Lipschitz continuity for isotropic matrix functions

2021 ◽  
Vol 624 ◽  
pp. 259-266
Author(s):  
Marcus Carlsson
Keyword(s):  
Lipschitz Continuity ◽  
Matrix Functions ◽  
Isotropic Matrix

scholarly journals Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions

2019 ◽  
Vol 374 (2) ◽  
pp. 823-871 ◽  
Author(s):  
Simon Becker ◽  
Nilanjana Datta
Keyword(s):  
Convergence Rates ◽  
Lipschitz Continuity ◽  
Open Quantum Systems ◽  
High Energy ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Infinite Dimensions ◽  
Quantum Brownian Motion ◽  
Infinite Dimensional ◽  
Energy Constrained

Abstract By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl’s law.

scholarly journals Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry

2012 ◽  
Vol 18 (4) ◽  
pp. 825-837 ◽  
Author(s):  
Raf Cluckers ◽  
Immanuel Halupczok
Keyword(s):  
Lipschitz Continuity

scholarly journals Very badly approximable matrix functions

2005 ◽  
Vol 11 (1) ◽  
pp. 127-154 ◽  
Author(s):  
V. V. Peller ◽  
S. R. Treil
Keyword(s):  
Matrix Functions ◽  
Badly Approximable

A New Random Data Description and Its Use in Transferring Road Roughness to Vehicle Response

1974 ◽  
Vol 96 (2) ◽  
pp. 676-679 ◽  
Author(s):  
J. C. Wambold ◽  
W. H. Park ◽  
R. G. Vashlishan
Keyword(s):  
Spectral Density ◽  
Frequency Distribution ◽  
Descriptive Analysis ◽  
Joint Probability ◽  
Amplitude Distribution ◽  
Matrix Functions ◽  
Initial Portion ◽  
Power Spectral ◽  
Road Roughness ◽  
Cross Spectral Density

The initial portion of the paper discusses the more conventional method of obtaining a vehicle transfer function where phase and magnitude are determined by dividing the cross spectral density of the input/output by the power spectral density (PSD) of the input. The authors needed a more descriptive analysis (over PSD) and developed a new signal description called Amplitude Frequency Distribution (AFD); a discrete joint probability of amplitude and frequency with the advantage of retaining amplitude distribution as well as frequency distribution. A better understanding was obtained, and transfer matrix functions were developed using AFD.

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