Related papers: Non-exponential decay in Floquet-Bloch bands
The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed…
While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying…
An unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from…
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times…
Periodically driven quantum systems suffer from heating via resonant excitation. While such Floquet heating guides a generic isolated system towards the infinite-temperature state, a driven open system, coupled to a thermal bath, will…
We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
We study the decay process of an unstable quantum system, especially the deviation from the exponential decay law. We show that the exponential period no longer exists in the case of the s-wave decay with small $Q$ value, where the $Q$…
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used.…
We analyze the temporal behavior of the survival probability of an unstable $^6$Li Feshbach molecule close to the BCS-BEC crossover. We find different instances of nonexponential decay as the magnetic field approaches the resonance value,…
We report the long-time nonlinear dynamical evolution of ultracold atomic gases in the P-band of an optical lattice. A Bose-Einstein condensate (BEC) is fast and efficiently loaded into the Pband at zero quasi-momentum with a non-adiabatic…
Motivated by recent experimental observations (C.V. Parker {\it et al.}, Nature Physics, {\bf 9}, 769 (2013)), we analyze the stability of a Bose-Einstein condensate (BEC) in a one-dimensional lattice subjected to periodic shaking. In such…
We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the…
Quantum systems are typically characterized by the inherent fluctuation of their physical observables. Despite this fundamental importance, the investigation of the fluctuations in interacting quantum systems at finite temperature continues…
We consider $N$ trapped bosons in the mean-field limit with coupling constant $\lambda_N=1 / (N-1)$. The ground state of such systems exhibits Bose--Einstein condensation. We prove that the probability of finding $\ell$ particles outside…
This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their…
Floquet dynamics of a quantum system subject to periodic modulations of system parameters provide a powerful tool for engineering new quantum matter with exotic properties. While system dynamics are significantly altered, the periodic…
Chaotic quantum systems at finite energy density are expected to act as their own heat baths, rapidly dephasing local quantum superpositions. We argue that in fact this dephasing is subexponential for chaotic dynamics with conservation laws…
We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady…
We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that…