Moving Wigner glasses and smectics: dynamics of disordered Wigner crystals

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conduction noise and I(V) curves. For strong disorder, we show criticality in the voltage onset just above depinning. We obtain the dynamic phase diagram for driven Wigner solids and demonstrate a finite threshold of force for transverse sliding, recently observed experimentally.     

Tunable Wigner states with dipolar atoms and molecules

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit nontrivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.     

Floating Wigner molecules and possible phase transitions in quantum dots

A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb coupling. Received 12 September 2001 / Received in final form 24 April 2002 Published online 9 July 2002     

Wigner dynamics of quantum semi-relativistic oscillator

The integral Wigner–Liouville equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected ‘protuberances’ in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated.     

The Wigner semi-circle law in quantum electro dynamics

In the present paper, the basic ideas of thestochastic limit of quantum theory are applied to quantum electro-dynamics. This naturally leads to the study of a new type of quantum stochastic calculus on aHilbert module. Our main result is that in the weak coupling limit of a system composed of a free particle (electron, atom,...) interacting, via the minimal coupling, with the quantum electromagnetic field, a new type of quantum noise arises, living on a Hilbert module rather than a Hilbert space. Moreover we prove that the vacuum distribution of the limiting field operator is not Gaussian, as usual, but a nonlinear deformation of the Wigner semi-circle law. A third new object arising from the present theory, is the so-calledinteracting Fock space. A kind of Fock space in which then quanta, in then-particle space, are not independent, but interact. The origin of all these new features is that we do not introduce the dipole approximation, but we keep the exponential response term, coupling the electron to the quantum electromagnetic field. This produces a nonlinear interaction among all the modes of the limit master field (quantum noise) whose explicit expression, that we find, can be considered as a nonlinear generalization of theFermi golden rule.     

Many-particle effects in resonant inelastic scattering of an X-ray photon by an atom

The influence of many-particle effects on the shape and values of the double differential cross section for the resonant inelastic scattering of a linearly polarized X-ray photon by a free atom near the K and KL₂₃ ionization thresholds has been theoretically analyzed for the neon atom. The calculations have been performed using the nonrelativistic Hartree-Fock approximation for single-electron wavefunctions and the dipole approximation for the anomalous dispersion component of the cross section. The analytical structure of the contact part of the scattering cross section has been obtained beyond the dipole approximation. The effects of the radial relaxation of electron shells, spin-orbit and multiplet splitting, and configuration interaction in the doubly excited atomic states, as well as the Auger and radiative decays of the produced vacancies, are taken into account. The nature and role of the effect of correlation amplitudes, which is responsible for the appearance of the nonzero amplitudes of nonradiative transitions between intermediate and final single-electron states of the same symmetry that are obtained in different Hartree-Fock fields, have been analyzed also. The calculations are predictive and, for an incident-photon energy of 5.41 keV, agree well with experimental results for the Kα X-ray emission spectrum of the neon atom.     

Many-particle excited states in nuclei

Energies, quadrupole moments and shapes of many-particle excited states in ¹²C and ¹⁶O are calculated. The connection of the obtained results with the cluster model is discussed.     

High-fidelity quantum memory realized via Wigner crystals of polar molecules

The collective excitations of spin states of an ensemble of polar molecules are studied as a candidate for high-fidelity quantum memory. To avoid the collisional properties of the molecules, they are arranged in dipolar crystals under one or two dimensional trapping conditions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms and estimating their effects on gate operations when a molecular ensemble qubit is transferred to a microwave cavity.     

Role of confinements on the melting of Wigner molecules in quantum dots

We explore the stability of a Wigner molecule (WM) formed in confinements with differentgeometries emulating the role of disorder and analyze the melting (or crossover) of such asystem. Building on a recent calculation [D. Bhattacharya, A. Ghosal, Eur. Phys. J.B 86, 499 (2013)] that discussed the effects of irregularities on thethermal crossover in classical systems, we expand our studies in the untested territory byincluding both the effects of quantum fluctuations and ofdisorder. Our results, using classical and quantum (path integral)Monte Carlo techniques, unfold complementary mechanisms that drive the quantum and thermalcrossovers in a WM and show that the symmetry of the confinement plays no significant rolein determining the quantum crossover scale n_X. This is because thezero-point motion screens the boundary effects within short distances. The phase diagramas a function of thermal and quantum fluctuations determined from independent criteria isunique, and shows “melting” from the WM to both the classical and quantum “liquids”. Anintriguing signature of weakening liquidity with increasing temperature, T, is found in the extreme quantum regime. The crossover is associated with production of defects. However, thesedefects appear to play distinct roles in driving the quantum and thermal “melting”. Ouranalyses carry serious implications for a variety of experiments on many-particle systems? semiconductor heterostructure quantum dots, trapped ions, nanoclusters, colloids and complex plasma.     

Controlling intershell rotations in mesoscopic electron clusters

A previously proposed idea (Microelectron. Eng. 63 (2002) 141) of controlling the angular mobility of electrons in a quantum dot by addition/removal of a single electron is verified and confirmed by computer simulation. Conditions for realization of the scheme in semiconductors are discussed.     

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2–3%.     

Determination of the intershell conductance in multiwalled carbon nanotubes

We report on the intershell electron transport in multiwalled carbon nanotubes (MWNTs). To do this, local and nonlocal four-point measurements are used to study the current path through the different shells of a MWNT. For short electrode separations less, similar 1 mum the current mainly flows through the two outer shells, described by a resistive transmission line with an intershell conductance per length of approximately (10 kOmega)(-1)/microm. The intershell transport is tunnel type and the transmission is consistent with the estimate based on the overlap between pi orbitals of neighboring shells.     

Hydrogen-bond dynamics of interior and surface molecules in a water nanocluster: temperature and size effects

Molecular dynamics simulations are employed to investigate the effects of temperature and size on the hydrogen-bond dynamics of interior molecules and surface molecules in a water nanocluster. The flexible three-centred (F3C) water model is invoked in the simulations. To inspect the dynamics of the interior hydrogen bonds and the surface hydrogen bonds, a spherical water nanocluster is modelled and then divided into interior molecules and surface molecules according to the density profile of the water nanocluster. It is observed that at higher temperatures the average number of hydrogen bonds decreases and yields faster hydrogen-bond relaxation for both interior molecules and surface molecules of the water nanocluster. Furthermore, the surface molecules have a lower average number of hydrogen bonds than the interior molecules. The lifetime of the surface hydrogen bonds is slightly longer than that of the interior hydrogen bonds, whereas the hydrogen-bond structural relaxation time of the surface molecules is more obviously slower than that of the interior molecules. Regarding the size effect, a larger water nanocluster is seen to have a larger average number of hydrogen bonds and a longer hydrogen-bond structural relaxation time.     

Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagonalization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact results allows us to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution can be identified with the classical charge distribution.Received: 24 October 2003, Published online: 6 January 2004PACS: 73.20.Qt Electron solids - 73.21.-b Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems     

Theoretical study of intershell transitions in C III

Energy levels, wavelengths, oscillator strengths, transition probabilities, lifetimes and branching ratios are evaluated for intershell transitions in C III using configuration interaction wavefunctions. The convergence of the results with respect to the basic set of orbitals is considered. Some significant differences from previous calculations are obtained. We give reasons why the main mode of decay of the 2p 3p ³ S is not to the 2p 3s ³ P ⁰ state, as indicated by experiment, but, to the 2s 2p ³ P ⁰ state with a lifetime of 0.57 ns.