Two electrons on a hypersphere: a quasi-exactly solvable model

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a $\mathcal{D}$-sphere ($\mathcal{D} \ge 1$), is a polynomial in the interelectronic distance $u$ for a countably infinite set of values of the radius $R$. A selection of these radii, and the associated energies, are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the $\mathcal{D}=3$ model bears the greatest similarity to normal physical systems.Comment: 4 pages, 0 figur

Carrier-density effects in many-polaron systems

Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the one-dimensional spinless Holstein model considered here. In this work, previous results obtained using numerical as well as analytical approaches are reviewed from a unified perspective, focussing on spectral properties which reveal the nature of the quasiparticles in the system. In the adiabatic regime and for intermediate electron-phonon coupling, a carrier-density driven crossover from a polaronic to a rather metallic system takes place. Further insight into the effects due to changes in density is gained by calculating the phonon spectral function, and the fermion-fermion and fermion-lattice correlation functions. Finally, we provide strong evidence against the possibility of phase separation.Comment: 13 pages, 6 figures, accepted for publication in J. Phys.: Condens. Matter; final versio

Optical conductivity of polaronic charge carriers

The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.Comment: 23 pages, 11 figure

Invariance of the correlation energy at high density and large dimension in two-electron systems

We prove that, in the large-dimension limit, the high-density correlation energy \Ec of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by \Ec \sim -1/(8D^2) for any radial confining potential $V(r)$. This result explains the observed similarity of \Ec in a variety of two-electron systems in three-dimensional space.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Phonon affected transport through molecular quantum dots

To describe the interaction of molecular vibrations with electrons at a quantum dot contacted to metallic leads, we extend an analytical approach that we previously developed for the many-polaron problem. Our scheme is based on an incomplete variational Lang-Firsov transformation, combined with a perturbative calculation of the electron-phonon self-energy in the framework of generalised Matsubara functions. This allows us to describe the system at weak to strong coupling and intermediate to large phonon frequencies. We present results for the quantum dot spectral function and for the kinetic coefficient that characterises the electron transport through the dot. With these results we critically examine the strengths and limitations of our approach, and discuss the properties of the molecular quantum dot in the context of polaron physics. We place particular emphasis on the importance of corrections to the concept of an antiadiabatic dot polaron suggested by the complete Lang-Firsov transformation.Comment: 30 pages, 15 figures, revised version including new figure

Photoemission spectra of many-polaron systems

The cross over from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points towards the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.Comment: 15 pages, 13 figures; final version, accepted for publication in Phys. Rev.

Infrared conductivity of a one-dimensional charge-ordered state: quantum lattice effects

The optical properties of the charge-ordering ($CO$) phase of the one-dimensional (1D) half-filled spinless Holstein model are derived at zero temperature within a well-known variational approach improved including second-order lattice fluctuations. Within the $CO$ phase, the static lattice distortions give rise to the optical interband gap, that broadens as the strength of the electron-phonon ($el-ph$) interaction increases. The lattice fluctuation effects induce a long subgap tail in the infrared conductivity and a wide band above the gap energy. The first term is due to the multi-phonon emission by the charge carriers, the second to the interband transitions accompanied by the multi-phonon scattering. The results show a good agreement with experimental spectra.Comment: 5 figure

Spectral functions of the spinless Holstein model

An analytical approach to the one-dimensional spinless Holstein model is proposed, which is valid at finite charge-carrier concentrations. Spectral functions of charge carriers are computed on the basis of self-energy calculations. A generalization of the Lang-Firsov canonical transformation method is shown to provide an interpolation scheme between the extreme weak- and strong-coupling cases. The transformation depends on a variationally determined parameterthat characterizes the charge distribution across the polaron volume. The relation between the spectral functions of polarons and electrons, the latter corresponding to the photoemission spectrum, is derived. Particular attention is paid to the distinction between the coherent and incoherent parts of the spectra, and their evolution as a function of band filling and model parameters. Results are discussed and compared with recent numerical calculations for the many-polaron problem.Comment: 20 pages, 15 figures, final versio

An ultrashort pulse ultra-violet radiation undulator source driven by a laser plasma wakefield accelerator

Narrow band undulator radiation tuneable over the wavelength range of 150–260 nm has been produced by short electron bunches from a 2 mm long laser plasma wakefield accelerator based on a 20 TW femtosecond laser system. The number of photons measured is up to 9 × 106 per shot for a 100 period undulator, with a mean peak brilliance of 1 × 1018 photons/s/mrad2/mm2/0.1% bandwidth. Simulations estimate that the driving electron bunch r.m.s. duration is as short as 3 fs when the electron beam has energy of 120–130 MeV with the radiation pulse duration in the range of 50–100 fs

A Survey of Satisfiability Modulo Theory

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches. We also cover quantifiers, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. 201