scholarly journals An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals

2018 ◽  
Author(s):  
Antonella Marchesiello ◽  
◽  
Libor Šnobl ◽  
Keyword(s):  
Magnetic Field ◽  
Infinite Family ◽  
Higher Order ◽  
Superintegrable Systems

scholarly journals An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Masatoshi Noumi ◽  
Ayako Sano
Keyword(s):  
Infinite Family ◽  
Type A ◽  
Higher Order ◽  
Difference Operators ◽  
Order Difference

AbstractWe introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’ operators through a formula of Wronski type.

scholarly journals Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 847 ◽  
Author(s):  
Dmitry V. Dolgy ◽  
Dae San Kim ◽  
Jongkyum Kwon ◽  
Taekyun Kim
Keyword(s):  
Random Variables ◽  
Infinite Family ◽  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Integer Power ◽  
Bernoulli Numbers And Polynomials ◽  
Power Sums ◽  
Power Sum ◽  
Invariant Integrals

In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p-adic invariant integrals on Z p . In particular, we derive various expressions for the polynomials associated with integer power sums, called integer power sum polynomials and also for their degenerate versions. Further, we compute the expectations of an infinite family of random variables which involve the degenerate Stirling polynomials of the second and some value of higher-order Bernoulli polynomials.

scholarly journals Integrable and Superintegrable Systems with Higher Order Integrals of Motion: Master Function Formalism

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Z. Alizadeh ◽  
H. Panahi
Keyword(s):  
Quantum Mechanics ◽  
Higher Order ◽  
Supersymmetric Quantum Mechanics ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Function Formalism ◽  
Superintegrable Systems ◽  
Master Function

We construct two-dimensional integrable and superintegrable systems in terms of the master function formalism and relate them to Mielnik’s and Marquette’s construction in supersymmetric quantum mechanics. For two different cases of the master functions, we obtain two different two-dimensional superintegrable systems with higher order integrals of motion.

scholarly journals Unveiling hidden multipolar orders with magnetostriction

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Adarsh S. Patri ◽  
Akito Sakai ◽  
SungBin Lee ◽  
Arun Paramekanti ◽  
Satoru Nakatsuji ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Degrees Of Freedom ◽  
Landau Theory ◽  
Length Change ◽  
Higher Order ◽  
Strongly Correlated ◽  
Cage Compounds ◽  
Broken Symmetries ◽  
Magnetostriction Coefficient ◽  
Hidden Orders

Abstract Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as “hidden orders” due to the formidable task of detecting them with conventional probes. In this work, we theoretically propose that magnetostriction provides a powerful and novel tool to directly detect higher-order multipolar symmetry breaking—such as the elusive octupolar order—by examining scaling behaviour of length change with respect to an applied magnetic field h. Employing a symmetry-based Landau theory, we focus on the family of Pr-based cage compounds with strongly correlated f-electrons, Pr(Ti,V,Ir)2(Al,Zn)20, whose low energy degrees of freedom are purely higher-order multipoles: quadrupoles $${\cal{O}}_{20,22}$$ O 20 , 22 and octupole $${\cal{T}}_{xyz}$$ T x y z . We demonstrate that a magnetic field along the [111] direction induces a distinct linear-in-h length change below the octupolar ordering temperature. The resulting “magnetostriction coefficient” is directly proportional to the octupolar order parameter, thus providing clear access to such subtle order parameters.

scholarly journals A Wireless, Passive pH Sensor Based on Magnetic Higher-Order Harmonic Fields

2009 ◽  
Vol 3 (2) ◽  
Author(s):  
B. Horton ◽  
E. Tan ◽  
B. Pereles ◽  
K. Ong
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Human Body ◽  
Remote Monitoring ◽  
Higher Order ◽  
Sensing Element ◽  
Dc Magnetic Field ◽  
Harmonic Field ◽  
Field Shift ◽  
Detection Coil

A wireless, passive sensor was fabricated for remote monitoring of chemical analytes in the human body. The sensor was made of a magnetically soft film (sensing element) and a permanent magnetic film (biasing element) sandwiching a reversibly swelling hydrogel. When subjected to a low frequency magnetic AC field, the sensing element generated higher-order harmonic magnetic fields that were detected with a remotely located detection coil. In the presence of a DC magnetic field (biasing field), such as that generated from the biasing element, the pattern of the higher-order harmonic magnetic fields varied, and the magnitude of change (referred to as the harmonic field shift) was proportional to the strength of the biasing field. The hydrogel, which acted as a transducer that converted variations in the chemical concentration into changes in dimensions, physically varied the separation distance between the sensing and the biasing elements. This causes a change in the magnitude of biasing field experienced by the sensing element, thus changing its higher-order harmonic field shift allowing remote measurement of chemical concentrations. The novelty of this sensor was its wireless and passive nature, which allows it to be used inside a human body for long term chemical monitoring. A scaled-up prototype was fabricated and tested to demonstrate the pH monitoring capability of the sensor. The main structure of the prototype sensor was a polycarbonate substrate containing a larger rectangular well of 36mm×8mm×4mm on top of a smaller well of 30mm×5mm×2mm (see Fig. 1). The smaller well was filled with hydrogel made of (poly)vinyl alcohol and (poly)acrylic acid. A commercial magnetoelastic thick film, Metglas 2826MB from Metglas Inc., was attached to the step at the bottom of the larger well and allowed to rest on the hydrogel. The DC magnetic field was provided by an Arnokrome III film (Arnold Magnetic Technologies) of 30mm×6mm attached at the bottom of the sensor structure. The sensor was placed on the detection coil, and its response was measured with a spectrum analyzer while exposed to test solutions of varying pH. The sensor's harmonic field shift, when cycled between pH 7 and pH 3, was measured and plotted in Fig. 2. As shown in the figure, the hydrogel swelled when the sensor was exposed to pH 3, decreasing the harmonic field shift. The response and recovery times of the hydrogel were below 2 minutes. This experiment proves the feasibility of the technology for real-time, remote monitoring of pH. Further work includes improving the response time and sensitivity of the hydrogel, as well as miniaturization of the sensor.

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