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Register a new userLifetime of metastable states and suppression of noise in Interdisciplinary Physical Models
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Transient properties of different physical systems with metastable states perturbed by external white noise have been investigated. Two noise-induced phenomena, namely the noise enhanced stability and the resonant activation, are theoretically predicted in a piece-wise linear fluctuating potential with a metastable state. The enhancement of the lifetime of metastable states due to the noise, and the suppression of noise through resonant activation phenomenon will be reviewed in models of interdisciplinary physics: (i) dynamics of an overdamped Josephson junction; (ii) transient regime of the noisy FitzHugh-Nagumo model; (iii) population dynamics.
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The changes in the lifetime of a metastable energy level in Er-doped Si nanocrystals in the presence of an external source of colored noise are analyzed for different values of noise intensity and correlation time. Exciton dynamics is simulated by a set of phenomenological rate equations which take into account all the possible phenomena inherent to the energy states of Si nanocrystals and Er$^{3+}$ ions in the host material of Si oxide. The electronic deexcitation is studied by examining the decay of the initial population of the Er atoms in the first excitation level $^4$I$_{13/2}$ through the fluorescence and the cooperative upconversion by energy transfer. Our results show that the deexcitation process of the level $^4$I$_{13/2}$ is slowed down within wide ranges of noise intensity and correlation time. Moreover, a nonmonotonic behavior of the lifetime with the amplitude of the fluctuations is found, characterized by a maximum variation for values of the noise correlation time comparable to the deexcitation time. The indirect influence of the colored noise on the efficiency of the energy transfer upconversion activated from the level $^4$I$_{13/2}$ is also discussed.
The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window $T$. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time $T$. The large deviation properties of any time-additive observable of the Markov trajectory before extinction can be derived from the Level 2.5 via the decomposition of the time-additive observable in terms of the empirical density and the empirical flows. This general formalism is described for continuous-time Markov chains, with applications to population birth-death model in a stable or in a switching environment, and for diffusion processes in dimension $d$.
We numerically study the metastable states of the 2d Potts model. Both of equilibrium and relaxation properties are investigated focusing on the finite size effect. The former is investigated by finding the free energy extremal point by the Wang-Landau sampling and the latter is done by observing the Metropolis dynamics after sudden heating. It is explicitly shown that with increasing system size the equilibrium spinodal temperature approaches the bistable temperature in a power-law and the size-dependence of the nucleation dynamics agrees with it. In addition, we perform finite size scaling of the free energy landscape at the bistable point.
We study dipolarly coupled three dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.
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 states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the systems Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.
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