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First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

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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...
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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

5.1K
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...
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Fermi Level Dynamics01:12

Fermi Level Dynamics

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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...
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Second Uniqueness Theorem01:16

Second Uniqueness Theorem

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Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the...
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Related Experiment Video

Updated: Jun 25, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Universal Composite Boson Formation in Strongly Interacting One-Dimensional Fermionic Systems.

Francesc Sabater1,2, Abel Rojo-Francàs1,2, Grigori E Astrakharchik1,2,3

  • 1Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain.

Physical Review Letters
|May 28, 2024
PubMed
Summary

Attractive one-dimensional fermions form composite bosons in the fermionic Tonks-Girardeau regime. This pairing mechanism leads to universal occupation numbers, mirroring Bose-Einstein condensate properties.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Many-body systems

Background:

  • Studying one-dimensional (1D) quantum systems provides insights into fundamental many-body physics.
  • The fermionic Tonks-Girardeau (FTG) regime describes strongly interacting 1D fermions, exhibiting unique properties.
  • Understanding attractive interactions is crucial for phenomena like fermion pairing and superfluidity.

Purpose of the Study:

  • Investigate the properties of attractive p-wave one-dimensional fermions in the FTG regime.
  • Analyze the off-diagonal properties and the one-body density matrix.
  • Explore the pairing mechanism and the formation of composite particles.

Main Methods:

  • Analytical derivation of eigenvalues for the one-body density matrix.
  • Analysis of occupation numbers of natural orbitals.
  • Comparison with the properties of ideal Bose gases and Bose-Einstein condensates.

Main Results:

  • Diagonal properties of the system are identical to those of an ideal Bose gas.
  • Universal occupation numbers of natural orbitals, independent of the external potential shape.
  • Occupation of natural orbitals occurs in pairs, signifying the formation of composite bosons from two attractive fermions.

Conclusions:

  • The formation of composite bosons explains the pairing mechanism in this system.
  • The system's density equals that of a Bose-Einstein condensate, highlighting emergent bosonic behavior.
  • Attractive interactions in 1D fermions can lead to universal pairing phenomena.