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Research Article

Quantum indistinguishability in chemical reactions

Matthew P. A. Fisher and Leo Radzihovsky
PNAS May 15, 2018 115 (20) E4551-E4558; first published April 30, 2018; https://doi.org/10.1073/pnas.1718402115
Matthew P. A. Fisher
aDepartment of Physics, University of California, Santa Barbara, CA 93106;
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  • For correspondence: mpaf@kitp.ucsb.edu radzihov@colorado.edu
Leo Radzihovsky
bCenter for Theory of Quantum Matter, Department of Physics, University of Colorado, Boulder, CO 80309;
cKavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106
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  • For correspondence: mpaf@kitp.ucsb.edu radzihov@colorado.edu
  1. Contributed by Matthew P. A. Fisher, March 26, 2018 (sent for review October 23, 2017; reviewed by Eduardo Fradkin and Ashvin Vishwanath)

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    Fig. 1.

    Schematic of a bond-breaking chemical reaction. (Left) Initial state of a C3 symmetric molecule with two molecular electrons (blue) bonding the three nuclei (red) together. (Center) An intermediate state where the reaction is catalyzed by an enzyme that “grabs” two of the nuclei, weakening their bonds to the third by depletion of electronic charge. (Right) Final product state composed of a molecular dimer and an isolated atom.

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    Fig. 2.

    Three representations of a rotating diatomic molecule composed of identical nuclei. (A) An explicit physical representation. (B) An effective model for the dynamics of the angular coordinate, φ=2ϕ∈[0,2π), for a molecule with C2 symmetry, represented as a quantum bead on a ring with Berry flux, Φ0 determined by the nuclear spin wavefunction. The bead wavefunction, ψa(φ), is discontinuous across an nth root branch cut (red squiggly line), ψ+=eiΦ0ψ−. (C) Placing the bead on an n-fold cover of the ring with φ∈[0,2πn)—a Mobius strip for the n=2 double cover—resolves any ambiguity in the placement of the branch cut.

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    Fig. 3.

    Two representations of a nonrotating diatomic molecule composed of identical nuclei. (A) An explicit physical representation with impenetrable potential wedges inserted around ϕ=0 and π that restrict the molecular rotation angle and constrain one nucleus to the upper half-plane and the other to the lower half-plane. These wedges strictly forbid all rotational motions that dynamically exchange the two nuclei. The identical nuclei thus become effectively distinguishable. (B) An effective quantum bead model, where the ring, now restricted to the angular range, φ∈[δ,2π−δ), has been cut open—and the bead is constrained to move on a line segment.

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    Fig. 4.

    Two representations of a bond-broken diatomic molecule composed of identical but distinguishable nuclei. (A) An explicit physical representation with impenetrable potential wedges inserted at ϕ=0 and π, allowing for a bond-breaking process to the distinguishable-nuclei state. (B) An effective quantum bead on a ring model, restricted to the angular coordinate range φ∈[δ,2π−δ), with bond breaking modeled by tunneling the bead off the ring.

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    Fig. 5.

    The enzymatic projective measurement that induces a transition from a rotating to a not-rotating molecular state can be described as a projective overlap between the rotating state with the quantum bead on the Mobius strip, ψa, and a not-rotating state where the bead is on the cut-open outer ring, ψb. This projective measurement implements a transition from an initial state in which the identical atoms are indistinguishable to a final distinguishable state—the enzyme acting as an observer.

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Quantum indistinguishability in chemical reactions
Matthew P. A. Fisher, Leo Radzihovsky
Proceedings of the National Academy of Sciences May 2018, 115 (20) E4551-E4558; DOI: 10.1073/pnas.1718402115

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Quantum indistinguishability in chemical reactions
Matthew P. A. Fisher, Leo Radzihovsky
Proceedings of the National Academy of Sciences May 2018, 115 (20) E4551-E4558; DOI: 10.1073/pnas.1718402115
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Proceedings of the National Academy of Sciences: 115 (20)
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