Related Experiment Video
Updated: Jul 7, 2026
05:30
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
Published on: September 8, 2023
Quantum transport on small-world networks: a continuous-time quantum walk approach
Oliver Mülken1, Volker Pernice, Alexander Blumen
1Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany. muelken@physik.uni-freiburg.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
Summary
Quantum mechanical transport of excitons on small-world networks (SWNs) is fast but does not lead to equipartition. Excitons tend to remain localized at the initial node, even with added network connections.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Network science
Background:
- Exciton transport is crucial for energy transfer in various physical systems.
- Small-world networks (SWNs) exhibit unique topological properties influencing transport dynamics.
- Understanding coherent quantum transport on complex networks is an active research area.
Purpose of the Study:
- To investigate the quantum mechanical transport of coherent excitons on SWNs.
- To analyze the influence of network topology on exciton delocalization and transport efficiency.
- To evaluate the exciton's transition probability across the network.
Main Methods:
- Modeling exciton dynamics using continuous-time quantum walks.
- Constructing SWNs from a 1D ring with randomly introduced additional bonds.
- Numerical evaluation of ensemble-averaged transition probabilities.
Main Results:
- Quantum transport on SWNs is found to be very fast for a sufficient number of additional bonds (B).
- The limiting transition probability is reached rapidly, indicating efficient initial spread.
- Despite fast initial spread, transport does not result in equipartition; excitons remain localized at the initial node on average.
Conclusions:
- SWNs facilitate rapid initial quantum transport of excitons.
- The interplay between network structure and quantum coherence leads to non-equipartitioned transport.
- Exciton localization at the origin persists even in highly connected SWNs.
Related Concept Videos
02:45The 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. Schrödinger...
02:12Short-distance Transport of Resources
Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
01:04Travelling Waves
A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...
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...
01:23Propagation of Action Potentials
The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
01:24Reynolds Transport Theorem
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.