Related papers: The time distribution of quantum events
We propose a general construction of an observable measuring the time of occurence of an effect in quantum theory. Time delay in potential scattering is computed as a straightforward application.
Time of arrival refers to the time a particle takes after emission to impinge upon a suitably idealized detector surface. Within quantum theory, no generally accepted solution exists so far for the corresponding probability distribution of…
Using standard results from statistics, we show that for any continuous quantum system (Gaussian or otherwise) and any observable $\widehat{A}$ (position or otherwise), the distribution $\pi_{a}\left(t\right)$ of time measurement at a fixed…
We further develop the general theory of quantum time distributions introduced in arXiv:2010.07575 and apply it to find the distribution of arrival times at the detector. Even though the Hamiltonian in the absence of detector is hermitian,…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
We consider the problem of computing, for a detector surface waiting for a quantum particle to arrive, the probability distribution of the time and place at which the particle gets detected, from the initial wave function of the particle in…
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of…
Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
The distribution of waiting times until the occurrence of a critical event is a crucial statistical problem across several disciplines in Science. In this work we present a statistical model in which a relevant quantity X accumulates until…
The time-of-arrival problem asks for the probability distribution for when a quantum particle reaches a specified location. It has been the subject of decades of debate, exemplifying the lack of a self-adjoint time observable in quantum…
There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
Using standard results from statistics, we show that for Gaussian quantum systems the distribution of a time measurement at a fixed position can be directly inferred from the distribution of a position measurement at a fixed time as given…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…