Energy levels of the Fröhlich polaron in a spherical quantum dot

The one-phonon variational state is suitably applied to describe the ground state and excited states of the Fröhlich polaron bound to a quantum dot. A general analytical expression for the electronic energy spectra and the polaron binding energy for different electronic subband bound states in a quantum dot is presented and discussed with reference to the parameters of a real solid.     

Unification of Poincaré, BRST and Parisi-Sourlas supersymmetries

Poincaré, BRST and Parisi-Sourlas supersymmetries are usually viewed as unrelated. Here we argue that they are in fact closely related. We argue that fermions in Poincaré SUSY theories can be interpreted as negative-dimensional phase space coordinates, in the Parisi-Sourlas sense. The Bose-Fermi balance then implies that the effective phase space dimensionality vanishes. We show that interacting Poincaré SUSY theories are related to the corresponding free theories by superrotations similar to BRST transformations. For superstrings we find that spacetime can be viewed as a zero-dimensional manifold in the sense of Parisi-Sourlas.     

Variational approaches to quantum impurities: from the Fröhlich polaron to the angulon

ABSTRACT

Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron – a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon – a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling.     

On two-dimensional supergravity and the quantum super-Möbius group

We describe the quantum-group structure of two-dimensionalN=1 supergravity in the conformal gauge. The operator-algebra of this (super-Liouville) theory is shown to correspond to a quantum deformation of the super-Möbius group, which provides a new solution of Yang and Baxter's equation. This structure is used to investigate the strong-coupling regime of the theory (1d9). Ford=5, a unitary truncation theorem-similar to the one of the bosonic case-is derived for the fundamental representation.Unité Propre du Centre National de la Recherche Scientifique, associée à l'École Normale Supérieure et à l'Université de Paris-Sud     

Nonradiative and radiative Förster energy transfer between quantum dots

We theoretically study nonradiative and radiative energy transfer between two localized quantum emitters, a donor (initially excited) and an acceptor (receiving the excitation). The rates of nonradiative and radiative processes are calculated depending on the spatial and spectral separation between the donor and acceptor states and for different donor and acceptor lifetimes for typical parameters of semiconductor quantum dots. We find that the donor lifetime can be significantly modified only due to the nonradiative Förster energy transfer process at donor–acceptor separations of approximately 10 nm (depending on the acceptor radiative lifetime) and for the energy detuning not larger than 1–2 meV. The efficiency of the nonradiative Förster energy transfer process under these conditions is close to unity and decreases rapidly with an increase in the donor–acceptor distance or energy detuning. At large donor–acceptor separations greater than 40 nm, the radiative corrections to the donor lifetime are comparable with nonradiative ones but are relatively weak.     

The symmetry of donor–bound electron wavefunctions in quantum wells

In order to investigate the symmetry (i.e. sphericity) of donor–bound electron wavefunctions in quantum wells, we have invoked a two-parameter trial wavefunction. One parameter is the Bohr radius λ, whilst the other is the eccentricity parameter ζ. The latter incorporates the effect of the quantum well (QW) on the carrier motion in the growth (i.e. the z) direction. Working within the envelope function approximation it is shown that the donor wavefunction has the form of a prolate spheroid. However, calculations of the ratio λ/ζ shows that it is the value of λ which determines the essential symmetry of the wavefunction.     

Combining relativity and quantum mechanics: Schrödinger's interpretation of ψ

The incongruence between quantum theory and relativity theory is traced to the probability interpretation of the former. The classical continium interpretation of removes the difficulty. How quantum properties of matter and light, and in particular the radiative problems, like spontaneous emission and Lamb shift, may be accounted in a first quantized Maxwell-Dirac system is discussed.     

New geometries associated with the nonlinear Schrödinger equation

We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations, to the nonlinear Schr?dinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation = ×, ( = 1). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained. Received 5 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: radha@imsc.ernet.in     

Kac-Moody symmetry of generalized non-linear Schrödinger equations

The classical non-linear Schrödinger equation associated with a symmetric Lie algebra =km is known to possess a class of conserved quantities which from a realization of the algebrak []. The construction is now extended to provide a realization of the Kac-Moody algebrak[, ^–1] (with central extension). One can then define auxiliary quantities to obtain the full algebra [, ^–1]. This leads to the formal linearization of the system.     

Painlevé analysis,conservation laws,and symmetry of perturbed nonlinear equations

We consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generator. When the perturbed KdV equation is subjected to Painlevé analysisa la Weiss, it is found that the resonance position changes compared to the unperturbed one. We prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter to be small. We determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation we determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painlevé analysis does not produce a positive answer for the perturbed NLS equation. So here we have two contrasting examples of perturbed nonlinear equations: one passes the Painlevé test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painlevé test, though its Lax pair is found in another way.     

CosmologicalΦ 4,Φ 6, and Sine-Gordon theories with broken symmetry

Particular solutions to the Einstein equations with cosmological constant are presented and discussed for an isotropic, spatially homogeneous, and spatially flat space-time in the case that the matter fields are ⁴, ⁶, and sine-Gordon fields.     

Generalized nonlinear Doebner-Goldin Schrödinger equation and the relaxation of quantum systems

We propose a new class of nonlinear homogeneous extension of the Doebner-Goldin Schrödinger equation, valid for arbitrary representations and operators, chosen in accordance with the investigated physical problem. We verify that the nonlinearity simulates an environment, thence, the new model leads to simple exact solutions as, for instance, the time-dependent squeezed coherent states and a special class of stationary states that we call pseudothermal, reached after relaxation. We illustrate the use of the new equation with applications to problems such as, the relaxation of a two-level or spin-1/2 system, and of the harmonic oscillator (HO) or equivalently, the emission-absorption process of photons in an electromagnetic cavity. Furthermore, in order to compare solutions for the HO example we introduce two different representations in the new equation, one continuous (positional representation) and the other discrete (Fock states).     

Density functional theory of transition metal phthalocyanines,II: electronic structure of MnPc and FePc—symmetry and symmetry breaking

We present a two-part systematic density functional theory (DFT) study of the electronic structure of selected transition metal phthalocyanines. We use a semi-local generalized gradient approximation (GGA) functional, as well as several hybrid exchange-correlation functionals, and compare the results to experimental photoemission data. Here, we study the intermediate spin systems MnPc and FePc. We show that DFT calculations of these systems are extremely sensitive to the choice of functional and basis set with respect to the obtained electronic configuration and to symmetry breaking. Interestingly, all simulated spectra are in good agreement with experiment despite the differences in the underlying electronic configurations.