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Related Concept Videos

Correlations02:20

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Coefficient of Correlation01:12

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Expected Frequencies in Goodness-of-Fit Tests01:19

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Related Experiment Video

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Surprising relations between parametric level correlations and fidelity decay.

H Kohler1, I E Smolyarenko, C Pineda

  • 1Fachbereich Physik, Universität Duisburg-Essen, Duisburg, Germany.

Physical Review Letters
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

This study reveals power law decay drives revivals in quantum fidelity and cross-form-factors. These findings, rooted in random matrix theory, are illustrated using a kicked Ising spin chain model.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • Understanding quantum system dynamics is crucial.
  • Random matrix theory provides a framework for complex systems.
  • Recent discoveries highlighted revivals in fidelity decay.

Purpose of the Study:

  • To investigate relations among fidelity, cross-form-factors, and level velocity correlations.
  • To explain the origin of recently discovered revivals in fidelity decay.
  • To illustrate these phenomena in a specific quantum system.

Main Methods:

  • Derivation of a Ward identity in a two-matrix model.
  • Application of supersymmetry techniques within random matrix theory.
  • Numerical study of a multiply kicked Ising spin chain.

Main Results:

  • Established relations between fidelity, cross-form-factors, and level velocity correlations.
  • Identified power law decay near Heisenberg time as the cause of fidelity decay revivals.
  • Demonstrated cross-form-factor revivals in the Ising spin chain model.

Conclusions:

  • Power law decay is fundamental to understanding quantum system dynamics and revivals.
  • Random matrix theory and supersymmetry are powerful tools for analyzing these correlations.
  • The multiply kicked Ising spin chain serves as a relevant model for these quantum phenomena.