Marginal picture of quantum dynamics related to intrinsic arrival times

Torres-Vega, Gabino

doi:10.1103/physreva.76.032105

Cited by 6 publications

(10 citation statements)

References 43 publications

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“…(4) and from the analytical perturbative expression in Eq. (16). It is clear that there is very good agreement between the direct results and those obtained from perturbation theory.…”

Section: Comparisons Between Perturbation Theory and Direct Numersupporting

confidence: 64%

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Detection of a quantum particle on a lattice under repeated projective measurements

et al. 2015

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We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time intervals τ , and we consider the evolution of the wave function till the time a detection occurs. We study the probabilities of its first detection at some time and conversely the probability of it not being detected (i.e., surviving) up to that time. We propose a general perturbative approach for understanding the dynamics which maps the evolution operator, consisting of unitary transformations followed by projections, to one described by a nonHermitian Hamiltonian. For some examples, of a particle moving on one and two-dimensional lattices with one or more detection sites, we use this approach to find exact expressions for the survival probability and find excellent agreement with direct numerical results. A mean field model with hopping between all pairs of sites and detection at one site is solved exactly. For the one-and two-dimensional systems, the survival probability is shown to have a power-law decay with time, where the power depends on the initial position of the particle. Finally, we show an interesting and non-trivial connection between the dynamics of the particle in our model and the evolution of a particle under a non-Hermitian Hamiltonian with a large absorbing potential at some sites.

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“…(4) and from the analytical perturbative expression in Eq. (16). It is clear that there is very good agreement between the direct results and those obtained from perturbation theory.…”

Section: Comparisons Between Perturbation Theory and Direct Numersupporting

confidence: 64%

“…The measurement of the arrival time of a quantum mechanical particle in a given detection region is a longstanding and fundamental problem in quantum mechanics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In spite of much effort, the construction of a time operator has been found to be controversial [18].…”

Section: Introductionmentioning

confidence: 99%

Detection of a quantum particle on a lattice under repeated projective measurements

et al. 2015

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“…In this section, we consider one-dimensional classical probability densities evolving on a non-constant potential function and we introduce classical 'probe functions' with support on 'time-front' curves in phase space. These functions are similar to the 'time eigenstates' used in quantum systems, as described by Aharonov [10], Kijowski [32], Muga [1], Skulimowski [18] and Torres-Vega [40]. The classical analysis in this paper is of great help in the elucidation of the physical meaning of quantum time eigentates.…”

Section: A Picture Of Classical Dynamicsmentioning

confidence: 62%

“…This is illustrated for the Eckart potential in figure 5. Thus, in a manner similar to that of quantum probe states, these probe functions are non-normalizable and overlap for the same X and different T; however, they do not overlap for different X and the same T [40].…”

Section: Orthogonalitymentioning

confidence: 86%

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Quantum-like picture for intrinsic, classical, arrival distributions

Torres-Vega

2009

J. Phys. A: Math. Theor.

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We introduce a marginal, quantum-like picture for the arrival of classical quantities in which the representation vectors are the quantities that evolve and probability densities remain static. The representation functions can be seen as probe functions which are the evolution of delta functions with support on a curve in phase space, the time fronts. This procedure provides a classical analog as well as a clear physical interpretation of the 'time eigenstates' used in quantum systems.

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Probability flow for a free particle: new quantum effects

Bracken

2021

Phys. Scr.

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New quantum probability flow bounds and associated eigenfunctions are determined numerically for a free non-relativistic particle, with momentum lying in the range (p 0, ∞), for each fixed p 0 chosen in the range (−∞ , ∞). It is found that as p 0 increases through positive values, the maximum possible probability backflow from right-to left (R to L), opposite to the direction of all contributing momenta, decreases monotonically from the well-known value ≈0.038452 at p 0 = 0 but never reaches 0. As p 0 decreases through negative values, the maximum R to L flow increases monotonically but never reaches 1. These new quantum effects are compared and contrasted with the corresponding classical behaviour. A surprising new effect is revealed: Even when p 0 is negative, L to R directed momenta contribute to the maximum R to L flow. The size of this contribution is indicated by comparing with the maximum R to L flow possible when only negative momenta with values between p 0 and 0 are allowed. The extended modeling admits a simple interpretation of the classical limit without the introduction of a mechanism external to the system, as an effective value of Planck’s constant approaches zero.

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Marginal picture of quantum dynamics related to intrinsic arrival times

Cited by 6 publications

References 43 publications

Detection of a quantum particle on a lattice under repeated projective measurements

Detection of a quantum particle on a lattice under repeated projective measurements

Quantum-like picture for intrinsic, classical, arrival distributions

Probability flow for a free particle: new quantum effects

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