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

Conservation of Linear Momentum for a System of Particles01:28

Conservation of Linear Momentum for a System of Particles

704
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
704
Introduction to Exponential Functions01:29

Introduction to Exponential Functions

522
Exponential functions are fundamental in modeling dynamic processes where the rate of change is proportional to the current value. Defined by f(x) = bx, where b is a positive constant not equal to one, they form the basis for describing processes of growth and decay depending on whether the base b is greater than or less than one.Exponential models describe situations where change occurs at a rate proportional to the current amount. These include phenomena such as bacterial proliferation,...
522
The de Broglie Wavelength02:32

The de Broglie Wavelength

25.5K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
25.5K
Accelerating Fluids01:17

Accelerating Fluids

2.2K
When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
2.2K
Fermi Level Dynamics01:12

Fermi Level Dynamics

1.1K
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
1.1K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.2K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.2K

You might also read

Related Articles

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

Sort by
Same author

Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard.

Physical review. E·2020
Same author

Fermi acceleration in chaotic shape-preserving billiards.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same author

Statistical properties of one-dimensional parametrically kicked Hamilton systems.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same author

Quantum localization of chaotic eigenstates and the level spacing distribution.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013

Related Experiment Video

Updated: Apr 22, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.1K

Exponential Fermi acceleration in general time-dependent billiards.

Benjamin Batistić1

  • 1CAMTP, Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2014
PubMed
Summary

Generic time-dependent billiards exhibit exponential Fermi acceleration in the adiabatic limit. This phenomenon arises from probabilistic path integrals in the abstract space of invariant components, as demonstrated numerically.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K
A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts
08:43

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts

Published on: December 1, 2018

10.5K

Related Experiment Videos

Last Updated: Apr 22, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.1K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K
A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts
08:43

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts

Published on: December 1, 2018

10.5K

Area of Science:

  • Physics
  • Dynamical Systems
  • Statistical Mechanics

Background:

  • Billiard systems are fundamental models in classical and quantum mechanics.
  • Understanding particle dynamics in time-dependent potentials is crucial for various physical phenomena.
  • The mixed-type phase space in static billiards complicates predicting long-term behavior.

Purpose of the Study:

  • To demonstrate exponential Fermi acceleration in generic time-dependent billiards under general conditions.
  • To theoretically model velocity dynamics in the adiabatic regime using path integrals.
  • To identify conditions leading to exponential Fermi acceleration.

Main Methods:

  • Analysis of velocity dynamics in the adiabatic regime via path integrals.
  • Probabilistic path generation using transition-probability matrices.
  • Numerical simulations in four distinct time-dependent billiard systems.

Main Results:

  • Exponential Fermi acceleration is shown to occur in generic time-dependent billiards with mixed-type phase spaces.
  • Velocity dynamics are accurately represented as integrals over probabilistic paths.
  • Numerical results confirm the theoretical predictions for exponential Fermi acceleration.

Conclusions:

  • The study provides a theoretical framework for understanding Fermi acceleration in time-dependent systems.
  • Probabilistic path analysis offers insights into the conditions for exponential energy gain.
  • The findings are validated across diverse numerical examples, highlighting the generality of the phenomenon.