scholarly journals Revisiting the minimum length in the Schwinger–Keldysh formalism

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Roberto Casadio ◽  
Iberê Kuntz
Keyword(s):  
General Relativity ◽  
Energy Scale ◽  
The Other ◽  
Minimum Length ◽  
Length Scale ◽  
Expectation Value ◽  
Proper Distance ◽  
Higher Derivative ◽  
Gravitational Theories ◽  
Minimum Length Scale

AbstractThe existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger–Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational theories to all orders in perturbation theory. Using non-perturbative techniques, we also show that neither the conformal sector of general relativity nor higher-derivative gravity features a minimum length. A minimum length scale, on the other hand, seems to always be present when one considers in-out amplitudes, from which one could extract the energy scale of scattering processes.

scholarly journals The Minimum Length Scale for Evaluating QG Omega Using High-Resolution Model Data

2017 ◽  
Vol 145 (5) ◽  
pp. 1659-1678 ◽  
Author(s):  
Michael Battalio ◽  
Jamie Dyer
Keyword(s):  
Vertical Motion ◽  
Minimum Length ◽  
Length Scale ◽  
Operational Model ◽  
The North ◽  
Upscaling Technique ◽  
Resolution Model ◽  
Box Method ◽  
The Cross ◽  
Minimum Length Scale

Abstract The minimum length scale to investigate quasigeostrophic (QG) vertical motion within a mesoscale operational model is determined using simulations of 28 baroclinic systems from the North American Mesoscale Forecast System (NAM) model. Two upscaling methods are tested to find the optimal QG characteristic length. The box method takes an average of each field before performing finite-differencing calculations. The cross method samples the data at increasing distances between finite-difference calculations. The traditional QG omega equation is evaluated with each upscaling technique and found to be reliable between 800 and 200 hPa. The minimum QG length scale is found to be L = 140 km considering correlations of QG omega back to operational model values, which are for both methods on an “extended” QG omega. The box method performs marginally better than the cross method due to a larger reduction of QG forcing in higher-order wavenumbers, but at the appropriate length scale, both methods have indistinguishable correlations.

BRANS–DICKE AND RELATED EUCLIDEAN WORMHOLES

1998 ◽  
Vol 13 (12) ◽  
pp. 961-971 ◽  
Author(s):  
D. H. COULE
Keyword(s):  
Gravitational Constant ◽  
Einstein Frame ◽  
Quantum Mechanical ◽  
Minimum Length ◽  
Length Scale ◽  
Conformal Transformations ◽  
Wormhole Solution ◽  
Euclidean Wormholes ◽  
Minimum Length Scale ◽  
Euclidean Wormhole

In a recent paper1 Euclidean wormhole solution has been obtained with a vacuum Brans–Dicke theory with parameter ω=0. These wormholes suffer from unphysical values of the gravitational constant. One can relate the various known wormholes by means of conformal transformations; although one should not transform them directly to the Einstein frame as the gravitational constant there is "forced" physical: so removing the wormholes. However, by arguing for the existence of a fundamental minimum length scale such wormholes can now be considered as representative of quantum gravitational phenomena. One can also obtain wormholes as solutions of the quantum mechanical Wheeler–De Witt equation; now in Brans–Dicke for any ω>-3/2.

Structured Abrasive CMP: Length Scales, Subpads, and Planarization

1999 ◽  
Vol 566 ◽  
Author(s):  
D. P. Goetz
Keyword(s):  
Contact Mechanics ◽  
Elastic Foundation ◽  
Chemical Mechanical Planarization ◽  
Minimum Length ◽  
Length Scale ◽  
Uniform Compression ◽  
Length Scales ◽  
Process Pressure ◽  
Edge Exclusion ◽  
Minimum Length Scale

Chemical-Mechanical Planarization with structured abrasive uses a subpad to manage the pressure variations due to loading over a range of length scales. The effect of subpad construction on pressure responses related to those scales is illustrated.A minimum length scale for the effect of the subpad is established via contact mechanics. Differences between one- and two-layer subpads are shown. Uniform compression, point loading, and edge exclusion are considered briefly. A model of the subpad as a plate on an elastic foundation is applied to the problem of die doming. The roles of process pressure, die size, and subpad construction are illustrated. Planarization at the intra-die, die, and wafer scales are related to the subpad construction.

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