Related Experiment Video
Updated: May 22, 2026
18:10
Isolation of Fidelity Variants of RNA Viruses and Characterization of Virus Mutation Frequency
Published on: June 16, 2011
Lower and upper bounds on the fidelity susceptibility
1Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation.
Summary
This study establishes bounds for fidelity susceptibility using macroscopic thermodynamic quantities. These bounds are validated against models like the Dicke superradiance and Kondo models, showing equivalence with thermodynamic susceptibility near critical points.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- Fidelity susceptibility quantifies the sensitivity of a quantum state to perturbations.
- Macroscopic thermodynamical quantities offer a simplified yet powerful description of complex systems.
- Understanding critical phenomena in many-body quantum systems is a key challenge.
Purpose of the Study:
- To derive general upper and lower bounds for fidelity susceptibility.
- To express these bounds using accessible macroscopic thermodynamical quantities.
- To demonstrate the utility of these bounds in exactly solvable many-particle models.
Main Methods:
- Derivation of analytical bounds on fidelity susceptibility.
- Comparison with exact solutions for a single spin in a magnetic field.
- Application to the Dicke superradiance and single-impurity Kondo models.
Main Results:
- Established bounds on fidelity susceptibility in terms of susceptibilities and thermal averages.
- Validated the bounds using exactly solvable models in the thermodynamic limit.
- Demonstrated the equivalence between fidelity susceptibility and thermodynamic susceptibility for critical systems.
Conclusions:
- The derived bounds provide a practical tool for analyzing quantum phase transitions.
- The equivalence highlights a deep connection between quantum state sensitivity and thermodynamic response.
- The findings are applicable to a broad range of quantum many-body systems exhibiting critical behavior.
Related Concept Videos
01:31Magnetic Susceptibility and Permeability
In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of proportionality, a dimensionless number, is called magnetic susceptibility. The value of the susceptibility depends on the type of material.
When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since...
When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since...
01:26Susceptibility, Permittivity and Dielectric Constant
When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.
01:13Accuracy and Errors in Hypothesis Testing
Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
00:54Uncertainty: Confidence Intervals
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
01:05Difference from Background: Limit of Detection
The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...
The LOD indicates the presence or absence...
01:21Confidence Intervals
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
A confidence...