Physics:Quantum boomerang effect - Revision history

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 | url = https://link.aps.org/doi/10.1103/RevModPhys.91.021001}}</ref>
-In 2019, theorists considered the behavior of a wavepacket not merely dropped, but actively launched through a disordered medium with some initial nonzero momentum, predicting that the wavepacket's center of mass would asymptotically return to the origin at long times — the quantum boomerang effect.<ref name="PratPRA"/> Shortly after, quantum simulation experiments in cold atom settings confirmed this prediction<ref name="SajjadPRX">
+In 2019, theorists considered the behavior of a wavepacket not merely dropped, but actively launched through a disordered medium with some initial nonzero momentum, predicting that the wavepacket's center of mass would asymptotically return to the origin at long times — the quantum boomerang effect.<ref name="PratPRA">
 {{Cite journal
 | doi = 10.1103/PhysRevX.12.011035
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	'''boomerang effect''' ~~is a Book I topic in~~ the ~~Quantum Collection. The~~ quantum boomerang effect is a quantum mechanical phenomenon whereby wavepackets launched through disordered media return, on average, to their starting points, as a consequence of Anderson localization and the inherent symmetries of the system. At early times, the initial parity asymmetry of the nonzero momentum leads to asymmetric behavior: nonzero displacement of the wavepackets from their origin. At long times, inherent time-reversal symmetry and the confining effects of Anderson localization lead to correspondingly symmetric behavior: both zero final velocity and zero final displacement. The quantum boomerang effect is a quantum mechanical phenomenon whereby wavepackets launched through disordered media return, on average, to their starting points, as a consequence of Anderson localization and the inherent symmetries of the system.		'''boomerang effect''' the quantum boomerang effect is a quantum mechanical phenomenon whereby wavepackets launched through disordered media return, on average, to their starting points, as a consequence of Anderson localization and the inherent symmetries of the system. At early times, the initial parity asymmetry of the nonzero momentum leads to asymmetric behavior: nonzero displacement of the wavepackets from their origin. At long times, inherent time-reversal symmetry and the confining effects of Anderson localization lead to correspondingly symmetric behavior: both zero final velocity and zero final displacement. The quantum boomerang effect is a quantum mechanical phenomenon whereby wavepackets launched through disordered media return, on average, to their starting points, as a consequence of Anderson localization and the inherent symmetries of the system. Anderson introduced the eponymous model of disordered lattices which exhibits localization, the confinement of the electrons' probability distributions within some small volume.
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	\| bibcode = 2022PhRvB.105r0202J		\| bibcode = 2022PhRvB.105r0202J
	\| s2cid = 247593916		\| s2cid = 247593916
	\| url = https://link.aps.org/doi/10.1103/PhysRevB.105.L180202}}</ref>), the probability density distribution <math>\|\Psi^2\|</math> exhibits off-diagonal, oscillatory elements in its ~~[[Eigenvalues and eigenvectors#Eigenspaces, geometric multiplicity, and the~~ eigenbasis~~\|eigenbasis]]~~ expansion that decay at long times, leaving behind only diagonal elements independent of the sign of the initial momentum. Since the direction of the launch does not matter at long times, the wavepacket ''must'' return to the origin.<ref name="PratPRA"/>		\| url = https://link.aps.org/doi/10.1103/PhysRevB.105.L180202}}</ref>), the probability density distribution <math>\|\Psi^2\|</math> exhibits off-diagonal, oscillatory elements in its eigenbasis expansion that decay at long times, leaving behind only diagonal elements independent of the sign of the initial momentum. Since the direction of the launch does not matter at long times, the wavepacket ''must'' return to the origin.<ref name="PratPRA"/>

	The same destructive interference argument used to justify Anderson localization applies to the quantum boomerang. The Ehrenfest theorem states that the variance (''i.e.'' the spread) of the wavepacket evolves thus:		The same destructive interference argument used to justify Anderson localization applies to the quantum boomerang. The Ehrenfest theorem states that the variance (''i.e.'' the spread) of the wavepacket evolves thus:

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	where <math>\ell</math> and <math>\tau</math> are the scattering [[Physics:Mean free path\|mean free path]] and scattering [[Physics:Mean free time\|mean free time]], respectively. The exact form of the boomerang can be approximated using the diagonal [[Padé approximant\|Padé approximants]] <math>R_{[n/n]}</math> extracted from a series expansion derived with the [[Biography:Vadim Berezinskii\|Berezinskii]] diagrammatic technique.<ref name="PratPRA"/>		where <math>\ell</math> and <math>\tau</math> are the scattering [[Physics:Mean free path\|mean free path]] and scattering [[Physics:Mean free time\|mean free time]], respectively. The exact form of the boomerang can be approximated using the diagonal [[Padé approximant\|Padé approximants]] <math>R_{[n/n]}</math> extracted from a series expansion derived with the [[Biography:Vadim Berezinskii\|Berezinskii]] diagrammatic technique.<ref name="PratPRA"/>

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	==References==		==References==
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	[[Category:Quantum mechanics]]		[[Category:Quantum mechanics]]

	{{Sourceattribution\|Quantum boomerang effect}}		{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum boomerang effect\|1}}

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