scholarly journals MINIMAL LENGTH IN QUANTUM SPACE AND INTEGRATIONS OF THE LINE ELEMENT IN NONCOMMUTATIVE GEOMETRY

2012 ◽  
Vol 24 (05) ◽  
pp. 1250010 ◽  
Author(s):  
PIERRE MARTINETTI ◽  
FLAVIO MERCATI ◽  
LUCA TOMASSINI
Keyword(s):  
Noncommutative Geometry ◽  
Line Element ◽  
Geodesic Distance ◽  
High Energy ◽  
Minimal Length ◽  
Quantum Space ◽  
Spectral Distance ◽  
Moyal Plane ◽  
The One ◽  
Quantum Spacetime

We question the emergence of a minimal length in quantum spacetime, comparing two notions that appeared at various points in the literature: on the one side, the quantum length as the spectrum of an operator L in the Doplicher Fredenhagen Roberts (DFR) quantum spacetime, as well as in the canonical noncommutative spacetime (θ-Minkowski); on the other side, Connes' spectral distance in noncommutative geometry. Although in the Euclidean space the two notions merge into the one of geodesic distance, they yield distinct results in the noncommutative framework. In particular, in the Moyal plane, the quantum length is bounded above from zero while the spectral distance can take any real positive value, including infinity. We show how to solve this discrepancy by doubling the spectral triple. This leads us to introduce a modified quantum length d′L, which coincides exactly with the spectral distance dD on the set of states of optimal localization. On the set of eigenstates of the quantum harmonic oscillator — together with their translations — d′L and dD coincide asymptotically, both in the high energy and large translation limits. At small energy, we interpret the discrepancy between d′L and dD as two distinct ways of integrating the line element on a quantum space. This leads us to propose an equation for a geodesic on the Moyal plane.

scholarly journals Spectral distance on Lorentzian Moyal plane

2020 ◽  
Vol 17 (06) ◽  
pp. 2050089
Author(s):  
Anwesha Chakraborty ◽  
Biswajit Chakraborty
Keyword(s):  
Noncommutative Geometry ◽  
Coherent States ◽  
Euclidean Case ◽  
Spectral Triples ◽  
Spectral Distance ◽  
Moyal Plane ◽  
Pure States ◽  
Math Phys ◽  
Distance Formula

We present here a completely operatorial approach, using Hilbert–Schmidt operators, to compute spectral distances between time-like separated “events”, associated with the pure states of the algebra describing the Lorentzian Moyal plane, using the axiomatic framework given by [N. Franco, The Lorentzian distance formula in noncommutative geometry, J. Phys. Conf. Ser. 968(1) (2018) 012005; N. Franco, Temporal Lorentzian spectral triples, Rev. Math. Phys. 26(8) (2014) 1430007]. The result shows no deformations of non-commutative origin, as in the Euclidean case, if the pure states are constructed out of Glauber–Sudarshan coherent states.

P20 phosphor on polyimide as a large area high-resolution transmission screen for slow scan CCD systems

1995 ◽  
Vol 53 ◽  
pp. 20-21
Author(s):  
C. C. Ahn ◽  
S. Karnes ◽  
M. Lvovsky ◽  
C. M. Garland ◽  
H. A. Atwater ◽  
...  
Keyword(s):  
Mechanical Stability ◽  
High Energy ◽  
Practical Implementation ◽  
Line Pair ◽  
Modulation Transfer ◽  
Large Area ◽  
Ccd Imaging ◽  
Transmission Electron ◽  
The One ◽  
Beam Broadening

The bane of CCD imaging systems for transmission electron microscopy at intermediate and high voltages has been their relatively poor modulation transfer function (MTF), or line pair resolution. The problem originates primarily with the phosphor screen. On the one hand, screens should be thick so that as many incident electrons as possible are converted to photons, yielding a high detective quantum efficiency(DQE). The MTF diminishes as a function of scintillator thickness however, and to some extent as a function of fluorescence within the scintillator substrates. Fan has noted that the use of a thin layer of phosphor beneath a self supporting 2μ, thick Al substrate might provide the most appropriate compromise for high DQE and MTF in transmission electron microcscopes which operate at higher voltages. Monte Carlo simulations of high energy electron trajectories reveal that only little beam broadening occurs within this thickness of Al film. Consequently, the MTF is limited predominantly by broadening within the thin phosphor underlayer. There are difficulties however, in the practical implementation of this design, associated mostly with the mechanical stability of the Al support film.

