Related papers: Exotic atoms in two dimensions
We develop an analytical expression for the self-energy of the infinite-dimensional Hubbard model that is correct in a number of different limits. The approach represents a generalization of the iterative perturbation theory to arbitrary…
It is shown that resonance scattering of fast ($pL > >pR > > 1$, $p$ is the particle momentum, $L$ is the longitudinal dimension of the potential, and $R$ is its transverse dimension) charged particles occurs in the extended potential. The…
We describe the resonant interaction of an atom with a strongly focused light beam by expanding the field in multipole waves. For a classical field, or when the field is described by a coherent state, we find that both intensity pattern and…
Coupled elliptic quantum dots with different aspect ratios containing up to two electrons are studied using a model confinement potential in the presence of magnetic fields. Single and two particle Schroedinger equations are solved using…
In this paper we present two atomistic models for the energy of a one-dimensional elastic crystal. We assume that the macroscopic displacement equals the microscopic one. The energy of the first model is given by a two-body interaction…
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle $\alpha$ off a bound state of two charged, or one charged and one neutral, particles at small momentum transfer $\Delta_{\alpha}$ or…
We analyze the zero energy collision of three identical bosons in the same internal state with total orbital angular momentum $L=2$, assuming short range interactions. By solving the Schr\"odinger equation asymptotically, we derive two…
A mechanism to modify the energy band structure is proposed by considering a chain of periodic scatterers forming a linear lattice around which an external cylindrical trapping potential is applied along the chain axis. When this trapping…
The behavior of an excess electron in a one, two and three dimensional classical liquid has been studied with the aid of Chandler, Singh and Richardson (CSR) theory [J. Chem. Phys. {\bf 81} 1975 (1984)] . The size or dispersion of the…
Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a non-zero projection of the electronic orbital angular momentum is presented. It is shown how the long-range…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
Excitons in low-dimensional materials behave mathematically as confined hydrogen atoms. An appealing unified description of confinement in quantum wells or wires, etc., is found by restricting space to a fractional dimension 1 < D <= 3…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…
We derive a generalized Low equation for the T-matrix appropriate for complex atom-molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.
We consider the defocusing, energy subcritical wave equation $\partial_t^2 u - \Delta u = -|u|^{p-1} u$ in dimension $d \in \{3,4,5\}$ and prove the exterior scattering of solutions if $3\leq d \leq 5$ and $1+6/d<p<1+4/(d-2)$. More…
The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time in which to perform the measurement. This paper considers the possibility that $\Delta E$, the uncertainty in the energy, may be…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
We study the interaction between dark matter and dark energy, with dark energy described by a scalar field having a double exponential effective potential. We discover conditions under which such a scalar field driven solution is a late…
Dark energy and dark matter are only indirectly measured via their gravitational effects. It is possible that there is an exchange of energy within the dark sector, and this offers an interesting alternative approach to the coincidence…