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Green's functions for random resistor networks.

Sayak Bhattacharjee1, Kabir Ramola2

  • 1Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India.

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Summary
This summary is machine-generated.

Researchers studied random resistor networks using lattice Green's functions. They developed a disorder expansion to analyze nodal voltages and bond currents, introducing a new parameter to characterize disorder regimes.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Random resistor networks are fundamental models in statistical physics.
  • Understanding the behavior of these networks under disorder is crucial for various applications.
  • Lattice Green's functions provide a powerful tool for analyzing such systems.

Purpose of the Study:

  • To develop a systematic method for analyzing random resistor networks with disorder.
  • To compute ensemble-averaged nodal voltages and bond currents.
  • To introduce a novel parameter for characterizing disorder regimes.

Main Methods:

  • Development of a systematic disorder perturbation expansion for weak disorder.
  • Hierarchical computation of ensemble-averaged nodal voltages and bond currents.
  • Construction of a recursive formalism for exact Green's functions with finitely many disordered bonds.
  • Numerical simulations of a square lattice with exponentially distributed resistances.

Main Results:

  • The disorder perturbation expansion accurately describes the weak disorder regime.
  • Explicit expressions for Green's functions with up to four disordered bonds were derived.
  • Nodal voltage distributions can be predicted for large disorder strengths.
  • A novel order parameter was introduced to distinguish weak and strong disorder regimes.

Conclusions:

  • The developed methods provide a comprehensive framework for analyzing random resistor networks.
  • The new order parameter effectively characterizes the different disorder regimes.
  • This work offers insights into the behavior of disordered electrical systems.