Detection Time Distribution for Several Quantum Particles

• URL: http://arxiv.org/abs/1601.03871v3
• Date: Tue, 12 Nov 2024 10:52:31 GMT
• Title: Detection Time Distribution for Several Quantum Particles
• Authors: Roderich Tumulka,
• Abstract summary: We address the question of how to compute the probability distribution of the time at which a detector clicks. A key element of this extension is that, upon a detection event, the wave function gets collapsed by inserting the detected position. We also describe an extension of the absorbing boundary rule to the case of moving detectors.
• Score: 0.0
• License:
• Abstract: We address the question of how to compute the probability distribution of the time at which a detector clicks, in the situation of $n$ non-relativistic quantum particles in a volume $\Omega\subset \mathbb{R}^3$ in physical space and detectors placed along the boundary $\partial \Omega$ of $\Omega$. We have previously [arXiv:1601.03715] argued in favor of a rule for the 1-particle case that involves a Schr\"odinger equation with an absorbing boundary condition on $\partial \Omega$ introduced by Werner; we call this rule the "absorbing boundary rule." Here, we describe the natural extension of the absorbing boundary rule to the $n$-particle case. A key element of this extension is that, upon a detection event, the wave function gets collapsed by inserting the detected position, at the time of detection, into the wave function, thus yielding a wave function of $n-1$ particles. We also describe an extension of the absorbing boundary rule to the case of moving detectors.

Related papers

• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• On a Derivation of the Absorbing Boundary Rule [0.0]
  detector waiting for a quantum particle to arrive at a surface $S$ in 3-space. For predicting the probability distribution of the time and place of detection, a rule was proposed in [arXiv:1601.03715], called the absorbing boundary rule (ABR) We derivation is non-rigorous, and it would still be desirable to have a rigorous version of it in the future.
  arXiv  Detail & Related papers  (2023-10-02T17:07:43Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Quantum delay in the time of arrival of free-falling atoms [0.0]
  We show that 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 by the Born rule. In an application to a quantum particle of mass $m$ falling in a uniform gravitational field $g, we use this approach to obtain an exact explicit expression for the probability density of the time-of-arrival.
  arXiv  Detail & Related papers  (2023-06-03T15:51:27Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• Detection time of Dirac particles in one space dimension [0.76146285961466]
  We consider particles emanating from a source point inside an interval in one-dimensional space and passing through detectors situated at the endpoints of the interval that register their arrival time. The arrival time at the boundary of a particle whose motion is being guided by a wave function is well-defined and unambiguous. We derive explicit formulas for the distribution of first arrival times at each detector, which we hope can be used to study issues related to non-locality.
  arXiv  Detail & Related papers  (2021-12-13T14:54:53Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)
• Energy-Time Uncertainty Relation for Absorbing Boundaries [0.0]
  We prove the uncertainty relation $sigma_T, sigma_E geq hbar/2$ between the time $T$ of detection of a quantum particle on the surface.
  arXiv  Detail & Related papers  (2020-05-29T12:04:57Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)
• Existence of Schrodinger Evolution with Absorbing Boundary Condition [0.0]
  Consider a non-relativistic quantum particle with wave function inside a region $Omegasubset mathbbR3$. The question how to compute the probability distribution of the time at which the detector surface registers the particle boils down to finding a reasonable mathematical definition of an ideal detecting surface. A particularly convincing definition, called the absorbing boundary rule, involves a time evolution for the particle's wave function $psi$ expressed by a Schrodinger equation in $Omega$ together with an "absorbing" boundary condition on $partial Omega$ first considered by Werner in
  arXiv  Detail & Related papers  (2019-12-27T10:53:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.