Related Experiment Video
Updated: Feb 11, 2026
10:49
Planar and Three-Dimensional Printing of Conductive Inks
Published on: December 9, 2011
37.8K
Gravity and the Spin-2 Planar Schrödinger Equation
Eric A Bergshoeff1, Jan Rosseel2, Paul K Townsend3
1Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands and Institut de Physique Théorique Philippe Meyer, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
Physical Review Letters
|April 26, 2018
Summary
Researchers derived a Schrödinger equation for fractional quantum Hall states from Fierz-Pauli and Einstein field equations. This reveals a harmonic oscillator potential for spin-2 particles in a uniform distribution.
Area of Science:
- Theoretical Physics
- Condensed Matter Physics
Background:
- Fractional quantum Hall states exhibit complex emergent phenomena.
- Spin-2 modes require advanced theoretical frameworks for description.
Purpose of the Study:
- To derive a Schrödinger equation for the Girvin-MacDonald-Platzman gapped spin-2 mode.
- To explore connections between field theory and quantum Hall states.
Main Methods:
- Novel nonrelativistic limit of massive spin-2 Fierz-Pauli field equations in 2+1 dimensions.
- Novel null reduction of linearized Einstein field equations in 3+1 dimensions.
- Brinkmann-wave solution of nonlinear Einstein equations.
Main Results:
- A Schrödinger equation for the spin-2 mode of fractional quantum Hall states was successfully derived.
- The study established a link between general relativity and quantum Hall physics.
- A uniform distribution of spin-2 particles implies a confining harmonic oscillator potential.
Conclusions:
- The findings provide a new theoretical tool for studying fractional quantum Hall states.
- The research bridges concepts from general relativity and condensed matter physics.
- A potential for individual spin-2 particles was identified within this framework.
Related Concept Videos
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
48.6K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
48.6K
03:10Chemical Equations
82.2K
Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right)...
82.2K
02:26Responses to Gravity and Touch
42.0K
Gravitropism: Plant Responses to Gravity
42.0K
02:55Thermochemical Equations
36.1K
For a chemical reaction (the system) carried out at constant pressure – with the only work done caused by expansion or contraction – the enthalpy of reaction (also called the heat of reaction, ΔHrxn) is equal to the heat exchanged with the surroundings (qp).
36.1K
00:58Center of Gravity
6.8K
The center of gravity (COG) of an object is the point where the object's total weight is considered to be concentrated. Knowing the location of the center of gravity is useful when predicting the behavior of a moving object or designing static structures. In a uniform gravitational field, the center of gravity is similar to the center of mass (COM); yet, these two points can be positioned differently. For example, the Moon's center of mass lies very close to its geometric center, but...
6.8K
02:59The Nernst Equation
47.2K
Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
47.2K