-being, job satisfaction, stress, and burnout in speech-language pathologists (SLPs), and to identify the impact of these variables on worker recruitment and retention. Method: A systematic literature search was conducted. Four electronic databases (PsycARTICLES & PsycINFO, PubMed/Medline, CINHAL and ABI/INFORM) were searched. The search was limited to articles published in English between 1998 and June 2018. To be eligible for inclusion, studies needed to investigate or report well-being, job satisfaction, stress or burnout in SLPs. The methodological quality of each paper was assessed using the “Strengthening the Reporting of Observational Studies in Epidemiology” (for quantitative data) and “Consolidated criteria for Reporting Qualitative research” (for qualitative data) checklists. A data-driven thematic analysis of the literature was used to identify key themes. Result: Seventeen of 2050 studies met the inclusion criteria, of which fifteen were cross-sectional surveys yielding quantitative data. Two were qualitative studies. There was consistent evidence for SLPs in the USA and Canada experiencing satisfaction in their jobs. Facet analysis revealed six contributory themes, three of which were clearly associated with well-being: workload/caseload size, professional support, and salary. The contribution of job control (autonomy), length of time in practice and work setting was inconclusive. Evidence for stress and dissatisfaction leading to workforce attrition was found. Conclusion: Job satisfaction, stress, and burnout were found to be associated with various occupational features, including elements of demand, support and reward. No previous studies have investigated the interaction between different elements of a job, which might boost satisfaction or ameliorate stress in SLPs. This is the first review using a systematic approach to focus on well-being, satisfaction, stress and burnout in SLPs and suggests more work needs to be done to help identify and improve the well-being of the workforce

Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian Screened Coulomb potential via Hamiltonian hierarchy inspired variational method

The supersymmetric solutions of PT-symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schrodinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired variational method is used to obtain the approximate energy eigenvalues and corresponding wave functions.Comment: 13 page

Spin-gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin-gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin-gravity coupling plays in particular problems.Comment: 18 pages, 1 figur

Energy-Momentum Tensor of Particles Created in an Expanding Universe

We present a general formulation of the time-dependent initial value problem for a quantum scalar field of arbitrary mass and curvature coupling in a FRW cosmological model. We introduce an adiabatic number basis which has the virtue that the divergent parts of the quantum expectation value of the energy-momentum tensor are isolated in the vacuum piece of , and may be removed using adiabatic subtraction. The resulting renormalized is conserved, independent of the cutoff, and has a physically transparent, quasiclassical form in terms of the average number of created adiabatic `particles'. By analyzing the evolution of the adiabatic particle number in de Sitter spacetime we exhibit the time structure of the particle creation process, which can be understood in terms of the time at which different momentum scales enter the horizon. A numerical scheme to compute as a function of time with arbitrary adiabatic initial states (not necessarily de Sitter invariant) is described. For minimally coupled, massless fields, at late times the renormalized goes asymptotically to the de Sitter invariant state previously found by Allen and Folacci, and not to the zero mass limit of the Bunch-Davies vacuum. If the mass m and the curvature coupling xi differ from zero, but satisfy m^2+xi R=0, the energy density and pressure of the scalar field grow linearly in cosmic time demonstrating that, at least in this case, backreaction effects become significant and cannot be neglected in de Sitter spacetime.Comment: 28 pages, Revtex, 11 embedded .ps figure

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method