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Register a new userBound states of a light atom and two heavy dipoles in two dimensions
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We study a three-body system, formed by a light particle and two identical heavy dipoles, in two dimensions in the Born-Oppenheimer approximation. We present the analytic light-particle wave function resulting from an attractive zero-range potential between the light and each of the heavy particles. It expresses the large-distance universal properties which must be reproduced by all realistic short-range interactions. We calculate the three-body spectrum for zero heavy-heavy interaction as a function of light to heavy mass ratio. We discuss the relatively small deviations from Coulomb estimates and the degeneracies related to radial nodes and angular momentum quantum numbers. We include a repulsive dipole-dipole interaction and investigate the three-body solutions as functions of strength and dipole direction. Avoided crossings occur between levels localized in the emerging small and large-distance minima, respectively. The characteristic exchange of properties such as mean square radii are calculated. Simulation of quantum information transfer is suggested. For large heavy-heavy particle repulsion all bound states have disappeared into the continuum. The corresponding critical strength is inversely proportional to the square of the mass ratio, far from the linear dependence from the Landau criterion.
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We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in heterostructures or dihalogenated materials). The bosons are classified in two species (a,b) such that a-a and b-b pairs repel each other and a-b attract each other, forming the two-particle bound state with binding energy $epsilon_b^{(2)}$ (such as bi-exciton). We developed an efficient routine based on the proper choice of basis for analytic and numerical calculations. For zero-angular momentum we found the energies of the three-particle bound states $epsilon^{(3)}_b$ for wide ranges of the scattering lengths, and found a universal curve of $epsilon^{(3)}_b/epsilon^{(2)}_b$ which depends only on the scattering lengths but not the microscopic details of the interactions, this is in contrast to the three-dimensional Efimov effect, where a non-universal three-body parameter is needed.
It is established within the Thomas -- Fermi model that a bound state of a proton with a heavy atom should exist. On the one hand, the electrons of the atom screen the protons field. This decreases the repulsion force between the proton and the nucleus. On the other hand, the attraction force between the proton and the electrons is directed towards the gradient of the electron density, i. e. towards the nucleus. For instance, for Z=80 both forces become equal at approximately 0.6a where a is the Bohr radius. The corresponding minimum of the proton potential energy is in the region of negative energies (attraction) that can be of the order of several tens of eV. We propose to call such a system a binuclear atom. In contrast to the molecules where a coupling with a hydrogen atom is due to an essential modification of one or several states of the outer electrons the formation of a binuclear atom is a result of collective response of the whole system of inner electrons to the screened potential of a proton that is well inside the electron system of the heavy atom. The variation of the wave function of each electron can be considered as a small perturbation. The bound state is formed as a result of joint action of a large number of perturbed inner electrons. The important problem concerning the accuracy of our calculation within the Thomas -- Fermi model is discussed.
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_is for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.
We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wavefunctions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a metal-insulator transition between this ordinary diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix $sigma$-model.
We study three-body Schrodinger operators in one and two dimensions modelling an exciton interacting with a charged impurity. We consider certain classes of multiplicative interaction potentials proposed in the physics literature. We show that if the impurity charge is larger than some critical value, then three-body bound states cannot exist. Our spectral results are confirmed by variational numerical computations based on projecting on a finite dimensional subspace generated by a Gaussian basis.
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