Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

Yannouleas, Constantine; Landman, Uzi

doi:10.1103/physreva.96.043610

Cited by 3 publications

(11 citation statements)

References 71 publications

(141 reference statements)

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“…Naturally, due to the very large masses of the ionic cores, the explicit symmetry-broken wave-packet state localized within a single minimum can be observed in cases when tunneling is suppressed (Bersuker, 2016). This is analogous to the observation of pinned classical Wigner crystals of trapped ultracold ions (Thompson, 2015;Yannouleas and Landman, 2017).…”

Section: Other Electronic Systemsmentioning

confidence: 71%

“…Namely the limit of a rigid 2D rotor is reached for strong Coulomb repulsion (e.g., R W = 200 >> 1) in the absence of an applied magnetic field; the rotational spectrum (yrast band) in this case exhibits energy levels ∝ L 2 . An opposite limit of a hyper floppy rotor is reached for smaller R W ∼ 10, but very high magnetic field (the lowest-Landau-level regime); in this case the rotational energies (yrast band) have a AL + B/ √ L dependence on the total angular momentum L. The limit of a 2D rigid rotor for R W → ∞ and low magnetic field was also demonstrated for the case of N = 9 and N = 8 ultracold ions confined in a 2D ring-shaped trap (Yannouleas and Landman, 2017). The limit of the 2D rigid-rotor rotational spectrum extracted in the papers above is reminiscent of the Kamlah expansion 11 in integer powers of L for strong symmetry breaking in rotating nuclei [see Sec.…”

Section: Quantum Dotsmentioning

confidence: 72%

“…Time evolution in finite systems out of equilibrium: Apart from the small-amplitude harmonic vibrations, broken-symmetry wave functions (single determinants or permanents) fail to describe the proper time-evolution behavior when propagated in time with the corresponding mean-field Hamiltonian (Lichtner and Griffin, 1976;Yannouleas and Landman, 2017); see also Ch. 12.2.4, p. 498 in (Ring and Schuck, 1980).…”

Section: Other Emerging Directionsmentioning

confidence: 99%

“…It is easily overcome by expressing the broken-symmetry wave function as a wave packet (superposition) of symmetry-restored wave functions and evolving independently in time (by multiplying by a time-dependent phase) each component of the wave packet. Using this approach, other symmetrybroken wave packets (different from the UHF solutions) can be envisaged that exhibit single-particle densities with controlled periodicities in both space and time, as was recently discussed in the framework of implementing a quantum space-time crystal of ultracold atoms or ions in a ring-shaped trap (Yannouleas and Landman, 2017). If the initial wave packet reproduces the UHF or Gross-Pitaevskii broken-symmetry solution, revival and recurrence in-time behavior is generated (Eriksson et al, 2018).…”

Section: Other Emerging Directionsmentioning

confidence: 99%

“…The use of the term "rotating" here refers to the finite system having good quantum-mechanical total angular momenta, unlike a symmetry-broken crystalline UHF wave function. Consideration of the time-evolution of wave packets formed through the superposition of several rotating Wigner molecules(Yannouleas and Landman, 2017) leads to the concept of a quantum spacetime crystal(Li et al, 2012a;Wilczek, 2012;Yannouleas and Landman, 2017) and to phenomena of quantum mechanical revival(Eriksson et al, 2018;Seideman, 1999;Yannouleas and Landman, 2017)…”

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confidence: 99%

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Symmetry restoration in mean-field approaches

Sheikh,

Dobaczewski,

Ring

et al. 2019

Preprint

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The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Examples are strongly interacting atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. However, mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group theoretical techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. We present applications of the projection methods to simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted. CONTENTSL. Other electronic systems 60 M. Other emerging directions 60 VIII. Projected statistics 61 A. Symmetry restoration at finite temperature 62 B. Thermo-field dynamics 63 IX. Summary, conclusions, and perspectives 63 X. Acknowledgments 64 A. Overlaps and matrix elements between HFB states: the generalized Wick's theorem 65

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Section: Other Electronic Systemsmentioning

confidence: 71%

Section: Quantum Dotsmentioning

confidence: 72%

Section: Other Emerging Directionsmentioning

confidence: 99%

Section: Other Emerging Directionsmentioning

confidence: 99%

mentioning

confidence: 99%

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Symmetry restoration in mean-field approaches

Sheikh,

Dobaczewski,

Ring

et al. 2019

Preprint

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show abstract

Symmetry restoration in mean-field approaches

Sheikh

Dobaczewski

Ring

et al. 2021

J. Phys. G: Nucl. Part. Phys.

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The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are strongly interacting medium and heavy mass atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrödinger equation for the exact many-body wave function is mapped onto a non-linear one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. In this way, additional correlations are subsumed in the system. However, the mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group-theory techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. Applications of the projection methods are presented for simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional (EDF) theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the EDF theories are highlighted in the present work.

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Tunable space-time crystal in room-temperature magnetodielectrics

et al. 2019

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We report the experimental realization of a space-time crystal with tunable periodicity in time and space in the magnon Bose-Einstein Condensate (BEC), formed in a room-temperature Yttrium Iron Garnet (YIG) film by radio-frequency space-homogeneous magnetic field. The magnon BEC is prepared to have a well defined frequency and non-zero wavevector. We demonstrate how the crystalline "density" as well as the time and space textures of the resulting crystal may be tuned by varying the experimental parameters: external static magnetic field, temperature, thickness of the YIG film and power of the radio-frequency field. The proposed space-time crystals provide a new dimension for exploring dynamical phases of matter and can serve as a model nonlinear Floquet system, that brings in touch the rich fields of classical nonlinear waves, magnonics and periodically driven systems. arXiv:1811.05801v1 [cond-mat.quant-gas]

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Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

Cited by 3 publications

References 71 publications

Symmetry restoration in mean-field approaches

Symmetry restoration in mean-field approaches

Symmetry restoration in mean-field approaches

Tunable space-time crystal in room-temperature magnetodielectrics

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