Entropic uncertainty relation and revival structure of quantum wave packets

Talukdar, B.; Saha, Asit; Chatterjee, Supriya; Sekh, Golam Ali

doi:10.1140/epjp/i2018-12277-5

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…Even more, it has been seen that the Hamiltonian of a quantum black hole, under certain conditions, can be transformed into one with a linear potential term [35]. As we shall see, the quantum bouncer presents collapses and revivals of the wave packet, which have recently been associated with entropic information measures of how classically the system behaves [36][37][38].…”

Section: Experiments and Applications Of The Quantum Bouncermentioning

confidence: 83%

Effective dynamics of the quantum falling particle

Chacón‐Acosta¹,

Hernandez-Hernandez²,

Velázquez³

2020

Eur. J. Phys.

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We analyze the problem of a quantum particle falling under the influence of a one-dimensional constant gravitational field, also known as the bouncing ball, employing a semiclassical approach for the effective equations of motion for the quantum system. In this formalism, the quantum evolution is described through a dynamical system of infinite dimensions for the position, the momentum, and all dispersions. Usually, the system is truncated to reduce it to a finite-dimensional one; however, in this case, equations of motion decouple and the system can be solved exactly. For a specific set of initial conditions, we find that the time-dependent dispersion in position follows the classical trajectory; however, for large times, it grows enough to allow a non-classical behavior for the rebounds. We also propose the study of an effective potential in terms of a pair of canonical variables for dispersions.

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Section: Experiments and Applications Of The Quantum Bouncermentioning

confidence: 83%

Effective dynamics of the quantum falling particle

Chacón‐Acosta¹,

Hernandez-Hernandez²,

Velázquez³

2020

Eur. J. Phys.

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Information theoretic measures on quantum droplets in ultracold atomic systems

Siddik,

Ali Sekh

2024

Phys. Scr.

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We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang correction gives a family of quantum droplets with different chemical potentials. At a larger value of chemical potential, quantum droplet with sharp-top probability density distribution starts to form while it becomes flat top for a smaller value of chemical potential. We show that entropic measures can distinguish the shape change of the probability density distributions and thus can identify the onset of the droplet phase. During the onset of droplet phase, the Shannon entropy decreases gradually with the decrease of chemical potential and attains a minimum in the vicinity where a smooth transition from flat-top to sharp-top QDs occurs. At this stage, the Shannon entropy increases abruptly with the lowering of chemical potential. We observe an opposite trend in the case of Fisher information. These results are found to be consistent with the R\'enyi and Tsallis entropic measures.

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Information entropy in spin–orbit coupled dipolar condensates with magnetic field

Zhao

2024

Int. J. Mod. Phys. B

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In this paper, we study the formation of Shannon information entropy in spin–orbit coupled (SOC) spin-1 antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results show that, in the absence of magnetic field and with an increase in dipole–dipole interaction (DDI), information entropy in position space [Formula: see text] and momentum space [Formula: see text] remains almost unchanged and increases, respectively. Meanwhile, the order parameter [Formula: see text] decreases, which implies that the system develops toward a disorder state. With the increase of SOC strength, [Formula: see text], [Formula: see text] and [Formula: see text] show similar dynamics behavior. Whereas, in the presence of magnetic field, [Formula: see text] and [Formula: see text] are localized in the small scope by increasing the dipole and SOC strength. In addition, the value of [Formula: see text] is nearly the same in this process. These results embody that the introduction of external magnetic field suppresses the role of SOC and DDI, and impedes the condensates towards disorder state. At last, the influence of geometric structure and atom number on information entropy is investigated. It is seen that a narrower trap and fewer atom number make [Formula: see text] decrease and [Formula: see text] increase.

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Entropic uncertainty relation and revival structure of quantum wave packets

Cited by 3 publications

References 35 publications

Effective dynamics of the quantum falling particle

Effective dynamics of the quantum falling particle

Information theoretic measures on quantum droplets in ultracold atomic systems

Information entropy in spin–orbit coupled dipolar condensates with magnetic field

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