A simplified Markov model for 1/f noise

ORAL

Abstract

If a system is weakly coupled to an effectively infinite heat bath, standard fluctuation theory predicts that the power spectral density will exhibit frequency-independent (or ``white'') noise. However, at low frequencies most materials exhibit 1/f (or ``pink'') noise, which still has no widely accepted general explanation. A recent mechanism is that 1/f noise arises from direct coupling between the system and its bath. We investigate a Markov model containing (Ising-like) binary degrees of freedom that define a system, and unary degrees of freedom that reside in a bath. The model takes the form of a rectangular matrix for which the rows represent the thermodynamic macrostates and the columns represent the thermodynamic microstates. The macrostates are a function of the system’s binary degrees of freedom alone, so that the bath states cause the dynamics of the system to pause. Although these pause states simply delay the dynamics of the system, they must be included in the total number of microstates to maintain maximum entropy. The partitioning of microstates between the system and the bath affects the transition probabilities between macrostates. Including these pause states in a Markov process yields 1/f noise, qualitatively agreeing with the behavior observed in materials.

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Authors

  • Andrew Shevchuk

    Department of Physics, Arizona State University

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra