Quantum breathing mode of trapped systems in one and two dimensions

Abraham, Jan Willem; Bönitz, M.; McDonald, Chris; Orlando, Gianfranco; Brabec, Thomas

doi:10.1088/1367-2630/16/1/013001

Cited by 15 publications

(18 citation statements)

References 58 publications

(129 reference statements)

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“…First of all, we confirmed that the breathing mode can be accurately described with equilibrium methods. After several numerical tests with independent methods, we can draw the following conclusions [125]:…”

Section: Discussion Of the 1d Resultsmentioning

confidence: 84%

“…While in 1D, ω rel → 2Ω, i.e. ω rel approaches its ideal quantum limit, in all considered 2D systems ω rel was found to converge to its strongly coupled classical asymptotic [125], i.e., to √ 3 Ω, for Coulomb interaction and √ 5 Ω, for dipole interaction. A physical explanation of this behavior was given from an analysis of the degree of localization of the particles which is governed by the competition of interparticle repulsion and potential (trap) energy.…”

Section: Discussionmentioning

confidence: 89%

“…Since the i-th shell is closed if it is occupied by i particles, the minima appear for N = 3, 6 and 10 particles. (3, 1)) and Hartree-Fock approximation (with sr * (1, −1)) [125]. For large N , the classical value √ 3 Ω is reached.…”

Section: Fermions With Coulomb Interactionmentioning

confidence: 96%

“…Fig. 41 N -dependent breathing frequencies for two-dimensional systems with Coulomb interaction [125]. The spin configurations follow Hund's rules.…”

Section: Fermions With Coulomb Interactionmentioning

confidence: 99%

“…Dependence of the breathing frequencies on the coupling parameter and the particle number [125]. The results were obtained in HF calculations for N ≤ 100 (with sr * (1, −1)) and TF calculations for larger particle numbers (with sr * (3, 1)).…”

Section: Fig 31mentioning

confidence: 99%

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Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Abraham

Bönitz

2014

Contrib. Plasma Phys.

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Particles spatially confined in trapping potentials have attracted increasing interest over the recent decade. Of particular importance are systems of charged particles, such as non-neutral plasmas, nanoplasmas, electrons in metal clusters, electrons in quantum-confined semiconductor structures ("artificial atoms"), electrons on the surface of liquid helium, ions in traps or highly charged particles (grains) in dusty plasmas. A second example of recent interest are systems with other kinds of pair interactions, including dipole interaction, which is important for excitons in quantum wells or ultracold Fermi and Bose gases in traps and optical lattices.Trapped systems are fundamentally different from macroscopic systems since they are dominated by strong spatial inhomogeneity and finite size effects (the properties depend on the exact particle number). Furthermore, by changing the strength of the confinement potential, the many-particle state of the system can be externally controlled-from weak coupling (gas-like) to strong coupling (crystal-like). While trapped classical particles are meanwhile well understood and accessible to first-principle computer simulations, their quantum counterparts still pose big challenges, both for experiment and theory. Therefore, collective properties that can be easily measured or computed and allow to diagnose the many-particle state of the system are of prime importance. It has been found that the quantum breathing mode (monopole oscillation) is one of the most important such properties. In recent years a number of theoretical studies has demonstrated that the quantum breathing mode is ideally suited to measure the coupling strength (the degree of nonideality) of a trapped system, its kinetic and interaction energy and other key observables. This give rise to a novel kind of "spectroscopy" of trapped systems.In this review these developments are summarized. The quantum breathing mode is studied for trapped fermions and bosons with Coulomb and dipole interaction, respectively. A systematic description of collective oscillations and especially the breathing mode is provided. Making use of time-dependent perturbation theory, it is shown how the corresponding breathing frequencies are connected to the properties of the initial equilibrium system. This gives rise to the application of the quantum mechanical sum rules. It is demonstrated how an improved version of the conventional sum rule formulas is suitable for an accurate description of the breathing mode in small systems. Finally, the dependence of the breathing mode on the particle number N is analyzed and the limit of large N is studied for one-dimensional and two-dimensional systems.

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Section: Discussion Of the 1d Resultsmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 89%

Section: Fermions With Coulomb Interactionmentioning

confidence: 96%

“…Fig. 41 N -dependent breathing frequencies for two-dimensional systems with Coulomb interaction [125]. The spin configurations follow Hund's rules.…”

Section: Fermions With Coulomb Interactionmentioning

confidence: 99%

Section: Fig 31mentioning

confidence: 99%

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Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Abraham

Bönitz

2014

Contrib. Plasma Phys.

