A probabilistic approach to some results by Nieto and Truax

In this paper, we reconsider some results by Nieto and Truax about generating functions for arbitrary order coherent and squeezed states. These results were obtained using the exponential of the Laplacian operator; more elaborated operational identities were used by Dattoli et al. \cite{Dattoli} to extend these results. In this note, we show that the operational approach can be replaced by a purely probabilistic approach, in the sense that the exponential of derivatives operators can be identified with equivalent expectation operators. This approach brings new insight about the kinks between operational and probabilistic calculus.Comment: 2nd versio

Explicit representations of biorthogonal polynomials

Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orthogonal polynomials

Solvable Systems of Linear Differential Equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQ

Salinity and temperature balances at the SPURS central mooring during fall and winter

Author Posting. © The Oceanography Society, 2015. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 28, no. 1 (2015): 56-65, doi:10.5670/oceanog.2015.06.One part of the Salinity Processes in the Upper-ocean Regional Study (SPURS) field campaign focused on understanding the physical processes affecting the evolution of upper-ocean salinity in the region of climatological maximum sea surface salinity in the subtropical North Atlantic (SPURS-1). An upper-ocean salinity budget provides a useful framework for increasing this understanding. The SPURS-1 program included a central heavily instrumented mooring for making accurate measurements of air-sea surface fluxes, as well as other moorings, Argo floats, and gliders that together formed a dense observational array. Data from this array are used to estimate terms in the upper-ocean salinity and heat budgets during the SPURS-1 campaign, with a focus on the first several months (October 2012 to February 2013) when the surface mixed layer was becoming deeper, fresher, and cooler. Specifically, we examine the salinity and temperature balances for an upper-ocean mixed layer, defined as the layer where the density is within 0.4 kg m–3 of its surface value. The gross features of the evolution of upper-ocean salinity and temperature during this fall/winter season are explained by a combination of evaporation and precipitation at the sea surface, horizontal transport of heat and salt by mixed-layer currents, and vertical entrainment of fresher, cooler fluid into the layer as it deepened. While all of these processes were important in the observed seasonal (fall) freshening at this location in the salinity-maximum region, the variability of salinity on monthly-to-intraseasonal time scales resulted primarily from horizontal advection.J.T. Farrar, A.J. Plueddemann, J.B. Edson, and the deployment of the central mooring were supported by NASA grant NNX11AE84G. L. Rainville, C. Lee, C. Eriksen, and the Seaglider program were supported by NASA grant NNX11AE78G. R. Schmitt was supported by NSF grant OCE-1129646. B. Hodges and D. Fratantoni were supported by NASA grant NNX11AE82G. The Prawler moorings were funded by PMEL. The data analysis was also supported by NASA grant NNX14AH38G

Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This consequently provides the solution for the exponential $e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005), Myczkowce, Poland. 13 pages, 31 reference

Optimized Planar Penning Traps for Quantum Information Studies

A one-electron qubit would offer a new option for quantum information science, including the possibility of extremely long coherence times. One-quantum cyclotron transitions and spin flips have been observed for a single electron in a cylindrical Penning trap. However, an electron suspended in a planar Penning trap is a more promising building block for the array of coupled qubits needed for quantum information studies. The optimized design configurations identified here promise to make it possible to realize the elusive goal of one trapped electron in a planar Penning trap for the first time - a substantial step toward a one-electron qubit

Brain responses to hypnotic verbal suggestions predict pain modulation

Background: The effectiveness of hypnosis in reducing pain is well supported by the scientific literature. Hypnosis typically involves verbal suggestions but the mechanisms by which verbal contents are transformed into predictive signals to modulate perceptual processes remain unclear. We hypothesized that brain activity during verbal suggestions would predict the modulation of responses to acute nociceptive stimuli. Methods: Brain activity was measured using BOLD-fMRI in healthy participants while they listened to verbal suggestions of HYPERALGESIA, HYPOALGESIA, or NORMAL sensation (control) following a standardized hypnosis induction. Immediately after the suggestions, series of noxious electrical stimuli were administered to assess pain-related responses. Brain responses measured during the suggestions were then used to predict changes in pain-related responses using delayed regression analyses. Results: Listening to suggestions of HYPERALGESIA and HYPOALGESIA produced BOLD decreases (vs. control) in the parietal operculum (PO) and in the anterior midcingulate cortex (aMCC), and increases in the left parahippocampal gyrus (lPHG). Changes in activity in PO, aMCC and PHG during the suggestions predicted larger pain-evoked responses following the HYPERALGESIA suggestions in the anterior cingulate cortex (ACC) and the anterior insula (aINS), and smaller pain-evoked responses following the HYPOALGESIA suggestions in the ACC, aMCC, posterior insula (pINS) and thalamus. These changes in pain-evoked brain responses are consistent with the changes in pain perception reported by the participants in HYPERALGESIA and HYPOALGESIA, respectively. Conclusions: The fronto-parietal network (supracallosal ACC and PO) has been associated with self-regulation and perceived self-agency. Deactivation of these regions during suggestions is predictive of the modulation of brain responses to noxious stimuli in areas previously associated with pain perception and pain modulation. The response of the hippocampal complex may reflect its role in contextual learning, memory and pain anticipation/expectations induced by verbal suggestions of pain modulation. This study provides a basis to further explore the transformation of verbal suggestions into perceptual modulatory processes fundamental to hypnosis neurophenomenology. These findings are discussed in relation to predictive coding models

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page

Autonomous multi-platform observations during the Salinity Processes in the Upper-ocean Regional Study

Author Posting. © The Oceanography Society, 2017. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 30, no. 2 (2017): 38–48, doi:10.5670/oceanog.2017.218.The Salinity Processes in the Upper-ocean Regional Study (SPURS) aims to understand the patterns and variability of sea surface salinity. In order to capture the wide range of spatial and temporal scales associated with processes controlling salinity in the upper ocean, research vessels delivered autonomous instruments to remote sites, one in the North Atlantic and one in the Eastern Pacific. Instruments sampled for one complete annual cycle at each of these two sites, which are subject to contrasting atmospheric forcing. The SPURS field programs coordinated sampling from many different platforms, using a mix of Lagrangian and Eulerian approaches. This article discusses the motivations, implementation, and first results of the SPURS-1 and SPURS-2 programs.SPURS is supported by multiple NASA grants, with important additional contributions from the US National Science Foundation, NOAA, and the Office of Naval Research, as well as international agencies. SVP drifters are deployed with support from NASA and the NOAA funded Global Drifter Program at the Lagrangian Drifter Laboratory of the Scripps Institution of Oceanography. SVP-S2 drifters are provided by NOAA-AOML and NASA. PRAWLER mooring development is supported by NOAA’s Office of Oceanic and Atmospheric Research, Ocean Observing and Monitoring Division, and by NOAA/PMEL