A quantum particle in a box with moving walls

Martino, Sara Di; Anzà, Fabio; Facchi, Paolo; Kossakowski, Andrzej; Marmo, Giuseppe; Messina, A.; Pascazio, Saverio

doi:10.1088/1751-8113/46/36/365301

Cited by 45 publications

(83 citation statements)

References 31 publications

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“…In the special case of scale-invariant driving, U q t , 0 ( ) undergoes expansions, contractions and translations. As shown in [29] (and anticipated in [22,27,53,[65][66][67][68]), simple expressions for CD and FF shortcuts can be 6 In fact, if…”

Section: Scale-invariant Dynamicsmentioning

confidence: 93%

Shortcuts to adiabaticity using flow fields

2017

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A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

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Section: Scale-invariant Dynamicsmentioning

confidence: 93%

Shortcuts to adiabaticity using flow fields

2017

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“…verify H |φ n = E n (t) |φ n where E n (t) = n 2 2 π 2 /2mL 2 (t) are the instantaneous eigenvalues, but, due to the time varying boundary conditions, the φ n are not solutions of the Schrödinger equation. To solve the Schrödinger equation different approaches have been proposed, like introducing a covariant time derivative [30], implementing an ad-hoc change of variables [31], or relying on a time-dependent quantum canonical transformation [14,32]. Here we follow the latter option, as implemented in Ref.…”

Section: A Particle In An Infinite Well With Moving Wallsmentioning

confidence: 99%

“…Second, by definition, when weakly measuring observable X, the pointer wavefunction incurs small shifts [see Eq. (14)] relative to its width, so many runs of the same experiment will be necessary in order to extract the weak values. Third even in a weak measurement there is inevitably a back action of the coupling interaction on the subsequent evolution leading to the post-selection.…”

Section: Weak Measurement Protocolmentioning

confidence: 99%

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

2018

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We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitraily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions.

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“…involves the difference of two vectors with different boundary conditions belonging to different Hilbert spaces [2]. Hence neither the difference ψ(x, t ′ ) − ψ(x, t) nor inner products taken at different times ψ(t ′ )| ψ(t) are defined.…”

Section: A Hamiltonian and Boundary Conditionsmentioning

confidence: 99%

Single particle nonlocality, geometric phases and time-dependent boundary conditions

Matzkin¹

2018

J. Phys. A: Math. Theor.

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We investigate the issue of single particle nonlocality in a quantum system subjected to timedependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall's motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary's motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

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A quantum particle in a box with moving walls

Abstract: We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schrödinger operator.

Cited by 45 publications

References 31 publications

Shortcuts to adiabaticity using flow fields

Shortcuts to adiabaticity using flow fields

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

Single particle nonlocality, geometric phases and time-dependent boundary conditions

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