An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum Attraction With No Classical Force

Goldhaber, Alfred S

doi:10.2172/812603

Title: An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum Attraction With No Classical Force

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Abstract

As a consequence of the Aharonov-Bohm effect, there is a quantum-induced attraction between a charged particle and a rigid impenetrable hoop made from an arbitrarily thin tube containing a superconductor quantum of magnetic flux. This is remarkable because in classical physics there is no force between the two objects, and quantum-mechanical effects (associated with uncertainty-principle energy) generally are repulsive rather than attractive. For an incident spinless charged particle in a P wave, in a configuration with total angular momentum zero, we verify a resonance just above threshold using the Kohn variational principle in its S-matrix form. Even if optimistic choices of parameters describing a model system with these properties turned out to be feasible, the temperature required to observe the resonance would be far lower than has yet been attained in the laboratory.

Authors:: Goldhaber, Alfred S

Publication Date:: Thu Jan 09 00:00:00 EST 2003

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (US)

OSTI Identifier:: 812603

Report Number(s):: SLAC-PUB-9606
TRN: US0303424

DOE Contract Number:: AC03-76SF00515

Resource Type:: Technical Report

Resource Relation:: Other Information: PBD: 9 Jan 2003

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AHARONOV-BOHM EFFECT; ANGULAR MOMENTUM; CHARGED PARTICLES; MAGNETIC FLUX; MESONS; P WAVES; RESONANCE; S MATRIX; SUPERCONDUCTORS; UNCERTAINTY PRINCIPLE

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                    Goldhaber, Alfred S. An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum Attraction With No Classical Force.  United States: N. p., 2003. 
        Web.  doi:10.2172/812603.

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                    Goldhaber, Alfred S. An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum Attraction With No Classical Force.  United States.  https://doi.org/10.2172/812603

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                    Goldhaber, Alfred S. 2003.  
        "An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum Attraction With No Classical Force".  United States.  https://doi.org/10.2172/812603.  https://www.osti.gov/servlets/purl/812603.

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@article{osti_812603,

  title        = {An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum Attraction With No Classical Force},

  author       = {Goldhaber, Alfred S},

  abstractNote = {As a consequence of the Aharonov-Bohm effect, there is a quantum-induced attraction between a charged particle and a rigid impenetrable hoop made from an arbitrarily thin tube containing a superconductor quantum of magnetic flux. This is remarkable because in classical physics there is no force between the two objects, and quantum-mechanical effects (associated with uncertainty-principle energy) generally are repulsive rather than attractive. For an incident spinless charged particle in a P wave, in a configuration with total angular momentum zero, we verify a resonance just above threshold using the Kohn variational principle in its S-matrix form. Even if optimistic choices of parameters describing a model system with these properties turned out to be feasible, the temperature required to observe the resonance would be far lower than has yet been attained in the laboratory.},

  doi          = {10.2172/812603},

  url          = {https://www.osti.gov/biblio/812603},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Thu Jan 09 00:00:00 EST 2003},

  month        = {Thu Jan 09 00:00:00 EST 2003}

}

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