Related Experiment Video
Updated: Jun 9, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Applicability of Mean-Field Theory for Time-Dependent Open Quantum Systems with Infinite-Range Interactions
Federico Carollo1, Igor Lesanovsky1,2
1Institut für Theoretische Physik, <a href="https://ror.org/03a1kwz48">Universität Tübingen</a>, Auf der Morgenstelle 14, 72076 Tübingen, Germany.
Mean-field theory precisely describes quantum many-body systems with infinite-range interactions in the thermodynamic limit. This study rigorously proves its applicability, offering bounds for finite-size effects in quantum dynamics.
Area of Science:
- Quantum physics
- Condensed matter theory
- Quantum optics
Background:
- Quantum many-body systems with long-range interactions are crucial in quantum optics, nuclear magnetic resonance, and nuclear physics.
- These systems are amenable to numerical study and are expected to follow mean-field theory in the thermodynamic limit.
- Experimental advancements allow precise control over long-range interacting systems, enabling exploration of nonequilibrium phases like time crystals and chaotic regimes.
Purpose of the Study:
- To rigorously prove the exact applicability of mean-field theory to time-dependent infinite-range interacting systems in the thermodynamic limit.
- To address the challenges in numerically establishing emergent phases in these systems.
- To provide bounds for finite-size effects and their time dependence.
Main Methods:
- Theoretical analysis of quantum many-body systems.
- Rigorous mathematical proof of mean-field theory's exactness.
- Derivation of bounds for finite-size corrections.
Main Results:
- Mean-field theory is proven to exactly capture the dynamics of infinite-range interacting quantum systems in the thermodynamic limit.
- Established bounds quantify finite-size effects and their dependence on evolution time.
- Resolved the debate on mean-field theory's applicability to time-dependent infinite-range systems.
Conclusions:
- Mean-field theory provides an exact description for the dynamics of quantum many-body systems with infinite-range interactions in the thermodynamic limit.
- The findings clarify the theoretical framework for studying complex quantum phenomena in these systems.
- Provides a foundation for future research into quantum dynamics and emergent phenomena.
More Related Videos
11:03An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
08:55Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Related Concept Videos
Mean free path and Mean free time
The Quantum-Mechanical Model of an Atom
The Pauli Exclusion Principle
First Law: Particles in One-dimensional Equilibrium
Theory of Metallic Conduction
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
The de Broglie Wavelength