Related Experiment Video
Updated: Aug 6, 2026
07:44
Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems
Published on: April 28, 2016
Classical scaling theory of quantum resonances
Sandro Wimberger1, Italo Guarneri, Shmuel Fishman
1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
Physical Review Letters
|March 5, 2004
Summary
Quantum resonances in delta-kicked particles are linked to classical resonances using a fictitious classical limit. A derived scaling law characterizes the structure of these resonant peaks and is numerically verified.
Area of Science:
- Quantum dynamics
- Classical mechanics
- Statistical physics
Background:
- Delta-kicked systems exhibit complex quantum resonances.
- Understanding the relationship between quantum and classical dynamics is crucial.
Purpose of the Study:
- To establish a correspondence between quantum resonances in delta-kicked particles and classical resonances.
- To derive and demonstrate a scaling law for the structure of quantum resonance peaks.
Main Methods:
- Utilizing a fictitious classical limit to study quantum resonances.
- Deriving a scaling law based on theoretical analysis.
- Numerical demonstration of the derived scaling law.
Main Results:
- A direct correspondence between nearly resonant quantum motion and classical resonances was established.
- A scaling law characterizing the structure of resonant peaks was derived.
- The scaling law was numerically demonstrated, confirming its validity.
Conclusions:
- The fictitious classical limit provides a powerful tool for understanding quantum resonances in delta-kicked systems.
- The derived scaling law offers insights into the quantitative structure of resonance phenomena.
Related Concept Videos
02:32The 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...
01:19Concept of Resonance and its Characteristics
If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...
01:17Standing Waves
Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
01:03Modes 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...
01:14Sound Waves: Resonance
Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
01:26Scaling
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...