Polarization catastrophe in the polaronic Wigner crystal

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a polaronic Wigner crystal at zero temperature, taking into account the quantum fluctuations of the polarization within the Feynman harmonic approximation. We show that, contrary to the ordinary electron crystal, the system undergoes a polarization catastrophe when the density is increased. An optical signature of this instability is derived, whose trend agrees with the experiments carried out in Nd-based cuprates. Received 4 July 2002 Published online 17 September 2002     

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring. Received 18 January 2002 Published online 13 August 2002     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Spin configuration transformation in laterally coupled few-electron artificial molecules

Artificial molecules, namely laterally coupled quantum dots with a three-dimensional spherical confinement potential well of radius R and depth V ₀, were studied by the unrestricted Hartree-Fock-Roothaan (UHFR) method. By varying the distance d between the centers of the two coupled quantum dots, the transition from the strong coupling situation to the weak one is realized. Hund's rule, suitable for a single quantum dot is destroyed in certain conditions in the artificial molecule. For example, in the few-electron system of the strongly coupled quantum-dot molecule, a transformation of spin configuration has been found. Received 8 March 2002 / Received in final form 29 May 2002 Published online 17 September 2002     

Random phase approximation and extensions applied to a bosonic field theory

An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the ϕ⁴ theory in 1 + 1 dimensions. We show that the standard RPA approach leads to an instability which can be removed when going to a superior version, i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many-electron problem to calculate the correlation energy and the RPA effective potential. Received: 18 February 2002 / Accepted: 8 May 2002     

Wigner lattice of ripplopolarons in a multielectron bubble in helium

The properties of ripplonic polarons in a multielectron bubble in liquid helium are investigated on the basis of a path-integral variational method. We find that the two-dimensional electron gas can form deep dimples in the helium surface, or ripplopolarons, to solidify as a Wigner crystal. We derive the experimental conditions of temperature, pressure and number of electrons in the bubble for this phase to be realized. This predicted state is distinct from the usual Wigner lattice of electrons: it melts by dissociation of the ripplopolarons when the electrons shed their localizing dimple as the pressure on the multielectron bubble drops below a critical value. Received 20 February 2003 Published online 11 April 2003 RID="a" ID="a"Also at: TU Eindhoven, Eindhoven, The Netherlands e-mail: devreese@uia.ua.ac.be     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Anisotropic emission of interface fluctuation quantum dots

We calculate energy levels, dipole moments and radiative broadening of interface fluctuation quantum dots. For optically allowed states, the dipole moment grows proportionally to the lateral quantum dot radius while the radiative broadening saturates towards the quantum well radiative broadening for large lateral quantum dot radii. This is accompanied by a change in the angular emission pattern, concentrating emission in forward and backward direction. Optically forbidden states do not couple to light propagating in the growth direction yet they may have a considerable radiative broadening due to spontaneous emission in other directions. Received 20 March 2002 Published online 25 June 2002     

Coherent and incoherent phonon processes in artificial atoms

Carrier-phonon interaction in semiconductor quantum dots leads to three classes of phenomena: coherent effects (spectrum reconstruction) due to the nearly-dispersionless LO phonons, incoherent effects (transitions) induced by acoustical phonons and dressing phenomena, related to non-adiabatic, sub-picosecond excitation. Polaron spectra, relaxation times and dressing-related decoherence rates are calculated, in accordance with experiment. Received 30 August 2002 / Received in final form 25 November 2002 Published online 28 January 2003     

A statistical analysis of hadron spectrum: Quantum chaos in hadrons

The nearest-neighbor mass-spacing distribution of the meson and baryon spectrum (up to 2.5 GeV) is described by the Wigner surmise corresponding to the statistics of the Gaussian orthogonal ensemble of random matrix theory. This can be viewed as a manifestation of quantum chaos in hadrons. Received: 30 September 2002 / Accepted: 21 November 2002 / Published online: 4 February 2003 RID="a" ID="a"Present address: Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA; e-mail: vlad@phy.ohiou.edu Communicated by G. Orlandini     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Electronic structure of three-dimensional quantum dots

