Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Großmann, Frank; Kramer, Tobias

doi:10.1088/1751-8113/44/44/445309

Cited by 13 publications

(11 citation statements)

References 50 publications

(77 reference statements)

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“…They obtained very good results for the binding energies of singlet and triplet states. Similar good agreement has been found for a harmonium system [15] (and for singlet states in Ref. [16]).…”

Section: Introductionsupporting

confidence: 85%

Spin effects and the Pauli principle in semiclassical electron dynamics

et al. 2014

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Several approaches to the semiclassical dynamics of fermions have been proposed in the past. The main subject under discussion was the inclusion of the Pauli principle, i.e., the fact that two electrons with parallel spins must be in orthogonal states. In the past, this was sometimes achieved by adding repulsive Pauli potentials or by using antisymmetric trial states. In this article we show that (a) the use of semiclassical propagators based on classical trajectories is sufficient to account for the Pauli principle, but (b) a semiclassical wave-function approach is not satisfactory.

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Section: Introductionsupporting

confidence: 85%

Spin effects and the Pauli principle in semiclassical electron dynamics

et al. 2014

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“…For the Hookean atom placed in a perpendicular magnetic field, Taut found analytical solutions for a 2D case at particular values of the magnetic field for the circular case [339]. The circular dot at arbitrary values of the magnetic field was studied in various approaches in order to find a closed-form solution [340][341][342][343]. Analytical solutions, developed for a 3D model of a QD [300,344], provide the explicit completion of five integrable cases [345].…”

Section: Two-electron Quantum Dot: a New Paradigm In Mesoscopic Physicsmentioning

confidence: 99%

Effects of symmetry breaking in finite quantum systems

2013

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The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose-Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.

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“…[25][26][27] It is thus distinguished from most of the previous nuclear wave packet (NWP) approaches in which a potential surface was given in advance by a separate modeling and, in many cases, expanded quadratically around the moving NWP centers to perturbatively take into account the NQEs. [28][29][30][31][32][33][34][35][36][37] We set up 211 H 2 molecules at the saturated vapor pressure; the molar volume, 23.06 × 10 −6 m 3 /mol, is taken from the saturated vapor pressure line at temperature ranging from 2.5 K to 13 K. 1 In cooling and equilibration runs started from the initial h.c.p. structure with randomly oriented H 2 molecules, atomic center momentum degrees of freedom are influenced by velocity scaling thermostat and Berendsen methods with each temperature.…”

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confidence: 99%

Communication: Dynamical and structural analyses of solid hydrogen under vapor pressure

Hyeon‐Deuk

Ando

2015

The Journal of Chemical Physics

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Nuclear quantum effects play a dominant role in determining the phase diagram of H2. With a recently developed quantum molecular dynamics simulation method, we examine dynamical and structural characters of solid H2 under vapor pressure, demonstrating the difference from liquid and high-pressure solid H2. While stable hexagonal close-packed lattice structures are reproduced with reasonable lattice phonon frequencies, the most stable adjacent configuration exhibits a zigzag structure, in contrast with the T-shape liquid configuration. The periodic angular distributions of H2 molecules indicate that molecules are not a completely free rotor in the vapor-pressure solid reflecting asymmetric potentials from surrounding molecules on adjacent lattice sites. Discrete jumps of librational and H–H vibrational frequencies as well as H–H bond length caused by structural rearrangements under vapor pressure effectively discriminate the liquid and solid phases. The obtained dynamical and structural information of the vapor-pressure H2 solid will be useful in monitoring thermodynamic states of condensed hydrogens.

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Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Cited by 13 publications

References 50 publications

Spin effects and the Pauli principle in semiclassical electron dynamics

Spin effects and the Pauli principle in semiclassical electron dynamics

Effects of symmetry breaking in finite quantum systems

Communication: Dynamical and structural analyses of solid hydrogen under vapor pressure

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