Introduction

Muga, J. G.; Mayato, R. Sala; Egusquiza, I. L.

doi:10.1007/3-540-45846-8_1

Cited by 7 publications

(6 citation statements)

References 104 publications

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“…Point (2) restricts the context of this study to observed transitions, i.e., to transitions associated with definite macroscopic facts of observation. The existence of a macroscopic record necessitates that we include a measurement apparatus in the quantum description of the process.…”

Section: A Preliminariesmentioning

confidence: 99%

“…The time-integrated probabilityP (L) is a density with respect to L, hence for a detector of size d in the x direction, the total fraction of detected particles equals P (L)d. For a monochromatic initial state with momentum p 0 , |ψ 0 | 2 2πδ(p − p 0 ), the total detection probability equals d p 0 |Ŝ(L)|p 0 /|v p 0 |. This implies that we can define an absorption coefficient α(p) for the detector 2 defined, standardly, as the fraction of incoming particles with momentum p > 0 absorbed per unit length of the absorbing medium 2 The definition of an absorption coefficient depends crucially on the property, established earlier, that the time-integrated probability is L independent.…”

Section: Detection Of a Coherent Particle Excitationmentioning

confidence: 99%

“…The time-of-arrival issue [1,2], in its simplest form, amounts to the following problem. One considers an initial wave function |ψ 0 for a particle centered around x = 0 and with a positive mean momentum.…”

Section: Introductionmentioning

confidence: 99%

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Time-of-arrival probabilities for general particle detectors

Anastopoulos

Savvidou

2012

Phys. Rev. A

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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. Thus, its definition is embedded within the larger issue of defining probabilities with respect to time for general quantum transitions. The key point in our analysis is that we manage to reduce the problem of defining a quantum time observable to a mathematical model where time is associated to a transition from a subspace of the Hilbert space of the total system to its complementary subspace. This property makes it possible to derive a general expression for the probability for the time of transition, valid for any quantum system, with the only requirement that the time of transition is correlated with a definite macroscopic record. The framework developed here allows for the consideration of any experimental configuration for the measurement of the time of arrival and it also applies to relativistic systems with interactions described by quantum field theory. We use the method in order to describe time-of-arrival measurements in high-energy particle reactions and for a rigorous derivation of the time-integrated probabilities in particle oscillations.Comment: 27 pages, latex. Changed title and added a conclusions section. Version to appear in PR

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Section: A Preliminariesmentioning

confidence: 99%

Section: Detection Of a Coherent Particle Excitationmentioning

confidence: 99%

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Time-of-arrival probabilities for general particle detectors

Anastopoulos

Savvidou

2012

Phys. Rev. A

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“…At first the research was oriented to define a "tunnelling time" for the particle. Several candidates were put forward, apart from the BL time, and an intense debate followed [3,4]. It was later understood that since the projectors for locating the particle at the barrier and for finding the particle eventually transmitted do not commute, many possible quantizations of the classical concept of a traversal time through the barrier region are possible, and that several of them may be relevant depending on the experimental setting and/or quantity observed [5,4].…”

Section: Introductionmentioning

confidence: 99%

“…Several candidates were put forward, apart from the BL time, and an intense debate followed [3,4]. It was later understood that since the projectors for locating the particle at the barrier and for finding the particle eventually transmitted do not commute, many possible quantizations of the classical concept of a traversal time through the barrier region are possible, and that several of them may be relevant depending on the experimental setting and/or quantity observed [5,4]. Thus, rather than seeking "the tunneling time", a research line aimed at describing the wave dynamics with a minimal number of elements emerged, which could include characteristic times for forerunners, main peaks, or transitions among different regimes [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a quantum wave emitted by a decaying and evanescent point source

Delgado

Muga

2015

Physica E: Low-dimensional Systems and Nanostructures

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Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times

2012

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We develop a wavepacket approach to the diffraction of charged particles by a thin material target and we use the de Broglie-Bohm quantum trajectories to study various phenomena in this context. We construct a particle wave function model given as the sum of two terms ψ = ψ ingoing +ψ outgoing , each having a wavepacket form with longitudinal and transverse quantum coherence lengths both finite. We find the form of the separator, i.e.the limit between the domains of prevalence of the ingoing and outgoing quantum flow. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of quantum vortices (nodal point -X point complexes). The X point gives rise to stable and unstable manifolds, whose directions determine the scattering of the de Broglie -Bohm trajectories. We show how the deformation of the separatior near Bragg angles explains the emergence of a diffraction pattern by the de Broglie -Bohm trajectories. We calculate the arrival time distributions for particles scattered at different angles. A main prediction is that the arrival time distributions have a dispersion proportional to v −1 0 × the largest of the longitudinal and transverse coherence lengths, where v 0 is the mean velocity of incident particles. We also calculate time-of-flight differences ∆T for particles scattered in different angles. The predictions of the de Broglie -Bohm theory for ∆T turn to be different from estimates of the same quantity using other theories on time observables like the sum-over-histories or the Kijowski approach. We propose an experimental setup aiming to test such predictions. Finally, we explore the semiclassical limit of short wavelength and short quantum coherence lengths, and demonstrate how, in this case, results with the de Broglie -Bohm trajectories are similar to the classical results of Rutherford scattering.

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Introduction

Cited by 7 publications

References 104 publications

Time-of-arrival probabilities for general particle detectors

Time-of-arrival probabilities for general particle detectors

Dynamics of a quantum wave emitted by a decaying and evanescent point source

Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times

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