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Thermodynamic uncertainty relations in mesoscopic devices.

I R A C Lucena1, R A Batista1, J G G S Ramos1

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We explored thermodynamic uncertainty relations (TURs) in chaotic quantum dots, finding distinct behaviors between two TUR measures, especially in the opaque regime. Quantum interference effects significantly impact these relations.

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Area of Science:

  • Mesoscopic physics
  • Quantum thermodynamics
  • Statistical mechanics

Background:

  • Thermodynamic uncertainty relations (TURs) provide fundamental bounds on the precision of thermodynamic measurements.
  • Understanding TURs in complex quantum systems like mesoscopic devices is crucial for advancing quantum technologies.
  • Previous studies have primarily focused on simpler systems, leaving the behavior of TURs in chaotic mesoscopic systems under-explored.

Purpose of the Study:

  • To investigate thermodynamic uncertainty relations (TURs) in mesoscopic devices across all universal symmetry classes.
  • To analyze two specific TUR measures: the ratio of mean noise to mean conductance (MS) and a novel ensemble mean ratio (R).
  • To examine the impact of quantum interference and various degrees of freedom on TUR validity in chaotic mesoscopic billiards.

Main Methods:

  • Concatenation of Landauer-Büttiker theory, Mahaux-Wendeinmüller theory, and TURs.
  • Simulation of chaotic quantum dots using random-matrix theory.
  • Comparison of numerical simulations with experimental data across varying channel numbers and tunneling rates.

Main Results:

  • A clear phenomenological distinction between the two TUR measures (MS and R) was observed across different regimes.
  • The opaque regime showed significant differences in observables, indicating a violation of the central limit theorem even in the semiclassical limit.
  • Quantum interference corrections were found to be remarkably robust, exceeding the semiclassical term for TUR (R) by an order of magnitude.

Conclusions:

  • The study reveals distinct behaviors of different TUR measures in chaotic mesoscopic systems.
  • The findings highlight the importance of considering quantum interference effects and the specific TUR definition in mesoscopic transport.
  • The results provide valuable insights into the fundamental limits of thermodynamic measurements in complex quantum systems.