Related papers: Quantizations of the classical time of arrival and…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the…
We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
Starting from a functional formulation of classical mechanics, we show how to perform its quantization by freezing to zero two Grassmannian partners of time.
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…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
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…
In relational quantum dynamics, evolution emerges via the correlations between some system of interest and a clock system, which plays the role of a temporal reference frame. Their combined state satisfies a Wheeler-de Witt-like constraint…
We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this…
We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the…
We discuss a systematic way in which a relational dynamics can be established relative to periodic clocks both in the classical and quantum theories, emphasising the parallels between them. We show that: (1) classical and quantum relational…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
The eigenvalue problem in quantum mechanics is reduced to quantization of the classical action of the physical system. State function of the system, $\psi_0(\phi)$, is written in the form of superposition of two plane waves in the phase…
In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival…
The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, whose idea goes back to Born and Jordan, and which has recently been revived in…