Related papers: Quantile clocks
We show that quadratic Hamiltonians in involution coming from a St\"ackel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols are the quadratic Hamiltonians. Moreover, they allow…
A general definition of a clock is proposed, and the role of clocks in establishing temporal pre-conditions in quantum mechanical questions is critically discussed. The different status of clocks as used by theorists external to a system…
We develop an abstract model of atomic clocks that fully describes the dynamics of repeated synchronization between a classical oscillator and a quantum reference. We prove existence of a stationary state of the model and study its…
The continuum clockwork is an extra-dimensional set-up to realize certain features of the clockwork mechanism generating exponentially suppressed or hierarchical couplings of light particles. We study the continuum clockwork in a general…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
A formalism for quantizing time reparametrization invariant dynamics is considered and applied to systems which contain an `almost ideal clock.' Previously, this formalism was successfully applied to the Bianchi models and, while it…
Algorithms for the synchronisation of clocks across networks are both common and important within distributed systems. We here address not only the formal modelling of these algorithms, but also the formal verification of their behaviour.…
Quantile classifiers for potentially high-dimensional data are defined by classifying an observation according to a sum of appropriately weighted component-wise distances of the components of the observation to the within-class quantiles.…
This paper discusses the possibility to find and construct \textit{piecewise constant martingales}, that is, martingales with piecewise constant sample paths evolving in a connected subset of $\mathbb{R}$. After a brief review of standard…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact…
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special…
In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator,…
It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the…
Conformable derivatives involve a fractional parameter while preserving locality: on smooth functions they reduce to a classical derivative multiplied by an explicit weight. Exploiting this structural feature, we show that conformable time…
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the…
We revisit a recent proposal for a definition of time in quantum cosmology, to investigate the effects of having more than one possible type of clock "at the same time". We use as test tube an extension of Einstein gravity with a massless…
We report an innovative model for predicting entanglement distribution between end parties of a quantum network using our in-house simulation algorithm. Our implementation is based on stochastic methods that are built upon a unique global…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…