Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

The de Broglie Wavelength

The de Broglie Wavelength

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...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

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:

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

First Law: Particles in One-dimensional Equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...

You might also read

Related Articles

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

Sort by

Same author

Absolutely maximally entangled pure states of multipartite quantum systems.

Reports on progress in physics. Physical Society (Great Britain)·2026

Same author

Disordering a permutation symmetric system: Revivals, thermalization, and chaos.

Physical review. E·2025

Same author

Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry.

Scientific reports·2025

Same author

Solvable Models of Many-Body Chaos from Dual-Koopman Circuits.

Physical review letters·2024

Same author

Probing dynamical sensitivity of a non-Kolmogorov-Arnold-Moser system through out-of-time-order correlators.

Physical review. E·2024

Same author

Quantum coherence controls the nature of equilibration and thermalization in coupled chaotic systems.

Physical review. E·2023

Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026

Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026

Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026

Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026

Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026

Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026

See all related articles

Search research articles

Related Experiment Video

Updated: May 27, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Quantum-classical correspondence in quantum channels.

Bidhi Vijaywargia¹, Arul Lakshminarayan¹

¹Indian Institute of Technology Madras, Department of Physics, & Center for Quantum Information, Computation and Communication, Chennai 600036, India.

Physical Review. E

|February 20, 2025

Summary

This summary is machine-generated.

This study introduces classical Koopman channels as analogs to quantum channels, enabling a comparative analysis of quantum and classical dynamics. Findings reveal quantum channel behavior is influenced by classical phase space stability and chaos.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Related Experiment Videos

Last Updated: May 27, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Quantum mechanics
Classical mechanics
Dynamical systems theory

Background:

Quantum channels model open-system evolution.
Classical Koopman operator theory analyzes function evolution in phase space.

Purpose of the Study:

To establish classical Koopman channels as analogs to quantum channels.
To explore quantum-classical correspondence at the channel level.
To compare spectral properties of quantum and classical channels.

Main Methods:

Identifying four classical Koopman channels analogous to quantum channels.
Interpreting channels as noisy single-particle systems.
Utilizing a coupled kicked rotor model for comparative spectral analysis.

Main Results:

Classical Koopman channels provide a framework for studying quantum-classical correspondence.
Quantum channel modes are significantly influenced by stable classical phase space regions.
Chaotic dynamics lead to annular spectral densities, described by random matrix theory.
Classical limit approach causes spectral rings to shrink, with surviving modes showing scarring.

Conclusions:

Classical Koopman channels offer new insights into quantum and classical limiting theories.
The study highlights the interplay between classical phase space structures and quantum spectral properties.
Scarring effects by unstable manifolds and periodic orbits are observed in surviving quantum modes.