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Measure for Chaotic Scattering Amplitudes.

Massimo Bianchi1, Maurizio Firrotta1, Jacob Sonnenschein2

  • 1Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy and INFN sezione di Roma Tor Vergata Via della Ricerca Scientifica 1, 00133 Roma, Italy.

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We introduce a new method to measure chaotic scattering amplitudes using log-normal distributions. This novel approach reveals surprising connections between quantum mechanics, string theory, and the Riemann zeta function.

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Area of Science:

  • Theoretical physics
  • Quantum mechanics
  • String theory

Background:

  • Chaotic scattering phenomena exhibit complex amplitude behavior.
  • Understanding these amplitudes is crucial in quantum mechanics and high-energy physics.
  • Previous measures have not fully captured the underlying statistical properties.

Purpose of the Study:

  • To develop a novel statistical measure for chaotic scattering amplitudes.
  • To explore the universality of this measure across different physical systems.
  • To investigate potential connections to number theory.

Main Methods:

  • Defining a log-normal distribution function for ratios of consecutive spacings between scattering amplitude peaks.
  • Applying this measure to quantum mechanical scattering on a leaky torus.
  • Analyzing the decay of highly excited string states into two tachyons.

Main Results:

  • The proposed log-normal distribution function effectively characterizes chaotic scattering amplitudes.
  • The same measure was found to be applicable to both leaky torus scattering and string state decay.
  • A remarkable finding is the shared distribution with nontrivial zeros of the Riemann zeta function.

Conclusions:

  • The novel measure provides a unified framework for understanding chaotic scattering.
  • This work highlights deep, unexpected connections between quantum scattering, string theory, and number theory.
  • The universality of the observed distribution suggests fundamental underlying principles.