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Related Concept Videos

Resonance and Hybrid Structures02:16

Resonance and Hybrid Structures

According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Modes of Standing Waves - I01:03

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
Resonance02:52

Resonance

The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N-O and N=O bonds.
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Series RLC Circuit without Source01:21

Series RLC Circuit without Source

Within the field of electrical circuits, source-free RLC circuits present an intriguing domain. These circuits comprise a series arrangement of a resistor, inductor, and capacitor, operating independently of external energy sources. Their initiation hinges upon utilizing the initial energy stored within the capacitor and inductor to instigate their functionality. Their mathematical equation, a second-order differential equation, sets these circuits apart. This equation captures how the...

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Related Experiment Video

Updated: Jul 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Semiclassical structure of chaotic resonance eigenfunctions.

J P Keating1, M Novaes, S D Prado

  • 1School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.

Physical Review Letters
|December 13, 2006
PubMed
Summary

We investigate quantum eigenstates in chaotic systems. Long-lived states concentrate on classical dynamics

Area of Science:

  • Quantum Chaos
  • Statistical Mechanics
  • Complex Systems

Background:

  • Open chaotic systems exhibit complex dynamics and decay rates.
  • Understanding resonance (Gamow) eigenstates is crucial for open quantum systems.
  • Distinguishing left and right eigenstates of the nonunitary quantum propagator is key.

Purpose of the Study:

  • To analyze resonance eigenstates in open chaotic systems in the semiclassical limit.
  • To differentiate between short-lived and long-lived states, and left/right eigenstates.
  • To explore the phase space structure and self-similarity properties of these eigenstates.

Main Methods:

  • Semiclassical analysis of the nonunitary quantum propagator.
  • Investigation of left and right eigenstates.

Related Experiment Videos

Last Updated: Jul 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

  • Study of the limit as Planck's constant approaches zero (variant Planck's over 2pi-->0).

    • Main Results:

    • Long-lived left (right) eigenstates concentrate on the forward (backward) trapped set of classical dynamics.
    • The limit of eigenstates exhibits a rich phase space structure dependent on decay rates.
    • Self-similarity properties are observed in the position space probability density for the open baker's map.

    Conclusions:

    • The study reveals a detailed structure of resonance eigenstates in open chaotic systems.
    • Classical trapped sets govern the localization of long-lived quantum eigenstates.
    • The open baker's map serves as a valuable model for illustrating these quantum-chaotic phenomena.