Related Experiment Video
Updated: Mar 17, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.8K
Efficient computations of quantum canonical Gibbs state in phase space
Denys I Bondar1, Andre G Campos1, Renan Cabrera1
1Princeton University, Princeton, New Jersey 08544, USA.
Physical Review. E
|July 15, 2016
Summary
Researchers developed a new method to accurately compute the Gibbs state Wigner function, crucial for quantum thermodynamics and simulations. This provides an efficient framework for nonequilibrium quantum simulations in phase space.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Computational physics
Background:
- The Gibbs canonical state is fundamental for quantum systems in equilibrium.
- It's essential for initiating nonequilibrium dynamical simulations.
- Accurate computation of the Gibbs state Wigner function has been a challenge.
Purpose of the Study:
- To develop a highly accurate method for computing the Gibbs state Wigner function.
- To establish an efficient computational framework for nonequilibrium quantum simulations.
- To provide algorithms for high-quality Wigner distributions of various quantum states.
Main Methods:
- Directly solving the Bloch equation in phase space.
- Developing numerical algorithms for Wigner function computation.
- Applying methods to pure stationary, Thomas-Fermi, and Bose-Einstein distributions.
Main Results:
- Achieved nearly machine accuracy in computing the Gibbs state Wigner function.
- Generated high-quality Wigner distributions for diverse quantum states.
- Established an efficient Wigner representation computation framework.
Conclusions:
- The developed numerical methods solve a long-standing problem in quantum thermodynamics.
- This work enables efficient nonequilibrium quantum simulations directly in the Wigner representation.
- The findings are crucial for advancing quantum simulations and understanding quantum systems.
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
61.2K
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.
61.2K
03:25Free Energy Changes for Nonstandard States
13.8K
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:
13.8K
02:39Gibbs Free Energy
40.5K
One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
40.5K
04:08The Uncertainty Principle
34.4K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
34.4K
01:23Equilibrium Conditions for a Particle
2.4K
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...
2.4K
01:12Fermi Level Dynamics
923
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
923