Large-time limit of the quantum Zeno effect

Abstract

If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t ∝ N α .The limit survival probability exhibits a sudden jump from 1 to 0 at α = 1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α ≥ 1 the limit probability becomes sensitive to the spectral properties of the initial state and to arithmetic properties of the measurement periods.

Generalized product formulas and quantum control

“…as n → ∞, that is (39). Notice that the dominant term in the convergence error comes from the difference of the unit vectors, u n − v n = O(1/n), the phase difference being of smaller order, φ n − nθ n = o(1/n).…”

Quantum Brownian motion under generalized position measurements: a converse Zeno scenario

“…On the other hand, at fixed γ, the width increases with μ, as the rate of energy pumping into the system by the measurement backaction increases (see equation (25)). Dotted black lines-predictions from the analytical, small-τ expressions for vanishing γ (equations (24)) and for finite γ at asymptotically large times t (equation (25)). Diamonds-evaluations for a spectral density function with Drude cutoff at ω D =100 ω 0 (see equations (B.2) and (B.4)).…”

Quantum cavities with alternating boundary conditions

“…• the value of the form (25) in the wave function ψ is given by the sum of two terms: the first one is common to all the extensions while the second one depends explicitly on the extension. Notice, indeed, that the matrix K U in (20) is, up to a sign, the inverse Cayley transform of the unitary matrix U with the eigenvalue 1 stripped out;…”