scholarly journals Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

2018 ◽  
Vol 97 (4) ◽  
Author(s):  
Emanuele Alesci ◽  
Gioele Botta ◽  
Gabriele V. Stagno
Keyword(s):  
Regularization Scheme ◽  
Statistical Regularization ◽  
Loop Gravity ◽  
Effective Hamiltonians

Quantum Resonances: Line Profiles and Dynamics

2003 ◽  
Vol 68 (3) ◽  
pp. 529-553 ◽  
Author(s):  
Ivana Paidarová ◽  
Philippe Durand
Keyword(s):  
Hydrogen Atom ◽  
Operator Theory ◽  
Quantum Dynamics ◽  
Line Profiles ◽  
Static Electric Field ◽  
Reversal Effect ◽  
Quantum Resonances ◽  
Energy Dependent ◽  
Effective Hamiltonians

The wave operator theory of quantum dynamics is reviewed and applied to the study of line profiles and to the determination of the dynamics of interacting resonances. Energy-dependent and energy-independent effective Hamiltonians are investigated. The q-reversal effect in spectroscopy is interpreted in terms of interfering Fano profiles. The dynamics of an hydrogen atom subjected to a strong static electric field is revisited.

Distributed learning with indefinite kernels

2019 ◽  
Vol 17 (06) ◽  
pp. 947-975 ◽  
Author(s):  
Lei Shi
Keyword(s):  
Large Scale ◽  
Substantial Reduction ◽  
Computation Time ◽  
Distributed Learning ◽  
Rates Of Convergence ◽  
Regression Problem ◽  
Data Set ◽  
Regularization Scheme ◽  
Original Algorithm ◽  
Indefinite Kernel

We investigate the distributed learning with coefficient-based regularization scheme under the framework of kernel regression methods. Compared with the classical kernel ridge regression (KRR), the algorithm under consideration does not require the kernel function to be positive semi-definite and hence provides a simple paradigm for designing indefinite kernel methods. The distributed learning approach partitions a massive data set into several disjoint data subsets, and then produces a global estimator by taking an average of the local estimator on each data subset. Easy exercisable partitions and performing algorithm on each subset in parallel lead to a substantial reduction in computation time versus the standard approach of performing the original algorithm on the entire samples. We establish the first mini-max optimal rates of convergence for distributed coefficient-based regularization scheme with indefinite kernels. We thus demonstrate that compared with distributed KRR, the concerned algorithm is more flexible and effective in regression problem for large-scale data sets.

scholarly journals Effective Hamiltonians for periodically driven systems

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
Saar Rahav ◽  
Ido Gilary ◽  
Shmuel Fishman
Keyword(s):  
Driven Systems ◽  
Periodically Driven ◽  
Effective Hamiltonians

Loop gravity and Schwarzschild spacetime

2017 ◽  
Vol 14 (04) ◽  
pp. 1750055
Author(s):  
Ahmida Bendjoudi ◽  
Noureddine Mebarki
Keyword(s):  
Schwarzschild Spacetime ◽  
Tetrahedral Structure ◽  
Spacetime Manifold ◽  
Loop Gravity

A discretization for the Schwarzschild spacetime manifold is introduced and investigated. It is shown that the discreteness of the area of space shown in loop gravity leads to a tetrahedral structure characterizing the Schwarzschild manifold.

scholarly journals Quantum reduced loop gravity: Extension to gauge vector field

2017 ◽  
Vol 95 (10) ◽  
Author(s):  
Jakub Bilski ◽  
Emanuele Alesci ◽  
Francesco Cianfrani ◽  
Pietro Donà ◽  
Antonino Marcianò
Keyword(s):  
Vector Field ◽  
Loop Gravity
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