Resonances and Quasi-exponential Decay

Christopher King

A. Petridis, Jon Vermedahl, L. P. Staunton +1 more

Urban Duh, Marko Žnidarič

We study Ruelle-Pollicott resonances of translationally invariant magnetization-conserving qubit circuits via the spectrum of the quasi-momentum-resolved truncated propagator of extensive observables. Diffusive transport of the conserved magnetization is reflected in the Gaussian quasi-momentum k k dependence of the leading eigenvalue (Ruelle-Pollicott resonance) of the truncated propagator for small k k . This, in particular, allows us to extract the diffusion constant. For large k k , the leading Ruelle-Pollicott resonance is not related to transport and governs the exponential decay of correlation functions. Additionally, we conjecture the existence of a continuum of eigenvalues below the leading diffusive resonance, which governs non-exponential decay, for instance, power-law hydrodynamic tails. We expect our conclusions to hold for generic systems with exactly one U(1) conserved quantity.

Stefano Longhi, Ermanno Pinotti

A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.

Vladislav Cheltsov

The nonperturbative theory of the cooperative spontaneous emission from a two level atom trapped in one-dimentional damped nanocavity with a single resonance mode is presented. The time-dependent spectral properties and nonlinear dynamics of a separate photon emission by the micro-molecular-like system "excited atom coupled to a resonance decaying mode" have been analyzed. The investigation has been carried out by solving the Schrödinger equation in the interaction picture with the help of the Green functions method in the Heitler-Ma's form. The formalism was supplemented with the novel algorithm in operating causal singular functions and with fundamentals of the theory of quasi-stationary systems. The proposed theory accounts automatically of both reabsorptions of emitted photon and its simultaneous escaping out of the cavity. Solutions of the wave equation were found without using intermediate virtual states and series expansions. In accordance with the theory of quasi-stationary systems the field of mode decaying exponentially in the empty nanocavity was represented with the Lorenz-shaped packet of stationary photonic states (quasi-modes). The electro-dipolar interaction between the atom and the mode field was adopted to be switched on suddenly. The expressions and plots of emission probabilities spectral densities together with photon emission probability dynamics as functions of time for various ratios Γ/4g of photon escaping rate Γ and coupling constant g are presented. For Γ/4g <1 the transient emission spectrum reveals the presence of two symmetrical side-bands and of the central peak, the latter decaying in time at the rate ∝ Γ/2 so that the final spectrum is a doublet. In this case the photon emission probability is described by decaying oscillations. On the contrary for Γ/4g ≥ 1 the spectrum is a singlet and the emission occurs in exponentially decaying ways.

Dmitrii Kouznetsov