Quantum few-body bound states of dipolar particles in a helical geometry

Abstract

We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting effective two-particle potential with an oscillating behaviour. For this system we calculate the spectrum and the wave functions of the bound states. The full quantum solutions show clear imprints of the tendency for the system to form chains of dipoles along the helix, i.e. a configuration in which the dipoles are sitting approximately one winding of the helix apart so that they can take maximal advantage of the strong head-to-tail attraction that is a generic feature of the dipole-dipole interaction.

External field-induced dynamics of a charged particle on a closed helix

“…It was demonstrated that, due to the geometry, ballistic long-range Coulomb interacting particles on a 1D helical path can form bound states [9,10] and can even build 1D lattice structures [10][11][12]. Novel physics resulting from this behavior has been reported in several works discussing relevant setups [13][14][15][16][17][18][19][20]. Effects range from mechanical properties like an unusual electrostatic bending response [12], to intriguing nonlinear dynamics, such as the scattering of bound states at an inhomogeneity in the 1D path [13] or the tuning of the dispersion relation of a 1D chain of bound particles by varying the helix radius [14,15].…”

Few-body quantum method in a d-dimensional space

“…where the radial function reveals the weight of each partial wave. As discussed in section 2, in our case of a squeezing potential with axial symmetry, m is a good quantum number, and since only s-waves are considered, we then have m = 0, and the partial wave components in the wave function (16) will depend only on r and the polar angle θ = arctan(r ⊥ /z). It is therefore evident how any observable can be computed via only d-calculated quantities.…”

“…(15), or Fig. 3b, by use of the ratio of b ext /r d , and finally, v) use the wave function (16) in order to compute whatever observable is of interest.…”

Local equilibria and state transfer of charged classical particles on a helix in an electric field

“…Meanwhile, less complex inorganic systems such as carbon nanotubes are shaped nowadays in different forms, including a helix [15][16][17]. Given a pre-established helical confinement, identical long-range interacting particles such as dipoles and charges can display a plethora of different intriguing phenomena [18][19][20][21][22][23][24]. Even on the level of classical mechanics a helical constraint restricts the motion of the particles inducing an oscillatory effective two-body potential for repulsively interacting electric charges [20,21].…”