Related papers: Cooper pairs and bipolarons
The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically…
The collective Hamiltonian including isovector pairing and $\alpha$-particle type correlation degrees of freedom is constructed. The Hamiltonian is applied to description of the relative energies of the ground states of even-even nuclei…
The symmetry properties of the Cooper pairing problem for multi-component ultra-cold dipolar molecular systems are investigated. The dipolar anisotropy provides a natural and robust mechanism for both triplet and singlet Cooper pairing to…
Whereas identification of Cooper pair symmetry is the first and crucial step in the investigation of unconventional superconductors, only a few have been established so far because of its own difficulties. To solve this problem, we develop…
Cooper pairing between a conduction electron ($c$ electron) and an $f$ electron, referred to as the "$c$-$f$ pairing," is examined to explain s-wave superconductivity in heavy-fermion systems. We first apply the Schrieffer-Wolff…
We consider a class of time dependent finite energy multi-soliton solutions of the U(N) integrable chiral model in $(2+1)$ dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary…
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…
Fr\"{o}hlich's polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron is approximated by an effective non-linear partial…
We consider a system which consists of a Cahn-Hilliard equation coupled with a Cahn-Hilliard-Oono equation in a bounded domain of $\mathbb{R}^d$, $d = 2, 3$. This system accounts for macrophase and microphase separation in a polymer mixture…
Nonoscillatory second order differential equations always admit ``special'', principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by \'A. Elbert, F. Neuman and J. Vosmansk\'y, {\em…
The problem of the pairing interaction is dealt with even Grassmann variables in the hamiltonian framework. Eigenfunctions of given energy, seniority and zero third component of angular momentum are given in terms of single particle and…
We calculate the effective interaction $W_{eff}$ between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a…
In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical Hamiltonian system depending on a finite number of…
We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak…
We show that fermionic dipoles in a two-layer geometry form Cooper pairs with both singlet and triplet components, when they are tilted with respect to the normal of the planes. The mixed parity pairing arises because the interaction…
Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…
Using for unperturbed electron and phonon Hamiltonians a representation by the Jacobi matrices a one-dimensional model of the electron-phonon interaction is constructed. In frame of the model the polaron and scattering spectral bands are…
We propose a simple phenomenological theory for quantum tunneling of Cooper pairs based on their boson like nature. Thus it applies in the absence of quasiparticle excitations (fermions), and should be suitable for boson like particles at…