Related Experiment Video
Updated: May 27, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Hamiltonian of mean force for damped quantum systems
Stefanie Hilt1, Benedikt Thomas, Eric Lutz
1Department of Physics, University of Augsburg, D-86135 Augsburg, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
Summary
Quantum systems coupled to reservoirs show deviations from standard thermodynamics. This study quantifies these deviations using the quantum Hamiltonian of mean force and the quantum Smoluchowski equation.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Thermodynamics
Background:
- Quantum systems coupled to reservoirs are fundamental in understanding dissipation and decoherence.
- Standard thermodynamics often assumes weak coupling, limiting its applicability to strongly coupled systems.
Purpose of the Study:
- To investigate and quantify the deviations of a damped quantum system's stationary distribution from standard thermodynamic predictions.
- To explore the role of coupling strength and temperature on these thermodynamic deviations.
Main Methods:
- Utilizing the quantum Hamiltonian of mean force to exactly analyze a harmonic oscillator.
- Employing the quantum Smoluchowski equation for semiclassical regimes and arbitrary potentials.
- Developing approximations for high/low temperatures and weak/strong coupling limits.
Main Results:
- The stationary distribution of a damped quantum system deviates from standard thermodynamics for finite coupling strengths.
- The deviation is precisely quantified for a harmonic oscillator and approximated for various limits.
- A physical interpretation of the deviation is provided, linked to initial system-reservoir coupling.
Conclusions:
- Deviations from standard thermodynamics in damped quantum systems are significant and quantifiable.
- The employed methods provide a robust framework for analyzing non-equilibrium quantum dynamics.
- Understanding these deviations is crucial for accurately modeling quantum systems in realistic environments.
Related Concept Videos
01:07Damped Oscillations
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
01:20Types of Damping
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
01:06Forced Oscillations
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
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...
01:23Equilibrium Conditions for a Particle
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
01:10First Law: Particles in One-dimensional Equilibrium
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...