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

scholarly journals High-resolution late Holocene sedimentary cores record the long history of the city of Cádiz (south-western Spain)

2020 ◽  
Vol 27 ◽  
pp. 35-47
Author(s):  
Ferréol Salomon ◽  
Darío Bernal-Casasola ◽  
José J. Díaz ◽  
Macarena Lara ◽  
Salvador Domínguez-Bella ◽  
...  
Keyword(s):  
Western Europe ◽  
High Energy ◽  
Mitigation Strategies ◽  
Urban Centre ◽  
Archaeological Data ◽  
Lisbon Earthquake ◽  
History Of ◽  
Western Spain ◽  
The One ◽  
The City

Abstract. Today, coastal cities worldwide are facing major changes resulting from climate change and anthropogenic forcing, which requires adaptation and mitigation strategies to be established. In this context, sedimentological archives in many Mediterranean cities record a multi-millennial history of environmental dynamics and human adaptation, revealing a long-lasting resilience. Founded by the Phoenicians around 3000 years ago, Cádiz (south-western Spain) is a key example of a coastal resilient city. This urban centre is considered to be one of the first cities of western Europe and has experienced major natural hazards during its long history, such as coastal erosion, storms, and also tsunamis (like the one in 1755 CE following the destructive Lisbon earthquake). In the framework of an international, joint archaeological and geoarchaeological project, three cores have been drilled in a marine palaeochannel that ran through the ancient city of Cádiz. These cores reveal a ≥50 m thick Holocene sedimentary sequence. Importantly, most of the deposits date from the 1st millennium BCE to the 1st millennium CE. This exceptional sedimentary archive will allow our scientific team to achieve its research goals, which are (1) to reconstruct the palaeogeographical evolution of this specific coastal area; (2) to trace the intensity of activities of the city of Cádiz based on archaeological data, as well as geochemical and palaeoecological indicators; and (3) to identify and date high-energy event deposits such as storms and tsunamis.

scholarly journals FRACTAL GEOMETRY AND QUARK-GLUON PLASMA PHYSICS

2020 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
N. G. Antoniou
Keyword(s):  
Plasma Physics ◽  
Quark Gluon Plasma ◽  
Fractal Geometry ◽  
Gluon Plasma ◽  
High Energy ◽  
Energy Collision ◽  
High Energy Collision ◽  
One Dimensional ◽  
Interaction Dynamics ◽  
The One

Incorporating fractal geometry in the Regge-Mueller approach to strong interaction dynamics one may formulate a model for the one-dimensional critical sector of the hadronic 5-matrix in a high energy collision. A non conventional component of the correlation functions in rapidity space is obtained, the phenomenological implications of which are related with the intermittency effects in quark-gluon plasma physics.

INSTANTON-INDUCED CROSS-SECTION AT HIGH ENERGIES: LEADING ORDER AND BEYOND

1990 ◽  
Vol 05 (24) ◽  
pp. 1983-1991 ◽  
Author(s):  
S. YU. KHLEBNIKOV ◽  
V. A. RUBAKOV ◽  
P. G. TINYAKOV
Keyword(s):  
Total Cross Section ◽  
Explicit Form ◽  
Cross Section ◽  
High Energy ◽  
Electroweak Theory ◽  
Leading Order ◽  
Instanton Action ◽  
High Energies ◽  
High Energy Collisions ◽  
The One