We study the electronic structure of three-dimensional quantum dots using the Hartree-Fock approximation. The confining potential of the electrons in the quantum dot is assumed to be spatially isotropic and harmonic. For up to 40 interacting electrons the ground-state energies and ground-state wavefunctions are calculated at various interaction strengths. The quadrupole moments and electron densities in the quantum dot are computed. Hund's rule is confirmed and a shell structure is identified via the addition energies and the quadrupole moments. While most of the shell structure can be understood on the basis of the unperturbed non-interacting problem, the interplay of an avoided crossing and the Coulomb interaction results in an unexpected closed shell for 19 electrons. Received 5 November 2001 / Received in final form 12 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: vorrath@physnet.uni-hamburg.de     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r _s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime. Received 22 October 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

Atom optics with rotating Bose-Einstein condensates

The atom optics of Bose-Einstein condensates containing a vortex of circulation one is discussed. We first analyze in detail the reflection of such a condensate falling on an atomic mirror. In a second part, we consider a rotating condensate in the case of attractive interactions. We show that for sufficiently large nonlinearity the rotational symmetry of the rotating condensate is broken. Received 16 September 2002 / Received in final form 17 November 2002 Published online 11 February 2003     

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. Received 8 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: demartino@hmi.de     

Off-center Li ions: solid state rotators described by Mathieu's nonlinear-oscillator equation

Substitutional impurity ions in crystals are known to displace off-center and to perform hindered rotations around the ideal lattice positions. The vibronic theory to describe both the off-center displacements and the hindered rotations by a single angular equation incorporates terms up to 3rd order in the off-center displacement coordinates. When the rotation is confined to a single plane, the corresponding vibronic equation is equivalent to Mathieu's equation. Extending our earlier work, we derive here the dipole-dipole coupling to take into account cooperative phenomena. We also derive the optical absorption band arising from dipolar transitions across “Mexican Hat” surfaces, and we show that hindered rotations gives rise to magnetic moments quantized in rotational bands. Received 18 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: allxrose@hotmail.com     

Eigenstates of an operating quantum computer: hypersensitivity to static imperfections

We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits n_q, it is shown that the ideal eigenstates become mixed and strongly modified by static imperfections above a certain threshold which drops exponentially with n_q. Above this threshold the quantum eigenstate entropy grows linearly with n_q but the computation remains reliable during a time scale which is polynomial in the imperfection strength and in n_q. Received 7 March 2002/ Received in final form 3 May 2002 Published online 19 July 2002     

Statistical properties of eigenvalues for an operating quantum computer with static imperfections

We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we discuss the quantum chaos border induced by static imperfections by analyzing the statistical properties of the quantum computer eigenvalues. For small imperfection strengths the level spacing statistics is close to the case of quasi-integrable systems while above the border it is described by the random matrix theory. We have found that the border drops exponentially with the number of qubits, both in the ergodic and quasi-integrable dynamical regimes of the map characterized by a complex phase space structure. On the contrary, the regime with integrable map dynamics remains more stable against static imperfections since in this case the border drops only algebraically with the number of qubits. Received 19 June 2002 / Received in final form 30 September 2002 Published online 17 Decembre 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Quantum computational gates with radiation free couplings

We examine a generic three level mechanism of quantum computation in which all fundamental single and double qubit quantum logic gates are operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. Under the time evolution imposed by these bias couplings the quantum state cycles between the two degenerate levels in the ground state and the quantum gates are realized by changing Hamiltonian at certain time intervals when the system collapses to a two state subspace. We propose a physical implementation of the mechanism using Aharonov-Bohm persistent-current loops in crossed electric and magnetic fields, with the output of the loop read out by using a quantum Hall effect aided mechanism. Received 26 March 2002 / Received in final form 8 July 2002 Published online 19 November 2002     

Conductivity of ultrathin Pb films during growth on Si(111) at low temperatures

The dipole modes of non-parabolic quantum dots are studied by means of their current and density patterns as well as with their local absorption distribution. The anticrossing of the so-called Bernstein modes originates from the coupling with electron-hole excitations of the two Landau bands which are occupied at the corresponding magnetic fields. Non-quadratic terms in the potential cause an energy separation between bulk and edge current modes in the anticrossing region. On a local scale the fragmented peaks absorb energy in complementary spatial regions which evolve with the magnetic field. Received 3 December 2001 / Received in final form 5 April 2002 Published online 9 July 2002