A formula for the spectral projection of the time operator
Maurice Courbage (MSC), Seyed Majid Saberi Fathi (MSC)
TL;DR
This paper investigates the spectral projection of the quantum time operator within the Friedrichs model, revealing how the survival probability decays over time through algebraic and exponential oscillations.
Contribution
It introduces a formula for the spectral projection of the time operator in the Friedrichs model, connecting quantum decay dynamics with spectral analysis.
Findings
Survival probability exhibits algebraic decay at long times.
Decay includes exponential and oscillatory components.
Provides a spectral projection formula for the quantum time operator.
Abstract
In this paper, we study the one-level Friedrichs model with using the quantum time super-operator that predicts the excited state decay inside the continuum. Its survival probability in long time limit is an algebraically decreasing function and an exponentially decreasing multiplied by the oscillating functions.
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Taxonomy
TopicsQuantum Mechanics and Applications · Advanced Thermodynamics and Statistical Mechanics · Quantum chaos and dynamical systems