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The concept of flux describes how much of something goes through a given area. More formally, it is the dot product of a vector field within an area. For a better understanding, consider an open rectangular surface with a small area that is placed in a uniform electric field. The larger the area, the more field lines go through it and, hence, the greater the flux; similarly, the stronger the electric field (represented by a greater density of lines), the greater the flux. On the other hand, if...
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The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). Magnetic flux is a scalar quantity. It depends on three factors: the strength of the magnetic field B, the area through which the field lines pass, and the relative orientation of the field with the surface area.
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Consider the electric field of an oppositely charged, parallel-plate system and an imaginary box between those plates. Let the bottom face of the box be ABCD, and the top face be FGHK. The electric field between the plates is uniform and points from the positive plate toward the negative plate. The calculation of this field's flux through the box's various faces shows that the net flux through the box is zero. Why does the flux cancel out here?
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Quantum Blobs.

Maurice A de Gosson1

  • 1Faculty of Mathematics, University of Vienna, NuHAG, 1090 Vienna, Austria.

Foundations of Physics
|December 23, 2014
PubMed
Summary

Quantum blobs represent the smallest phase space units consistent with quantum mechanics. This research proposes them as a novel phase space substitute, linking them to squeezed coherent states and geometric quantum state representations.

Area of Science:

  • Quantum mechanics
  • Mathematical physics
  • Quantum information theory

Background:

  • The uncertainty principle fundamentally limits phase space resolution in quantum mechanics.
  • Standard quantum mechanics utilizes squeezed coherent states to describe quantum states.
  • A need exists for a geometrically intuitive representation of quantum states in phase space.

Purpose of the Study:

  • To introduce and define quantum blobs as the minimal phase space units.
  • To establish a bijective correspondence between quantum blobs and squeezed coherent states.
  • To propose quantum blobs as a substitute for traditional phase space in quantum mechanics.
  • To explore the geometric representation of quantum states using quantum blobs and Fermi level sets.

Main Methods:

Keywords:
Coherent statesFermi’s functionQuantum phase spaceSymplectic capacityWigner function

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  • Definition of quantum blobs based on the uncertainty principle and symplectic symmetry.
  • Establishing a bijective mapping between quantum blobs and squeezed coherent states.
  • Investigating the relationship between quantum blobs and Fermi level sets for geometric state representation.

Main Results:

  • Quantum blobs are identified as the smallest phase space units respecting quantum mechanical constraints.
  • A one-to-one correspondence is demonstrated between quantum blobs and squeezed coherent states.
  • A novel phase space representation for quantum mechanics is proposed using quantum blobs.
  • The geometric relationship between quantum blobs and Fermi level sets for quantum state visualization is studied.

Conclusions:

  • Quantum blobs offer a fundamental, geometrically interpretable framework for quantum mechanics.
  • This framework provides a new perspective on phase space and quantum state representation.
  • The connection to Fermi level sets opens avenues for advanced geometric quantum state analysis.