Spin dependent point potentials in one and three dimensions

Abstract

We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.

15 pages, some misprints corrected, one example added, some references modified or added

References in corpus (6)

• Collisional decoherence reexamined
• Resolvents of self-adjoint extensions with mixed boundary conditions
• On the mathematical Structure of Quantum Measurement Theory
• A remark on Krein's resolvent formula and boundary conditions
• Two-component model of a spin-polarized transport
• On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

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• Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models
• Decoherence and determinism in a one-dimensional cloud-chamber model
• Spectrum of a family of spin-orbit coupled Hamiltonians with singular perturbation
• Transverse quantum decoherence of a fast particle in a gas
• Computation of unitary group for the Rashba spin-orbit coupled operator, with application to point-interactions