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Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2018, Volume 51, Issue 49, p. 495003
We investigate the first and second moments of the inverse participation ratio (IPR) for all eigenvectors of the Laplacian on finite random regular graphs with... 
localization | random regular graphs | inverse participation ratio | graph theory | Laplacian | DENSITY | EIGENVALUES | PHYSICS, MULTIDISCIPLINARY | LIMIT | PHYSICS, MATHEMATICAL
Journal Article
Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 06/2015, Volume 2015, Issue 6, pp. P06029 - 10
Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions... 
fluctuations (theory) | quantum phase transitions (theory) | electrical and magnetic phenomena (theory) | graphene (theory) | MECHANICS | PHYSICS, MATHEMATICAL | Graphene | Fluctuation | Eigenfunctions | Insulators | Inverse | Statistical mechanics | Two dimensional | Localization | Physics - Mesoscale and Nanoscale Physics
Journal Article
Physical Review B (Condensed Matter and Materials Physics), ISSN 1098-0121, 08/2015, Volume 92, Issue 8
After Anderson's prediction of disorder-induced insulating behavior, extensive work found no singularities in the density of states of localized systems.... 
Density of states | Singularities | Condensed matter | Disorders | Boundaries | Localization | Position (location) | Generalized inverse
Journal Article
Journal of the Physical Society of Japan, ISSN 0031-9015, 2008, Volume 77, Issue 9, pp. 094601 - 094601
We have studied the inverse participation ratio (IPR) denoted by P−1 of vibrational modes in one-dimensional graded elastic chains. The size dependence of IPR... 
vibrational gradons | graded elastic lattice | inverse participation ratio | Vibrational gradons | Inverse participation ratio | Graded elastic lattice | PHYSICS, MULTIDISCIPLINARY
Journal Article
Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 07/2015, Volume 92, Issue 1
The isolated one-dimensional Heisenberg model with static random magnetic fields has become paradigmatic for the analysis of many-body localization. Here, we... 
PHYSICS, CONDENSED MATTER | METAL-INSULATOR-TRANSITION | STATES | PHYSICS, APPLIED | INVERSE PARTICIPATION RATIO | MATERIALS SCIENCE, MULTIDISCIPLINARY | DIFFUSION | ANDERSON LOCALIZATION | Physics - Disordered Systems and Neural Networks
Journal Article
Chemical Physics Letters, ISSN 0009-2614, 09/2019, Volume 731, p. 136618
We calculate Fisher information and the inverse participation ratio normalised by the electric binding energy for the relativistic hydrogenic atoms based on... 
Inverse participation ratio | Radial electron density | Relativistic hydrogenic atoms | Fisher information | CHEMISTRY, PHYSICAL | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL
Journal Article
Reviews of Modern Physics, ISSN 0034-6861, 10/2008, Volume 80, Issue 4, pp. 1355 - 1417
Journal Article
Physical Review Letters, ISSN 0031-9007, 01/1999, Volume 83, Issue 7, pp. 1471 - 1474
We use methods of random matrix theory to analyze the cross-correlation matrix C of stock price changes of the largest 1000 U.S. companies for the 2-year... 
DISORDERED-SYSTEMS | LAW | INVERSE PARTICIPATION RATIO | PHYSICS, MULTIDISCIPLINARY | STOCK-MARKET | FLUCTUATIONS | DYNAMICS | MODEL | VOLATILITY | FOREIGN-EXCHANGE RATES | SCALING BEHAVIOR
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2017, Volume 50, Issue 47, p. 475005
The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the... 
obstinate kernel | participation ratio | Rényi entropy | TASEP | WALKS | STATES | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | MODEL | PHYSICS, MATHEMATICAL | INVERSE PARTICIPATION RATIO | OPEN BOUNDARIES | SYSTEMS | DIVERSITY | QUARTER PLANE | Renyi entropy | Physics - Statistical Mechanics
Journal Article
by Lu, DY
JOURNAL OF CHEMICAL PHYSICS, ISSN 0021-9606, 08/2016, Volume 145, Issue 5, p. 054121
A systematic route to go beyond the exact exchange plus random phase approximation ( RPA) is to include a physical exchange-correlation kernel in the... 
INVERSE PARTICIPATION RATIO | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | SURFACE | GAS | CHEMISTRY, PHYSICAL | DENSITY-FUNCTIONAL THEORY | CORRELATION ENERGY
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2004, Volume 70, Issue 2, pp. 1 - 26110
We confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory (RMT) for the cross correlation matrix of the... 
DISORDERED-SYSTEMS | INVERSE PARTICIPATION RATIO | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2015, Volume 433, pp. 92 - 99
In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko–Pastur distribution.... 
Inverse participation ratio | Correlation matrix | Random matrix theory | DISORDERED-SYSTEMS | MARKET | LAW | PHYSICS, MULTIDISCIPLINARY | CROSS-CORRELATIONS | Stock-exchange | Portfolio management | Analysis
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 06/2002, Volume 65, Issue 6, p. 066126/18
We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we... 
DISORDERED-SYSTEMS | INVERSE PARTICIPATION RATIO | PHYSICS, FLUIDS & PLASMAS | FLUCTUATIONS | ARBITRAGE PRICING THEORY | RETURNS | TIME-SERIES | STATISTICAL PROPERTIES | STOCK MARKETS | MODEL | PHYSICS, MATHEMATICAL | VOLATILITY
Journal Article
Journal of Complex Networks, ISSN 2051-1310, 02/2018, Volume 6, Issue 1, pp. 54 - 78
Abstract The theory of zeta functions provides an expression for the generating function of non-backtracking walk counts on a directed network. We show how... 
Graph spectrum | Generating function | Multilayer | Backtracking walks | Inverse participation ratio | Localization | Loops | Katz
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 10/2018, Volume 507, pp. 499 - 509
Journal Article
Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 11/2008, Volume 78, Issue 19
We study the multifractal analysis (MFA) of electronic wave functions at the localization-delocalization transition in the three-dimensional Anderson model for... 
DISORDERED-SYSTEMS | LOCALIZATION | PHYSICS, CONDENSED MATTER | WAVE-FUNCTIONS | STATES | MOBILITY EDGE | FLUCTUATIONS | Anderson model | FRACTAL DIMENSIONALITY | CHARACTER | INVERSE-PARTICIPATION-RATIO | metal-insulator transition
Journal Article
TEMA (São Carlos), ISSN 1677-1966, 09/2014, Volume 15, Issue 2
Chaotic sequences are sequences generated by chaotic maps. A particle moving in a one-dimensional space has its behavior modeled according to the... 
Journal Article
Physica Scripta, ISSN 0031-8949, 04/2017, Volume 92, Issue 5, p. 54003
The interaction of a quantized electromagnetic field in a cavity with a set of two-level atoms inside it can be described with algebraic Hamiltonians of... 
Husimi function | chaos | participation ratio | Dicke model | Lyapunov exponent | LOCALIZATION | SPIN | PHYSICS, MULTIDISCIPLINARY | QUANTUM | RADIATION-FIELD | LEVEL | INVERSE PARTICIPATION RATIO | NUMERICAL-SOLUTIONS | SUPERRADIANT PHASE-TRANSITION | MANY-BODY SYSTEMS | DICKE-MODEL
Journal Article