On the lifetime-width relation for a decaying state and the uncertainty principle

Quantum speed limit for physical processes

The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.

Influence of a nanorod molecular layer on the biological activity of neuronal cells. A semiclassical model for complex solid/liquid interfaces with carbon nanotubes

A general account of electric effects is given for a biological phase interacting with a nanorod molecular layer by means of the formed hard-soft and solid-liquid interfaces. In particular, the frequency enhancement previously detected for the spontaneous activity of neuronal cultures interfaced with carbon nanotubes is quantitatively explained upon a quantum/semiclassical description, where the duration of a biological signal is viewed as the (average) lifetime of a decaying state (or population of states), and the effect of the carbon phase as a linewidth broadening. Four contributions were principally accounted for, one biological, for the synaptic strength, one electrochemical, for the overall capacitance increase implied by the nanotube double layers, one geometric, for the typical scales ruling the electron and ion conduction mechanisms, and one electromagnetic-like, translating the membrane polarization changes. These calculations predict an enhancement factor equal on average to ≃6.39, against a former experimental value ≃6.08.

On the repulsion of energy eigenstates in the time domain

The rate and extent of the exploration of the available phase space of a bound quantum mechanical system are shown to depend on the repulsion of energy eigenstates. Central to the argument is the Fourier transform relating the survival probability (in time) of an initially prepared nonstationary state and the (frequency) autocorrelation function of the excitation spectrum. Strong repulsion of states, as in the Wigner surmise, leads to a rapid dephasing of the initially coherently prepared state. The rate and extent of sampling of phase space depend not only on the spacing distribution but also on the intensity fluctuations. The rate of dephasing is equal to that inferred from the width of the spectral autocorrelation function.