In this paper the spectral properties of Dirac operators Aη with electrostatic δ-shell interactions of constant strength η supported on compact smooth surfaces in R3 are studied. Making use of boundary triple techniques a Krein type resolvent formula and a Birman-Schwinger principle are obtained. With the help of these tools some spectral, scattering, and asymptotic properties of Aη are investi...

We study a Fermi Hamilton operator K̂ which does not commute with the number operator N̂ . The eigenvalue problem and the Schrödinger equation is solved. Entanglement is also discussed. Furthermore the Lie algebra generated by the two terms of the Hamilton operator is derived and the Lie algebra generated by the Hamilton operator and the number operator is also classified.

An effective intra-and inter-ladder charge-spin hamiltonian for the quarter-filled ladder compound α ′-NaV 2 O 5 has been derived by using the standard canonical transformation method. In the derivation, it is clear that a finite inter-site Coulomb repulsion is needed to get a meaningful result otherwise the perturbation becomes ill-defined. Various limiting cases depending on the values of the...

Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. A PDM-pseudo-momentum operator Π̂1 = −i [μ (x)∂x + g (x)] is introduced (the Hermiticity of which is secured by the condition g (x) = ∂xμ (x) /2) and generalized to ddimensions. Intertwining our Hamiltonian, HMM = Π̂ 2 d + V (x), with the von Roos d-dimensional PDM-Hamiltonian, HvR = T̂d (α, β,...

“Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods or operator splitting methods ” proposed by Misawa 2001 . In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error...

The Nielsen Hamiltonian of the general polyatomic molecule including anharmonicity and its resonances, Coriolis-coupling and its resonances, and rotation-vibration interaction are treated by statistical perturbat ion theory in its operator form. By generating function methods and operator theorems, which are treated in an appendix, cumbersome calculations with non-commuting operators are avoide...

For a finite-dimensional (but possibly noncompact) symplectic manifold with a compact group acting with a proper moment map, we show that the square of the moment map is an equivariantly perfect Morse function in the sense of Kirwan, and that the set of critical points of the square of the moment map is a countable discrete union of compact sets. We show that certain integrals of equivariant co...

Let H be the discrete Schrödinger operator Hu(n) := u(n − 1) + u(n + 1) + v(n)u(n), u(0) = 0 acting on l(Z) where the potential v is real-valued and v(n) → 0 as n → ∞. Let P be the orthogonal projection onto a closed linear subspace L ⊂ l(Z). In a recent paper E.B. Davies defines the second order spectrum Spec2(H,L) of H relative to L as the set of z ∈ C such that the restriction to L of the op...

We have shown in our previous works how to introduce the quantization procedure into the theory of heat conduction. In the present paper we point out where and why we need to complete the previous results to obtain the Hamiltonian by which we can bring ‘zero point’ energy into the theory of thermal field. We calculate the energy and the quasi-particle number operator for heat conduction.

Let H be the discrete Schrödinger operator Hu(n) := u(n − 1) + u(n + 1) + v(n)u(n), u(0) = 0 acting on l(Z) where the potential v is real-valued and v(n) → 0 as n → ∞. Let P be the orthogonal projection onto a closed linear subspace L ⊂ l(Z). In a recent paper E.B. Davies defines the second order spectrum Spec2(H,L) of H relative to L as the set of z ∈ C such that the restriction to L of the op...