Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Improper Integrals: Infinite Intervals01:29

Improper Integrals: Infinite Intervals

An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
Indefinite Integrals01:25

Indefinite Integrals

The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Iterated Integrals and Fubini's Theorem01:28

Iterated Integrals and Fubini's Theorem

A double integral generalizes the concept of a single-variable integral to functions of two variables, enabling the computation of the volume beneath a surface z = f(x, y) over a planar region R . For a rectangular region defined by a ≤ x ≤ b and c ≤ y ≤ d, and for functions continuous on this domain, the double integral can be evaluated as an iterated integral. This approach simplifies computation by reducing the problem to successive integrations with respect to one variable at a...
Current Growth And Decay In RL Circuits01:30

Current Growth And Decay In RL Circuits

The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Induction of a NOTCH3 Lehman syndrome mutation in osteocytes causes osteopenia in male C57BL/6J mice.

Bone·2022
Same author

Role of nuclear factor of activated T cells in chondrogenesis osteogenesis and osteochondroma formation.

Journal of endocrinological investigation·2022
Same author

Comparative transcriptome analysis of inner blood-retinal barrier and blood-brain barrier in rats.

Scientific reports·2021
Same author

Predicting late magnetic resonance image changes in glioma patients after proton therapy.

Acta oncologica (Stockholm, Sweden)·2019
Same author

[The use of sunglasses during leisure time and work : Lack of prevention of sun-induced eye damage].

Der Ophthalmologe : Zeitschrift der Deutschen Ophthalmologischen Gesellschaft·2019
Same author

[Postmenopausal lichen planopilaris also known as fibrosing frontotemporal alopecia Kossard : An evidence-oriented practical guide to treatment from the University of the Saarland, Hair Research Center of the Dr. Rolf M. Schwiete Foundation].

Der Hautarzt; Zeitschrift fur Dermatologie, Venerologie, und verwandte Gebiete·2018

Related Experiment Video

Updated: Jul 6, 2026

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy
10:28

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy

Published on: May 27, 2018

Regular-to-chaotic tunneling rates using a fictitious integrable system.

A Bäcker1, R Ketzmerick, S Löck

  • 1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany.

Physical Review Letters
|March 21, 2008
PubMed
Summary

We developed a formula to predict dynamical tunneling rates in systems with mixed phase space. This method accurately models tunneling from regular states to chaotic regions, validated by numerical results.

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Related Experiment Videos

Last Updated: Jul 6, 2026

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy
10:28

Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy

Published on: May 27, 2018

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

  • Physics
  • Quantum Mechanics
  • Dynamical Systems

Background:

  • Systems with mixed phase space exhibit both regular and chaotic dynamics.
  • Understanding transitions between regular and chaotic states is crucial in physics.
  • Dynamical tunneling is a key phenomenon in quantum chaos.

Purpose of the Study:

  • To derive a predictive formula for dynamical tunneling rates.
  • To quantify tunneling from regular states to the chaotic sea.
  • To provide a theoretical framework for systems with mixed phase space.

Main Methods:

  • Introduction of a fictitious integrable system to model regular dynamics.
  • Development of a formula based on this fictitious system.
  • Comparison of theoretical predictions with numerical simulations.

Main Results:

  • A formula predicting dynamical tunneling rates was successfully derived.
  • The formula shows agreement with numerical results for various kicked systems.
  • The model is effective for regular states in a mixed phase space.

Conclusions:

  • The proposed method accurately predicts dynamical tunneling rates.
  • The fictitious integrable system provides a useful approximation for regular dynamics.
  • This work offers a new tool for studying quantum chaos and mixed phase space systems.