Related Experiment Video
Updated: Feb 13, 2026
08:43
Calibration Procedures for Orthogonal Superposition Rheology
Published on: November 18, 2020
2.4K
Orthogonality catastrophe and fractional exclusion statistics
Filiberto Ares1, Kumar S Gupta2, Amilcar R de Queiroz3
1Departamento de Fisica Teorica, Universidad de Zaragoza, 50009, Zaragoza, Spain.
Physical Review. E
|March 18, 2018
Summary
The N-particle Sutherland model demonstrates an orthogonality catastrophe, a phenomenon where ground state wave functions lose overlap exponentially. This finding extends beyond fermionic systems, suggesting broader applicability of the catastrophe.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Many-body systems
Background:
- The Sutherland model describes interacting particles with specific potentials.
- Orthogonality catastrophe is a known phenomenon in quantum systems.
Purpose of the Study:
- To investigate the orthogonality catastrophe in the N-particle Sutherland model.
- To analyze the behavior of wave function overlaps under varying interaction parameters.
Main Methods:
- Theoretical analysis of the N-particle Sutherland model.
- Calculation of ground state wave function overlaps.
- Numerical analysis of coupling parameter effects.
Main Results:
- The Sutherland model exhibits an orthogonality catastrophe for inverse-square and harmonic interactions.
- Wave function overlap shows exponential suppression, differing from Anderson's power law.
- An analytic expression for wave function overlaps was derived.
Conclusions:
- The orthogonality catastrophe is present in the Sutherland model.
- The phenomenon exhibits unique exponential suppression characteristics.
- Findings suggest the orthogonality catastrophe may apply to systems with generalized statistics beyond fermionic types.
Related Concept Videos
01:26Orthogonal Trajectories
72
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
72
01:50Statistical Significance
22.2K
Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...
22.2K
03:06The Pauli Exclusion Principle
59.6K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
59.6K
01:14Probability in Statistics
23.5K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
23.5K
01:17Introduction to Statistics
64.7K
The science of statistics involves collecting, analyzing, interpreting, and presenting data. The method of collecting, organizing, and summarizing data is called descriptive statistics. The systematic method of drawing inferences from the sample data and predicting unknown characteristics of a population is called inferential statistics.
In statistics, the collection of individuals or objects under study is called population. The idea of sampling is to select a portion of the larger population...
In statistics, the collection of individuals or objects under study is called population. The idea of sampling is to select a portion of the larger population...
64.7K
01:11Statistical Analysis: Overview
16.6K
When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...
16.6K