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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Linear response and modified fluctuation-dissipation relation in random potential.

Fattah Sakuldee1, Sujin Suwanna1

  • 1MU-NECTEC Collaborative Research Unit on Quantum Information, Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

This study modifies the Kubo formula and fluctuation-dissipation relation (FDR) for physical systems with random potentials. These modifications account for randomness and memory effects, recovering the standard FDR under specific equilibrium conditions.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Investigating physical systems with Hamiltonians comprising a solvable model and a time-dependent random potential.
  • Examining the impact of external random and time-dependent potentials on system dynamics.

Purpose of the Study:

  • To derive the mean dynamics of a quantum system subjected to a random, time-dependent potential.
  • To modify the Kubo formula and fluctuation-dissipation relation (FDR) to include effects of randomness and time dependence.

Main Methods:

  • Defining an adjusted equilibrium state as a reference for systems with smoothly evolving potentials and time-independent average potentials.
  • Averaging equations of motion with respect to the configuration parameter to derive mean dynamics.
  • Utilizing Heisenberg and Liouville-von Neumann equations to describe state evolution.

Main Results:

  • The Kubo formula and FDR are modified, incorporating contributions from randomness and memory effects.
  • The modified Kubo formula includes an antisymmetric cross-correlation term and a term accounting for the propagation of randomness effects.
  • The standard FDR is recovered when the system is in the adjusted equilibrium state at the time of measurement.

Conclusions:

  • The study provides a framework for understanding quantum dynamics in systems with complex potentials.
  • The derived modified Kubo formula and FDR offer a more comprehensive description of physical systems with random and time-dependent perturbations.
  • The findings highlight the importance of considering system state and potential characteristics for accurate physical predictions.