Mobility of spin polarons with vertex corrections

The mobility of holes in the spin polaron theory is discussed in this paper using a representation where holes are described as spinless fermions and spins as normal bosons. The hard-core bosonic operator is introduced through the Holstein–Primakoff transformation. Mathematically, the theory is implemented in the finite temperature (Matsubara) Green’s function method. The expressions for the zeroth-order term of the hole mobility is determined explicitly for hole occupation factor taking the form of Fermi–Dirac distribution and the classical Maxwell–Boltzmann distribution function. These are proportional to the relaxation time and the square of the renormalization factor. In the Ising limit, we showed that the mobility is zero and the holes are localized. The calculation of the hole mobility is generalized by considering the vertex corrections, which included the ladder diagrams. One of the vertex functions in the hole mobility can be evaluated using the Ward identity for hole-spin wave weak interaction. We also derived an expression for the hole mobility with vertex corrections in the low-temperature limit and vanishing self-energy effects. Our calculation is made up to second-order correction in the case where the hole occupation factor follows the Fermi–Dirac distribution.

QUANTUM STATE OF JOSEPHSON JUNCTION AS COOPER PAIR NUMBER-PHASE ENTANGLED STATE IN THE BOSONIC OPERATOR JOSEPHSON MODEL

Based on Feynman's explanation about Cooper pair that "a bound pair acts as a Bose particle" and the bosonic operator Hamiltonian of the Josephson junction, we realize that the quantum state of the Josephson junction is a Cooper pair number-phase entangled state constructed by the phase operator across the junction. Its Schmidt decomposition is derived. The Cooper pair number-phase squeezed state's projection onto this entangled state leads to a geometric distribution.

BOSONIC OPERATOR HAMILTONIAN MODELS OF JOSEPHSON JUNCTIONS IN SERIES AND IN PARALLEL AND THEIR PROJECTIONS ONTO ENTANGLED STATE REPRESENTATIONS

We present the bosonic operator Hamiltonian models of two Josephson junctions which are connected in series and in parallel, respectively. By introducing the entangled state representations (|η〉 representation and Cooper pairs representation) and projecting the operator Hamiltonian onto the |η〉 representation we obtain the correct Josephson current and phase equations consistent with the classical Hamiltonian cases.

EFFECTIVE PHOTON EXCHANGE CORRELATIONS IN FERROELECTRICS

We propose a photon correlation theory for ferroelectrics especially focused on KDP-type where we consider a photon field from its constituent electrons and ions. We derive a Curie–Weiss type dielectric susceptibility from the microscopic Hamiltonian and we obtain the ferroelectric transition temperature, Tc. We calculate the free energy by applying the bosonic operator formalism to the Hamiltonian. A linear temperature-dependent specific heat Cv conforming with experimental data for some ferroelectric materials is obtained. We calculate the isotope exponent, α, on Tc. We also derive phonon dispersion relations in the presence of electron-phonon interactions to show soft modes at Tc.

ENTANGLED STATE REPRESENTATION FOR A PARTICLE ON A CIRCLE STUDIED IN TERMS OF BOSONIC OPERATOR REALIZATION OF ANGULAR MOMENTUM

By introducing the bosonic operator realization of angular momentum, we establish the entangled state representation for describing quantum mechanics of a particle on a circle. The phase operator, the angular momentum eigenstates, the lowering and ascending operators for angular momentum are all well expressed in the bosonic realization with the aid of appropriate entangled states, i.e. we establish a new formalism for the quantum mechanics of a particle on a circle.

COOPER-PAIR-NUMBER–PHASE SQUEEZING FOR THE BOSONIC HAMILTONIAN MODEL OF JOSEPHSON JUNCTION

Based on Feynman's explanation about the Cooper pair that "a bound pairs act as a Bose particle" and the bosonic operator Hamiltonian of Josephson junction (H.-Y. Fan, Int. J. Mod. Phys. B17 (2003) 2599) as well as the entangled state representation, we establish a possible number–phase squeezing mechanism for the Cooper-pair and the phase difference between the two sides of the junction. We find that when an extra energy (e.g. microwave radiation) is provided to the junction, then this squeezing mechanism can happen.