Exact calculation of distributions for excitonic oscillator strength and inverse participation ratio in disordered quantum wires

2003 ◽  
Vol 67 (20) ◽  
Author(s):  
Helge Ludwig ◽  
Erich Runge ◽  
Roland Zimmermann
Keyword(s):  
Oscillator Strength ◽  
Quantum Wires ◽  
Exact Calculation ◽  
Inverse Participation Ratio ◽  
Participation Ratio

scholarly journals Displacement Transformations as a Tool to Study Many-Body Localization

2021 ◽  
Vol 9 ◽  
Author(s):  
Pablo Serna ◽  
Miguel Ortuño ◽  
Andrés M. Somoza
Keyword(s):  
Excited States ◽  
Short Range ◽  
The State ◽  
Large System ◽  
Many Body ◽  
Inverse Participation Ratio ◽  
One Dimensional ◽  
Participation Ratio

We obtain eigenstates of interacting disorder Hamiltonians using unitary displacement transformations that rotate the state of the system. The method generates excited states if the strength of these transformations is chosen to optimize the energy, while decreasing the energy variance. We apply the method to analyse the localization properties of one-dimensional spinless fermions with short range interactions, reaching relatively large system sizes. We quantify the degree of localization through the size and disorder dependence of the inverse participation ratio.

scholarly journals Indicators of wavefunction (de)localisation for avoided crossing in a quadrupole quantum billiard

2021 ◽  
Author(s):  
Kyu-Won Park ◽  
Juman Kim ◽  
Jisung Seo ◽  
Songky Moon ◽  
Kabgyun Jeong
Keyword(s):  
Root Mean Square ◽  
Image Contrast ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Mean Square ◽  
Inverse Participation Ratio ◽  
Participation Ratio ◽  
Avoided Crossing ◽  
Quantum Billiard ◽  
The Relationship

Abstract The relationship between wavefunction (de)localisation and avoided crossing in a quadrupole billiard is analysed. The following three-types of measures are employed for wavefunction (de)localisation: inverse participation ratio, inverse of Rényi entropy, and root-mean-square (RMS) image contrast. All these measures exhibit minimal values at the centre of the avoided crossing, where the wavefunction is maximally delocalised. Our results indicate that these quantities can be sufficient for the indication of wavefunction (de)localisation.

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