Related papers: On Lennard-Jones-type potentials on the half-line
We consider a model of a leaky quantum wire with the Hamiltonian $-\Delta -\alpha \delta(x-\Gamma)$ in $L^2(\R^2)$, where $\Gamma$ is a compact deformation of a straight line. The existence of wave operators is proven and the S-matrix is…
A novel method for detecting Luttinger-liquid behavior is proposed. The idea is to measure the tunneling conductance between a quantum wire and a parallel two-dimensional electron system as a function of both the potential difference…
We study the conductance of a quantum wire in the presence of weak electron-electron scattering. In a sufficiently long wire the scattering leads to full equilibration of the electron distribution function in the frame moving with the…
We study the quantization of a model proposed by Newton to explain centripetal force namely, that of a particle moving on a regular polygon. The exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a particle moving…
A novel analytically solvable deformed Woods-Saxon potential is investigated by means of the Supersymmetric Quantum Mechanics. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. The energy levels…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
We consider a two-dimensional array of ultra-small superconducting grains, weakly coupled by Josephson junctions with large charging energy. We start from an effective action based on a microscopic tunneling Hamiltonian, which includes…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
The quantum description of an atom with a magnetic quadrupole moment in the presence of a uniform effective magnetic field is analysed. The atom is also subject to rotation and a scalar potential proportional to the inverse of the radial…
The possibility of excitations with fractional spin and statististics in $1+1$ dimensions is explored. The configuration space of a two-particle system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary…
We study single- and two-atom van der Waals interactions of ground-state atoms which are both polarizable and paramagnetizable in the presence of magneto-electric bodies within the framework of macroscopic quantum electrodynamics. Starting…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
Electronic transport properties of the disordered quantum wires are considered. The disorder is introduced via impurities (point scatterers), distributed uniformly over the two-dimensional strip, which represents a model quantum wire.…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
Recent advances in single atom manipulation have made it possible to create "wires" in the form of atomic scale linear structures on a semiconductor surface. If such structures are to be used in future electronic devices, it will be…
The work is dedicated to the theoretic analysis of wire media, i.e. lattices of perfectly conducting wires comprised of two or three doubly periodic arrays of parallel wires which are orthogonal to one another. An analytical method based on…
The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the…
A behaviour of molecular cluster with Lennard-Jones potential of interactions as Hamiltonian system is studied by computer simulation (molecular dynamics method). It is shown that complex periodic oscillations of the cluster as a whole are…
We provide a self-contained theoretical analysis of the dynamical response of a one dimensional electron system, as confined in a semiconductor quantum wire, within the random phase approximation. We carry out a detailed comparison with the…
A detailed study of the classical and quantum mechanics of a free particle on a double cone and the particle bounded to its tip by the harmonic oscillator potential is presented.