Related Experiment Video
Updated: May 16, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Physics in one dimension: theoretical concepts for quantum many-body systems.
1Institut für Theoretische Physik, Universität Göttingen, Germany. schoenh@theorie.physik.uni-goettingen.de
Journal of Physics. Condensed Matter : an Institute of Physics Journal
|December 11, 2012
Summary
This paper introduces the Luttinger liquid concept for one-dimensional fermionic systems. We explore how these simplified systems allow for exact theoretical solutions, offering insights into quantum many-body physics.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Many-body systems
Background:
- Sophisticated approximation methods are used for quantum many-body systems.
- One-dimensional systems offer simplified theoretical descriptions with exact solutions.
- The Luttinger liquid concept is a key theoretical framework in this field.
Purpose of the Study:
- To provide an introductory overview of the Luttinger liquid concept.
- To highlight the advantages of studying one-dimensional fermionic systems.
- To bridge the gap between general many-body approximations and specific 1D solutions.
Main Methods:
- Focus on theoretical analysis of one-dimensional fermionic systems.
- Discussion of exact solution methodologies applicable to these systems.
- Introduction to the foundational principles of the Luttinger liquid theory.
Main Results:
- Demonstration of significant theoretical simplification in 1D quantum systems.
- Explanation of the emergence and properties of Luttinger liquids.
- Highlighting the existence of exact solutions in specific 1D fermionic models.
Conclusions:
- One-dimensional fermionic systems provide a tractable platform for understanding complex quantum phenomena.
- The Luttinger liquid concept is crucial for describing emergent behaviors in these systems.
- Exact solutions in 1D systems offer valuable benchmarks for theoretical advancements.
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...
01:05Collisions in Multiple Dimensions: Introduction
It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
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...
04:08The Uncertainty Principle
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 mathematically...
01:18First Law: Particles in Two-dimensional Equilibrium
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Newton's first law tells us about the...
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...