Квантовое тороидальное поле

The speaker will talk about the toroidal dipole of a quantum particle confined to a quasi-2D torus, demonstrating its corresponding operator’s self-adjointness (and thus observability). While numerically solving the free Hamiltonian’s eigenvalue problem is straightforward, the toroidal dipole operator projected onto the torus’s symmetry axis z presents convergence challenges. This stems from the operator’s analytically derived discrete, equidistant eigenvalues but infinitely normed eigenvectors, preventing wavefunction collapse upon measurement. Introducing an external current along the z-axis induces a non-zero, measurable toroidal dipole. The energy eigenvalues exhibit a non-monotonic, periodic dependence on the current, with avoided crossings and sign changes in the toroidal dipole (corresponding to induced current reversals) at intervals of I_per/2, where I_per is the period. This provides a method for observing and manipulating the toroidal dipole in nanostructures: adiabatically increasing the external current leads to discrete jumps and eventual sign changes in the toroidal dipole, enabling quasistatic switching.