Related Experiment Video
Updated: Jun 24, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Nonequilibrium steady state transport via the reduced density matrix operator
Joseph E Subotnik1, Thorsten Hansen, Mark A Ratner
1School of Chemistry, Tel-Aviv University, Tel-Aviv 69978, Israel. subotnik@post.harvard.edu
The Journal of Chemical Physics
|April 17, 2009
Summary
We developed a simple model for steady-state dynamics in systems interacting with baths. This model accurately predicts electron transport and molecular populations in both equilibrium and nonequilibrium conditions.
Area of Science:
- Condensed Matter Physics
- Quantum Chemistry
- Materials Science
Background:
- Understanding steady-state dynamics in quantum systems is crucial for designing nanoscale electronic devices.
- Existing models often struggle to capture nonequilibrium phenomena accurately.
- Describing systems interacting with a bath of states is a fundamental challenge.
Purpose of the Study:
- To present a simple numerical model for steady-state dynamics of quantum systems coupled to baths.
- To apply the model to both equilibrium and nonequilibrium scenarios.
- To demonstrate its capability in predicting electron transport and population dynamics.
Main Methods:
- Numerical modeling of a one-state system coupled to two free electron reservoirs.
- Application of the model to calculate steady-state populations and currents.
- Extension of the model to include electron-electron interactions and correlations.
Main Results:
- The model successfully reproduces the Landauer formula for equilibrium current.
- It accurately predicts nonequilibrium steady-state populations on a molecule.
- The approach suggests a link between electronic structure and conduction properties.
Conclusions:
- The presented model offers a straightforward yet powerful tool for studying quantum system dynamics.
- It is applicable to a range of problems, from equilibrium transport to nonequilibrium phenomena.
- The model provides a foundation for more complex investigations including electron interactions.
Related Concept Videos
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.
01:26Reaction Mechanisms: The Steady-State Approximation
The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
01:21Carrier Transport
The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
03:25Free Energy Changes for Nonstandard States
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
02:20Dynamic Equilibrium
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
01:16Non-equilibrium in the Cell
An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both directions, releasing energy into their environment in one direction, and absorbing it from the environment in the other direction. The same is true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of proteins into and from individual amino acids, respectively. Reactants within a closed system...