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Localization of plane waves in the stochastic telegrapher's equation
1Comision Nacional de Energía Atómica, Avenida E. Bustillo 9500, CP 8400 Bariloche, Argentina and CONICET, Centro Atómico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Avenida E. Bustillo 9500, CP 8400 Bariloche, Argentina.
Physical Review. E
|February 23, 2022
Summary
Strong energy absorption fluctuations in the stochastic telegrapher
Area of Science:
- Mathematical Physics
- Wave Propagation
- Stochastic Processes
Background:
- The stochastic telegrapher's equation models systems with abrupt changes.
- Understanding wave transport in fluctuating media is crucial for various applications.
Purpose of the Study:
- To analyze the impact of energy absorption fluctuations on plane-wave modes.
- To investigate the delocalization of plane-wave modes due to these fluctuations.
Main Methods:
- Derived exact solutions for the stochastic telegrapher's equation.
- Introduced and analyzed Fourier plane-wave-like modes.
- Studied the time evolution of these modes under fluctuating absorption.
Main Results:
- Fluctuations in energy loss create a localized gap, dependent on fluctuation correlation time.
- Increased correlation time significantly reduces this gap, leading to delocalization of plane-wave modes.
- Observed delocalization contrasts with the behavior of plane waves in the standard telegrapher's equation.
Conclusions:
- Energy absorption fluctuations play a critical role in wave transport dynamics.
- These fluctuations can induce delocalization, impacting wave propagation in conducting media.
- The findings offer insights into the functional role of energy loss fluctuations in stochastic systems.
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