We study the total cross-section of high energy collisions in the one-instanton sector of purely bosonic theories with instantons. We find that in the limit g2 → 0, E/E sph = fixed , the leading behavior of the total cross-section is σ lot ~ exp [1/g2(−2S0 + F(E/E sph ))], where S0 is the instanton action. In the electroweak theory at E/E sph ≪ 1, the function F(E/E sph ) is determined by the gauge boson part of the instanton configuration and its explicit form is found.

scholarly journals Heuristic derivation of Casimir effect in minimal length theories

2020 ◽  
Vol 29 (02) ◽  
pp. 2050011 ◽  
Author(s):  
Massimo Blasone ◽  
Gaetano Lambiase ◽  
Giuseppe Gaetano Luciano ◽  
Luciano Petruzziello ◽  
Fabio Scardigli
Keyword(s):  
Field Theory ◽  
Parallel Plate ◽  
Casimir Effect ◽  
Generalized Uncertainty Principle ◽  
Casimir Energy ◽  
Minimal Length ◽  
Quadratic Term ◽  
Quantum Field ◽  
The One ◽  
Plate Geometry

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory (QFT). Experimental developments are finally discussed.

The Minimum Wave Damping Selects the Most Favored Solution from Multiple Ones to Acoustic-Like Problems

2011 ◽  
Vol 673 ◽  
pp. 11-20
Author(s):  
Hyoung In Lee ◽  
El Hang Lee
Keyword(s):  
Noble Metals ◽  
Continuous Wave ◽  
Stokes Equations ◽  
Temporal Frequency ◽  
Radiation Condition ◽  
High Energy ◽  
Wave Mode ◽  
Detonation Waves ◽  
Surrounding Space ◽  
The One

Back in 1990, D. S. Stewart and the first author contributed significantly to understanding the one-dimensional stability of detonation waves [1]. For this purpose, the reactive Euler’s equation with the one-component reaction term was linearized around the steady state of the well-known ZND (Zeldovich-Doering-von Neumann) model. The key aspect of this paper was to derive the linearized radiation condition (named after A. Sommerfeld). They numerically found multiple eigenvalues for pairs of the temporal frequency and temporal attenuation rate (TAR). Of course, the propagating-wave mode having the least value of the TAR (in the sense of its absolute value) was selected. The successful numerical implementation of the far-field radiation condition is a must when it comes to incorporating a large surrounding space into a problem of finite extent. To one of the sure examples in this category belong the problems involving detonation waves, where high-energy-rate processes take place in spatially confined spaces while the surrounding space should be taken into account for reasons of energy loss (or leaky waves in the language of optics). In another fascinating area of science is nano-photonics, where energy transport should be handled in highly confined regions of space, yet being surrounded by unbounded (dielectric) media. The total energy release in nano-photonics is certainly much smaller than that involved in detonation. However, the energy per unit nanometer-scale volume is not negligibly small in nano-photonics. Over the years, the first author has been successful in implementing both theory and numerical methods to find a multitude of eigenvalues in optics [2]. In this case, the governing Maxwell’s equations are already in a linearized form, being in a sense similar to the linearized Euler equations. In addition, the noble metals such as gold and silver are instrumental in enhancing local electric-field intensities, for which the science of plasmonics is being vigorously investigated in nano-photonics. Even the Bloch’s hydrodynamic equation describing the collective motion of the electrons is akin to the Navier-Stokes equations [3]. Meanwhile, assuming a real-valued frequency has been an old tradition in optics, partly because the real-valued photon’s energy is proportional to frequency and normally the continuous-wave (cw) approximation holds true. In a radical departure from this optical scientists’ tradition, we have recently attempted to deal with complex-valued frequencies in examining the wave propagations around nanoparticles [4, 5]. In consequence, the stability of multiple propagating waves was successfully determined for selecting most realizable wave mode. Further interesting points of the interplay between the two seemingly disparate branches of science (fluid dynamics and photonics) will be expounded in this talk.

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