Browsing by Subject "Polaron"
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Item Open Access Ground state energy of the fröhlich polaron as a function of dimensionality and the phonon coupling strength(Bilkent University, 2018-09) Bayrak, Hamdi BurakWe use the trial polaron wave function introduced by Devreese et al. [1] to estimate the ground state energies of the Fröhlich polaron over a broad range of the phonon coupling strength by a variational approach. We calculate the binding energy of the polaron as a function of dimensionality interpolating between two and three dimensions. We compare these results with the outcomes obtained by the Strong and Weak Coupling Theories and conclude that in the strong coupling regime, the present work leads to a significantly improved upper bound for the ground state energy.Item Open Access Mixtures of charged-neutral superfluids(Bilkent University, 2016-12) Ünal, FatmanurMotivated by the developments of artificial magnetic fields (AMFs) enabling cou- pling to the neutral particles of ultracold quantum gases, we have theoretically studied charged-neutral mixtures in various settings. The techniques that have been used to manufacture these AMFs are highly sensitive to the internal de- grees of freedom of the atoms, resulting in unequal coupling to the components of a mixture. We demonstrate the possible consequences of this unequal coupling by considering two different systems. First, we examine an impurity problem in a fermion background under an AMF coupling selectively to the impurity in a ring trap. We calculate the response of the system exactly by using Bethe Ansatz and argue that the AMF can be employed as a probe to analyze polaron formation. Secondly, we explore Bardeen-Cooper-Schrieffer theory of supercon- ductivity in the presence of a charge imbalance under an AMF. We analytically calculate the gap equation for any degree of asymmetry between the Landau level spectra of up and down spin particles, and show that the system displays reentrant superconductivity both in magnetic field and temperature. Apart from mixtures, we also investigate the non-equilibrium Hall response of a topological system. The strength of an AMF applied on a optical lattice can be suddenly changed without creating Eddy currents, allowing us to quench the system across a topological phase boundary. We report a fractional Hall response for the result- ing non-equilibrium system and discuss possible implementations for cold atom experiments.Item Open Access Superconducting systems of low dimensionality(Bilkent University, 1992) Gedik, M. ZaferIt is possible to call the last five years as the golden age of superconductivity. The two most important developments in the field are the discovery of copper oxide and fullerene superconductors. In this work, some possible pairing mechanisms for these materials ai’e examined by giving emphasis on the reduced dimensionality. First, an older problem, spatially separated electron-hole system, is investigated to identify the possible phases in coupled double quantum well structures in electric field. Secondly, the superconducting transition temperature and response to external magnetic fields of layered systems with varying number of layers are studied by means of a microscopic model and its GinzburgLandau version. It is also shown that an interlayer pairing mechanism, phonon assisted tunneling, can induce superconductivity. Finally, effects of the spherical structure of fullerenes are examined by solving a two fermion problem on an isolated molecule where the particles interact via a short range attractive potential. As a possible mechanism of superconductivity in alkali metal doped fullerenes, coupling between electrons and the radial vibrations of the molecule is investigated.