Particle detectors and the zero mode of a quantum field

We study the impact of the zero-mode of a quantum field on the evolution of a particle detector. For a massless scalar field in a periodic cavity, we show that the impact of the zero mode on the Unruh-DeWitt detector and its derivative-coupling generalisation is necessarily nonvanishing but can be made negligible in some limits, including those commonly occurring in non-relativistic quantum optics. For the derivative-coupling detector this can be accomplished by just tuning the zero mode's initial state, but the standard Unruh-DeWitt detector requires a more subtle and careful tuning. Applications include an inertial detector with arbitrary velocity, where we demonstrate the regularity of the ultrarelativistic limit, and a detector with uniform acceleration.Comment: 14 pages, 3 Figures. RevTex 4.1. v2: Added journal reference and minor edits to match published versio

Quantum gates via relativistic remote control

We harness general relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build universal quantum gates.Comment: 4 pages (+ 4 pages Appendix). 4 figures. RevTex 4.

Stochastic model for the vocabulary growth in natural languages

We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i) a finite number of core-words which have higher frequency and do not affect the probability of a new word to be used; and (ii) the remaining virtually infinite number of noncore-words which have lower frequency and once used reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the google-ngram database of books published in the last centuries and its main consequence is the generalization of Zipf's and Heaps' law to two scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model the main change on historical time scales is the composition of the specific words included in the finite list of core-words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.Comment: corrected typos and errors in reference list; 10 pages text, 15 pages supplemental material; to appear in Physical Review