arXiv subjects

Mircea Dolineanu

Publications and source records attributed to Mircea Dolineanu.

3 recordsLinked to original sources

arXiv2024

Unveiling the Quantum Toroidal Dipole

The electromagnetic response of matter is governed by three fundamental multipole families: electric, magnetic, and toroidal. While the electric and magnetic are cornerstones of physics, the toroidal dipole (TD) has eluded direct, quantitative measurement for over 60 years. Its far-field signature is masked by the electric dipole, and its behavior in the quantum regime remains largely unexplored. We address this long-standing problem by presenting a complete quantum-mechanical formalism for the TD in a nanostructure and proposing the first spectroscopic method for its direct measurement. We analyze a particle confined to a toroidal manifold subjected to an external current. We demonstrate that the resulting Aharonov-Bohm-like energy shifts in the system's spectrum are directly proportional to the expectation value of the TD operator. The transition energies exhibit a linear dependence on this current, with a quantized slope that directly reveals the change in the TD quantum number between eigenstates. This provides a clear experimental blueprint to unveil, measure, and characterize this elusive third multipole moment and its quantum nature, opening new avenues in quantum metamaterials, nanoscience, and the study of fundamental symmetries.

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arXiv2022

The eigenvalues and eigenfunctions of the toroidal dipole operator in a mesoscopic system

We give analytical expressions for the eigenvalues and generalized eigenfunctions of $\hat{T}_3$, the $z$-axis projection of the toroidal dipole operator, in a system consisting of a particle confined in a thin film bent into a torus shape. We find the quantization rules for the eigenvalues, which are essential for describing measurements of $\hat{T}_3$. The eigenfunctions are not square-integrable, so they do not belong to the Hilbert space of wave functions, but they can be interpreted in the formalism of rigged Hilbert spaces as kernels of distributions. While these kernels appear to be problematic at first glance due to singularities, they can actually be used in practical computations. In order to illustrate this, we prescribe their action explicitly and we also provide a normalization procedure.

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arXiv2022

The self-adjoint toroidal dipole operator in nanostructures

The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole ${\bf T}$ (the lowest order multipole) is the most common. In quantum systems, this corresponds to the toroidal dipole operator $\hat{\bf T}$, with the projections $\hat{T}_i$ ($i=1,2,3$) on the coordinate axes. Here we analyze a quantum particle in a system with cylindrical symmetry, which is a typical system in which toroidal moments appear. We find the expressions for the Hamiltonian, momenta, and toroidal dipole operators in adequate curvilinear coordinates, which allow us to find analytical expressions for the eigenfunctions of the momentum operators. While the toroidal dipole is hermitian, it is not self-adjoint, but in the new set of coordinates the operator $\hat{T}_3$ splits into two components, one of which is (only) hermitian, whereas the other one is self-adjoint. The self-adjoint component is the one that is physically significant and represents an observable. Furthermore, we numerically diagonalize the Hamiltonian and the toroidal dipole operator and find their eigenfunctions and eigenvalues. We write the partition function and calculate the thermodynamic quantities for a system of ideal particles on a torus. Besides proving that the toroidal dipole is self-adjoint and therefore an observable (a finding of fundamental relevance) such systems open up the possibility of making metamaterials that exploit the quantization and the quantum properties of the toroidal dipoles.

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