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Coulomb's Law01:30

Coulomb's Law

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Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
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The electric potential energy of a test charge in a uniform eclectic field can be generalized to any electric field produced by static charge distribution. Consider a positive test charge in an electric field produced by another static positive charge. If the test charge is moved away from the static charge, then the electric field does the positive work on the test charge, and the electric potential energy of the test charge decreases as it moves away from the static charge. Here the electric...
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Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
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Magnetic Field due to Moving Charges01:23

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A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
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First Law: Particles in Two-dimensional Equilibrium01:18

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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.
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Updated: May 7, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-Dimensional Insulators.

Pok Man Tam1, Jonah Herzog-Arbeitman2, Jiabin Yu2,3

  • 1Princeton Center for Theoretical Science, <a href="https://ror.org/00hx57361">Princeton University</a>, Princeton, New Jersey 08544, USA.

Physical Review Letters
|January 3, 2025
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Summary

Corner charge fluctuations in lattice systems directly measure quantum geometry. This research develops a method to isolate corner contributions, revealing their angle dependence probes the quantum metric, crucial for quantum simulators and information theory.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Quantum Geometry

Background:

  • Bipartite fluctuations of conserved charges offer insights into quantum systems.
  • Corner contributions to bipartite fluctuations show universal angle dependence in 2D uniform systems.

Purpose of the Study:

  • To establish the direct relationship between corner charge fluctuations and quantum geometry in generic lattice systems.
  • To develop a practical method for isolating corner contributions on lattices.
  • To demonstrate the use of corner charge fluctuations as a probe of quantum geometry in quantum simulators.

Main Methods:

  • Development of a practical scheme to isolate corner contributions to bipartite fluctuations on lattices.
  • Analytical proof of the angle dependence in the small-angle limit measuring the integrated quantum metric.
  • Introduction of a compact obstructed atomic insulator model for analytical illustration.
  • Numerical verification using various Chern insulator models.

Main Results:

  • Corner charge fluctuation's angle dependence in the small-angle limit exclusively measures the integrated quantum metric for generic lattice systems.
  • Analytical and numerical evidence confirms the link between corner charge fluctuations and quantum geometry.
  • Demonstration of corner charge fluctuation's experimental relevance in finite-size quantum simulators.
  • Unveiling a connection between quantum geometry and quantum information via corner entanglement entropies for free fermions.

Conclusions:

  • Corner charge fluctuations provide a direct and experimentally relevant probe of quantum geometry in lattice systems.
  • The study bridges quantum geometry, quantum information, and condensed matter physics through lattice observable measurements.
  • Findings have implications for understanding topological phases and designing quantum information processing protocols.