large-fluctuations-open-quantum

name	large-fluctuations-open-quantum
description	Large fluctuation theory for open quantum systems — analyzing atypical measurement outcomes in driven dissipative steady states. Shows large-deviation functions develop lines and surfaces with discontinuous derivatives, unlike equilibrium analytic Wigner functions. Provides framework for rare event statistics in non-equilibrium quantum systems. Activation: large fluctuations, open quantum systems, large-deviation, non-equilibrium, driven dissipative, Wigner function, rare events, steady state statistics, atypical outcomes
metadata	{"arxiv_id":"2606.11822","published":"2026-06-10","authors":"V. Yu. Mylnikov, S. O. Potashin, A. Kamenev","tags":["quantum","open-systems","large-deviation","non-equilibrium","statistical-physics","fluctuations"]}

Large Fluctuations in Open Quantum Systems

Core Insight

In equilibrium, probability distributions over phase space (e.g., Wigner functions) are analytic in phase-space coordinates. In driven dissipative quantum systems, this property is generically lost: large-deviation functions develop lines and surfaces where derivatives are discontinuous.

Mathematical Framework

Large-Deviation Function

For steady-state probability distribution P(α) in phase space:

P(α) ~ exp(-N · Φ(α))

where Φ(α) is the large-deviation function and N is a large parameter (e.g., photon number, system size).

Key Phenomenon: Non-Analyticity

• Equilibrium: Φ(α) is smooth and analytic everywhere
• Driven dissipative: Φ(α) develops non-analytic structures:
  • Lines (1D) in 2D phase space where derivatives jump
  • Surfaces (2D) in higher dimensions
  • Caused by competing relaxation pathways

Analysis Methodology

1. Identify steady state of driven dissipative system
2. Compute large-deviation function Φ(α) via path integral or Keldysh technique
3. Locate non-analytic structures (caustics, shock lines)
4. Classify singularity type (first-order, second-order transitions)
5. Relate to physical observables (measurement outcome probabilities)

Physical Interpretation

Non-analytic large-deviation functions indicate:

• Phase transitions in fluctuation space: Different fluctuation mechanisms dominate in different regions
• Optimal fluctuation paths: Most likely trajectory to rare state changes abruptly
• Dynamical phase coexistence: Multiple competing steady-state configurations

When to Apply

• Rare event analysis in quantum optics
• Quantum jump statistics in driven systems
• Non-equilibrium phase transitions
• Quantum thermodynamics of small systems
• Measurement-induced phase transitions

Pitfalls

• Large-deviation asymptotics require large N — finite-size corrections significant
• Non-analyticity location depends sensitively on driving parameters
• Path integral formulation may have multiple saddle points
• Numerical evaluation of large-deviation functions challenging in high dimensions