According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Fröhlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert the strong-coupling term in the Hamiltonian into the form of an effective hopping integral and derive the singleparticle Green's function describing propagation of the small Fröhlich polaron. One and two dimensional spectral functions are studied by expanding the Green's function perturbatively. Numerical calculations of the spectral functions are produced. Remarkably, the coherent spectral weight (Z) and effective mass (Z ′ ) renormalisation exponents are found to be different with Z ′ >> Z, which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.PACS numbers:74.20. Mn,74.25.Jb IntroductionThe problem of a fermion on a lattice coupled with the bosonic field of lattice vibrations has an exact solution in terms of the coherent (Glauber) states in the extreme strong-coupling limit, λ = ∞ for any type of electronphonon interaction conserving the on-site occupation numbers of fermions 1,2 . For the intermediate coupling the 1/λ perturbation diagrammatic technique has been developed both for a single 3 and multi-polaron systems 4 . The expansion parameter actually is 1/2zλ 23,5,6,4 , so the analytical perturbation theory might have a wider region of applicability than one can expect from a naive variational estimate (z is the lattice coordination number). However, it is not clear how fast the expansion converges. The exact numerical diagonalisation of vibrating clusters, variational calculations 7-17 , dynamical mean-field approach in infinite dimensions 18 , and Quantum-MonteCarlo simulations [19][20][21][22] revealed that the ground state energy (the polaron binding energy E p ) is not very sensitive to the parameters. On the contrary, the effective mass, the bandwidth and the shape of polaron density of states strongly depend on polaron size and adiabatic ratio in case of a short-range (Holstein) interaction. In particular, numerical diagonalisation of the two-site-one-electron Holstein model in the adiabatic ω 0 /t < 1 as well as in the nonadiabatic ω 0 /t > 1 regimes shows that perturbation theory is almost exact in the nonadiabatic regime f or all values of the coupling constant. However, there is no agreement in the adiabatic region, where the first order perturbation expression overestimates the polaron mass by a few orders of magnitude in the intermediate coupling regime 8 . Here ω 0 is the characteristic phonon frequency and t is the nearest-neighbour hopping integral so that

We consider a fundamental quantum mechanical bound-state problem in the form of the quartic-well potential . The analytical transfer matrix method is applied. This yields a quantization condition from which we can calculate the phase contributions and ground-state energy eigenvalues numerically. We also compare the results with those obtained from other typical means popular among physics students, namely the numerical shooting method, perturbation theory and the standard WKB method.

A single-particle spectral density is proposed for cuprates taking into account the bipolaron formation, realistic band structure, thermal fluctuations and disorder. Tunnelling and photoemission (PES) spectra are described, including the temperature independent gap observed both in the superconducting and normal states, the emission/injection asymmetry, the finite zero-bias conductance, the spectral shape in the gap region and its temperature and doping dependence, dip-hump incoherent asymmetric features at high voltage (tunnelling) and large binding energy (PES).PACS numbers: 74.65.+n,74.60.Mj Typeset using REVT E X

No abstract