arXiv subjects

Dror Meidan

Publications and source records attributed to Dror Meidan.

3 recordsLinked to original sources

arXiv2020

Alternating quarantine for sustainable epidemic mitigation

Absent a drug or vaccine, containing epidemic outbreaks is achieved by means of social distancing, specifically mobility restrictions and lock-downs. Such measures impose a hurtful toll on the economy, and are difficult to sustain for extended periods. As an alternative, we propose here an alternating quarantine strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and quarantine. This regime affords a dual partition:\ half of the population interacts for only half of the time, resulting in a dramatic reduction in transmission, comparable to that achieved by a population-wide lock-down. All the while, it enables socioeconomic continuity at $50\%$ capacity. The proposed weekly alternations also address an additional challenge, with specific relevance to COVID-19. Indeed, SARS-CoV-2 exhibits a relatively long incubation period, in which individuals experience no symptoms, but may already contribute to the spread. Unable to selectively isolate these invisible spreaders, we resort to population-wide restrictions. However, under the alternating quarantine routine, if an individual was exposed during their active week, by the time they complete their quarantine they will, in most cases, begin to exhibit symptoms. Hence this strategy isolates the majority of pre-symptomatic individuals during their infectious phase, leading to a rapid decline in the viral spread, thus addressing one of the main challenges in COVID-19 mitigation.

q-bio.PE↗

arXiv2019

Dark states of quantum search cause imperfect detection

We consider a quantum walk where a detector repeatedly probes the system with fixed rate $1/\tau$ until the walker is detected. This is a quantum version of the first-passage problem. We focus on the total probability, $P_{\mathrm{det}}$, that the particle is eventually detected in some target state, for example on a node $r_{\mathrm{d}}$ on a graph, after an arbitrary number of detection attempts. Analyzing the dark and bright states for finite graphs, and more generally for systems with a discrete spectrum, we provide an explicit formula for $P_{\mathrm{det}}$ in terms of the energy eigenstates which is generically $\tau$ independent. We find that disorder in the underlying Hamiltonian renders perfect detection: $P_{\mathrm{det}}=1$, and then expose the role of symmetry with respect to sub-optimal detection. Specifically, we give a simple upper bound for $P_{\mathrm{det}}$ that is controlled by the number of equivalent (with respect to the detection) states in the system. We also extend our results to infinite systems, for example the detection probability of a quantum walk on a line, which is $\tau$-dependent and less than half, well below Polya's optimal detection for a classical random walk.

quant-ph↗

arXiv2019

Running Measurement Protocol for the Quantum First-detection problem

The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time $τ$, with the detector moving right before every detection attempt. For a tight-binding quantum walk on the line, the moving detector allows one to target a specific range of group velocities of the walker, qualitatively modifying the behavior of the quantum first-detection probabilities. We map the problem to that of a stationary detector with a modified unitary evolution operator and use established methods for the solution of that problem to study the first-detection statistics for a moving detector on a finite ring and on an infinite 1D lattice. On the line, the system exhibits a dynamical phase transition at a critical value of $τ$, from a state where detection decreases exponentially in time and the total detection is very small, to a state with power-law decay and a significantly higher probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical $τ$ is 10/3, as opposed to 3 for every larger $τ$. In addition, the moving detector strongly modifies the Zeno effect.

cond-mat.stat-mech↗