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Quantum hydrodynamics for plasmas—Quo vadis?

2019

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Quantum plasmas are an important topic in astrophysics and high pressure laboratory physics for more than 50 years. In addition, many condensed matter systems, including the electron gas in metals, metallic nanoparticles, or electron-hole systems in semiconductors and heterostructures, exhibit—to some extent—plasmalike behavior. Among the key theoretical approaches that have been applied to these systems are quantum kinetic theory, Green function theory, quantum Monte Carlo, semiclassical and quantum molecular dynamics, and more recently, density functional theory simulations. These activities are in close contact with the experiments and have firmly established themselves in the fields of plasma physics, astrophysics, and condensed matter physics. About two decades ago, a second branch of quantum plasma theory emerged that is based on a quantum fluid description and has attracted a substantial number of researchers. The focus of these studies has been on collective oscillations and linear and nonlinear waves in quantum plasmas. Even though these papers pretend to address the same physical systems as the more traditional papers mentioned above, the former appear to form a rather closed community that is largely isolated from the rest of the field. The quantum hydrodynamics (QHD) results have—with a few exceptions—not found application in astrophysics or in experiments in condensed matter physics. Moreover, these results practically did not have any impact on the former quantum plasma theory community. One reason is the unknown accuracy of the QHD for dense plasmas. In this paper, we present a novel derivation, starting from reduced density operators that clearly point to the deficiencies of QHD, and we outline possible improvements. It is also to be noted that some of the QHD results have attracted negative attention being criticized as unphysical. Examples include the prediction of “novel attractive forces” between protons in an equilibrium quantum plasma, the notion of “spinning quantum plasmas,” or the new field of “quantum dusty plasmas.” In the present article, we discuss the latter system in some detail because it is a particularly disturbing case of formal theoretical investigations that are detached from physical reality despite bold and unproven claims of importance for, e.g., dense astrophysical plasmas or microelectronics. We stress that these deficiencies are not a problem of QHD itself, which is a powerful and efficient method, but rather are due to ignorance of its properties and limitations. We analyze the common flaws of these works and come up with suggestions to improve the situation of QHD applications to quantum plasmas.

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Controlling strongly correlated dust clusters with lasers

Thomsen

Ludwig

Bönitz

et al. 2014

J. Phys. D: Appl. Phys.

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Lasers have been used extensively to manipulate matter in a controlled way -from single atoms and molecules up to macroscopic materials. They are particularly valuable for the analysis and control of mesoscopic systems such as few-particle clusters. Here we report on recent work on finite size complex (dusty) plasma systems. These are unusual types of clusters with very strong inter-particle interaction so that, at room temperature, they are practically in their ground state. Lasers are employed as a tool to achieve excited states and phase transitions.The most attractive feature of dusty plasmas is that they allow for a precise diagnostic with single-particle resolution. From such measurements, the structural properties of finite two-dimensional (2D) clusters and three-dimensional (3D) spherical crystals in nearly harmonic traps-so-called Yukawa balls-have been explored in great detail. Their structural features-the shell compositions and the order within the shells-have been investigated and good agreement to theoretical predictions was found. Open questions on the agenda are the excitation behavior, the structural changes, and phase transitions that occur at elevated temperature.Here we report on recent experimental results where laser heating methods were further improved and applied to finite 2D and 3D dust clusters. Comparing to simulations, we demonstrate that laser heating indeed allows to increase the temperature in a controlled manner. For the analysis of thermodynamic properties and phase transitions in these finite systems, we present theoretical and experimental results on the basis of the instantaneous normal modes, pair distribution function and the recently introduced center-two-particle correlation function.arXiv:1402.7182v2 [physics.plasm-ph] 7 Jul 2014 ‡ Strictly, the definition (1) is an appropriate measure for the potential energy only when the pair interaction is Coulombic. In the case of screening, the effective coupling parameter depends on the screening length λ D [7]. For the results reported in this paper, the dust-dust interaction is moderately screened and the definition (1) is sufficiently accurate.

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Quantum breathing mode of trapped systems in one and two dimensions

Cited by 15 publications

References 58 publications

Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Quantum hydrodynamics for plasmas—Quo vadis?

Controlling strongly correlated dust clusters with lasers

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