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Computing large deviations of first-passage-time statistics in open quantum systems: Two methods.

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Summary
This summary is machine-generated.

We present two novel methods for calculating large deviations in open quantum systems, crucial for understanding quantum dynamics and predicting system behavior. These techniques enhance the analysis of first-passage-time statistics in complex quantum scenarios.

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Area of Science:

  • Quantum Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Open quantum systems exhibit complex dynamics that are challenging to model.
  • First-passage-time statistics are essential for characterizing transient behaviors in quantum systems.
  • Accurate computation of large deviations is vital for understanding rare events and system stability.

Purpose of the Study:

  • To develop and validate two new methods for computing large deviations of first-passage-time statistics in general open quantum systems.
  • To provide theoretical and computational tools for analyzing complex quantum dynamics.
  • To bridge the gap between theoretical models and simulation-based approaches.

Main Methods:

  • Method 1: Analytical approach involving the joint Laplace and z-transform of the first-passage time distribution, solving pole equations, and deriving scaled cumulant generating functions.
  • Method 2: Simulation-based approach utilizing the wave-function cloning algorithm for analyzing quantum system dynamics.
  • Theoretical underpinning: Unraveling open quantum system dynamics into piecewise deterministic processes and utilizing a tilted Liouville master equation.

Main Results:

  • Derived analytical expressions for scaled cumulant generating functions in field-driven two-level and three-level systems.
  • Validated both proposed methods through theoretical derivations and numerical simulations.
  • Presented numerical results and cloning simulations for a specific system of two interacting two-level atoms.

Conclusions:

  • The proposed methods offer robust frameworks for computing large deviations in open quantum systems.
  • These techniques are applicable to various quantum systems, including multi-level and interacting systems.
  • The study provides valuable tools for both theoretical analysis and numerical simulation of quantum dynamics.