Related Concept Videos
01:23Stability of Equilibrium Configuration
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
01:24Pole and System Stability
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
03:06The Pauli Exclusion Principle
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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...
01:13Stability of Equilibrium Configuration: Problem Solving
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Problem-solving in the context of the stability of equilibrium configuration...
01:12Reduced Mass Coordinates: Isolated Two-body Problem
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
You might also read
Related Articles
Articles linked to this work by shared authors, journal, and citation graph.
Sort by
Same author
Proposed Robust Entanglement-Based Magnetic Field Sensor Beyond the Standard Quantum Limit.
Physical review letters·2015
Related Experiment Video
Updated: Jul 8, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Parent Hamiltonians for Stabilizer Quantum Many-Body Scars.
1Dublin Institute for Advanced Studies, School of Theoretical Physics, 10 Burlington Road, Dublin 4, Ireland.
Physical Review Letters
|July 7, 2026
Summary
We developed a general method to embed stabilizer states as quantum many-body scars (QMBS) in local Hamiltonians. This approach unifies known QMBS examples and constructs new ones with complex entanglement structures.
Area of Science:
- Quantum Physics
- Condensed Matter Theory
- Many-Body Systems
Background:
- Quantum many-body scars (QMBS) are crucial for understanding ergodicity breaking in quantum systems.
- Stabilizer states are important in quantum information and error correction.
Purpose of the Study:
- To present a general construction for embedding stabilizer states as QMBS.
- To systematically construct parent Hamiltonians with zero-energy stabilizer QMBS.
- To unify and extend known QMBS examples.
Main Methods:
- Utilizing the factorizability of Pauli strings on a lattice.
- Converting stabilizer elements into local, few-body operators.
- Employing exact diagonalization for verification.
Main Results:
- A general framework for constructing stabilizer QMBS from stabilizer states.
- Reproduction of known QMBS, including volume-law entangled states.
- Construction of new QMBS with complex entanglement, like cluster and toric code states.
Conclusions:
- The developed method provides a unified approach to stabilizer QMBS.
- The framework successfully generates QMBS with diverse entanglement properties.
- Stabilizer states are confirmed as exact eigenstates of the constructed Hamiltonians.