On the behaviour of quantum systems with time-dependent boundary conditions

Makowski, Adam J.; Pepłowski, P.

doi:10.1016/0375-9601(92)90397-5

Cited by 57 publications

(50 citation statements)

References 13 publications

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“…Recently, the dynamical properties of classical time-dependent two-dimensional billiards have attracted major attention, especially in the context of Fermi acceleration [1,2,3,4,5,6,7,8], which is defined as the unbounded energy gain of an ensemble of particles exposed to some external driving force [9]. Concerning the quantum dynamics of time-dependent billiards, there exist several studies investigating the quantum version of the one-dimensional Fermi-Ulam model (or variants of it) [10,11,12,13,14,15,16,17,18,19,20,21], but, to our knowledge, only two studies [22,23] investigate time-dependent billiards in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Resonant population transfer in the time-dependent quantum elliptical billiard

et al. 2011

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We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time-propagation of an arbitrary initial state is developed, based on a series of transformations thereby removing the time-dependence of the boundary conditions. The time-evolution of the energies of different initial states is studied. The maximal and minimal energy that is reached during the time-evolution shows a series of resonances as a function of the applied driving frequency. At these resonances, higher (or lower) lying states are periodically populated, leading to the observed change in energy. The resonances occur when the driving frequency or a multiple of it matches exactly the mean energetic difference between the two involved states. This picture is confirmed by a few-level Rabi-like model with periodic couplings, reproducing the key results of our numerical study.

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Section: Introductionmentioning

confidence: 99%

Resonant population transfer in the time-dependent quantum elliptical billiard

et al. 2011

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“…Perhaps the most widely known problem in this class is the Fermi-Ulam bouncer [1, 2, 3] that concerns a particle that moves between two reflective walls, one of which is oscillating. Here we are interested in models with one receding wall, as the ones addressed in [4] in the one-dimensional case. In three dimensions there are solutions for expanding cylindrical [5] and spherical [6] wells.…”

Section: Introductionmentioning

confidence: 99%

Quantifying the failure of Schrödinger dynamics in the free expansion of relativistic particles

Ximenes

Parisio

2016

Eur. Phys. J. Plus

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It is known that Schrödinger equation fails in describing the dynamics of highly energetic particles. We propose to quantify this lack of Lorentz covariance by evaluating the probability for a particle to be measured outside the set of light cones which are compatible to its initial wave function. We consider a simple case of a particle released from a box, which, in turn, is inside a larger container. It is shown that besides the increasing error at relativistic energies, there may be a complete breakdown, with Schrödinger dynamics implying in deterministic, superluminal signaling for Lorentz factors above 129. In addition, we give an exact asymptotic expression for the violation in local causality by employing the stationary exponent method, from which the Compton wave length of the particle naturally arises as the relevant scale for the stationary points.

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“…Treatment of such system requires solving the Schrödinger equation with time-dependent boundary conditions. Earlier, the problem of time-dependent boundary conditions in the Schrödinger equation has attracted much attention in the context of quantum Fermi acceleration [12][13][14], although different aspects of the problem were treated by many authors [16][17][18][19][20][21][22][23][24][25][26][27]. Detailed study of the problem can be found in a series of papers by Makowski and co-authors [21][22][23].…”

Section: Introductionmentioning

confidence: 99%