Related papers: Relativistic Time-of-Arrival and Traversal Time
We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…
We construct a one-particle TOA operator $\mathcal{\hat{T}}$ canonically conjugate with the Hamiltonian describing a free, charged, spin-$0$, relativistic particle in one spatial dimension and show that it is maximally symmetric. We solve…
We discuss alternatives to the usual quantization of relativistic particles which result in discrete spectra for position and time operators.
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…
The time delay between the receptions of ultra-relativistic particles emitted simultaneously is a useful observable for both fundamental physics and cosmology. The expression of the delay when the particles travel through an arbitrary…
The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial-current phase-space density of spin-1/2 particles in the relaxation time approximation. The resulting approach can…
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially…
We consider a run-and-tumble particle on a finite interval $[a,b]$ with two absorbing end points. The particle has an internal velocity state that switches between three values $v,0,-v$ at exponential times, thus incorporating positive…
We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For…
Time it takes to travel from one position to another, devoid of any quantum mechanical description, has been modeled variously, especially for quantum tunneling. The model time, if universally valid, must be subluminal, must hold everywhere…
A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained…
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 relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
Local time of a stochastic process quantifies the amount of time that sample trajectories $x(\tau)$ spend in the vicinity of an arbitrary point $x$. For a generic Hamiltonian, we employ the phase-space path-integral representation of random…
We give full account of our recent report in [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)] where it is shown that formulating the free quantum time of arrival problem in a segment of the real line…
We study the construction of probability densities for time-of-arrival in quantum mechanics. Our treatment is based upon the facts that (i) time appears in quantum theory as an external parameter to the system, and (ii) propositions about…
The visit probability, quantifying whether a particle has reached a given point for the first time by a specified time, provides access to various extreme value statistics and serves as a fundamental tool for characterising active matter…
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…
A phenomenological model for a measurement of barrier traversal times for particles is proposed. Two idealized detectors for passage and arrival provide entrance and exit times for the barrier traversal. The averaged traversal time is…
We investigate a detector scheme designed to measure the arrival of a particle at $x=0$ during a finite time interval. The detector consists of a two state system which undergoes a transition from one state to the other when the particle…