Related papers: On a fractional binomial process
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
Fluctuation theorems have elevated the second law of thermodynamics to a statistical realm by establishing a connection between time-forward and time-reversal probabilities, providing invaluable insight into nonequilibrium dynamics. While…
Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
This article presents a variant of Fleming-Viot particle systems, which are a standard way to approximate the law of a Markov process with killing as well as related quantities. Classical Fleming-Viot particle systems proceed by simulating…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
We show how the quantum process of splitting light may be modelled in classical optics. A second result is the possibility to engineer specific forms of a classical field.
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…
In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
In recent years a quantum information theoretic framework has emerged for incorporating non-classical phenomena into fluctuation relations. Here we elucidate this framework by exploring deviations from classical fluctuation relations…
We propose a mechanism for the enhancement of vacuum fluctuations by means of a classical field. The basic idea is that if an observable quantity depends quadratically upon a quantum field, such as the electric field, then the application…