scholarly journals Data-Driven Model Reduction and Transfer Operator Approximation

2018 ◽  
Vol 28 (3) ◽  
pp. 985-1010 ◽  
Author(s):  
Stefan Klus ◽  
Feliks Nüske ◽  
Péter Koltai ◽  
Hao Wu ◽  
Ioannis Kevrekidis ◽  
...  
Keyword(s):  
Model Reduction ◽  
Transfer Operator ◽  
Data Driven ◽  
Operator Approximation

A High-Dimensional Inverse Frame Operator Approximation Technique

2016 ◽  
Vol 54 (4) ◽  
pp. 2282-2301 ◽  
Author(s):  
Guohui Song ◽  
Jacqueline Davis ◽  
Anne Gelb
Keyword(s):  
High Dimensional ◽  
Approximation Technique ◽  
Frame Operator ◽  
Operator Approximation

A Framework for Regularization via Operator Approximation

2015 ◽  
Vol 37 (2) ◽  
pp. B332-B359 ◽  
Author(s):  
Julianne M. Chung ◽  
Misha E. Kilmer ◽  
Dianne P. O'Leary
Keyword(s):  
Operator Approximation

scholarly journals Reduced Operator Approximation for Modelling Open Quantum Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 1550008
Author(s):  
A. Werpachowska
Keyword(s):  
Quantum Dynamics ◽  
Quantum Coherence ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Interaction Strength ◽  
Quantum Systems ◽  
Computationally Efficient ◽  
Memory Length ◽  
Open Quantum ◽  
Operator Approximation

We present the reduced operator approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order in the system–bath interaction operators, defining them for either general quantum harmonic oscillator baths or specialising them for independent baths with Lorentzian spectral densities. Its wide applicability is demonstrated on the examples of systems coupled to different baths (with varying system–bath interaction strength and bath memory length), and compared with the exact pseudomode and the popular quantum state diffusion approach. The method captures the decoherence of the system interacting with the bath, while conserving the total energy. Our results suggest that quantum coherence effects persist in open quantum systems for much longer times than previously thought.

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