Related papers: Quantum mechanics of layers with a finite number o…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
We use an exact solution to the fundamental finite Kronig-Penney model with arbitrary positions and strengths of scattering sites to show that this iconic model can possess topologically non-trivial properties. By using free parameters of…
Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are…
We consider mathematical models of the weak decay of the vector bosons $W^{\pm}$ into leptons. The free quantum field hamiltonian is perturbed by an interaction term from the standard model of particle physics. After the introduction of…
We formulate a simple condition for reconstructibility of a certain class of Hamiltonians with real potentials from the knowledge of their complex-valued eigenfunctions. This may be relevant to the question of preparability of quantum…
We study effects of perturbation Hamiltonian to quantum spin systems which can include quenched disorder. Model-independent inequalities are derived, using an additional artificial disordered perturbation. These inequalities enable us to…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a…
The quantum-mechanical scattering on a compact Riemannian manifold with semi-axes attached to it (hedgehog-shaped manifold) is considered. The complete description of the spectral structure of Schroedinger operators on such a manifold is…
Advantages of using a low-energy effective theory to study bound state properties are briefly discussed, and a nonperturbative implementation of such an effective theory is described within the context of nonrelativistic quantum mechanics.…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the…
The physical properties induced by a quenched surface magnetic field in the Ising model are investigated by means of boundary quantum field theory in replica space. Exact boundary scattering amplitudes are proposed and used to study the…
In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different…
Plasmons are fundamental excitations of metals which can be described in terms of electron dynamics, or in terms of the electromagnetic fields associated with them. In this work we develop a quantum description of plasmons in a double layer…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
We solve the bound state problem for the Hamiltonian with the spin-orbit and the Raman coupling included. The Hamiltonian is perturbed by a one-dimensional short-range potential V which describes the impurity scattering. In addition to the…