Related papers: On the discrete spectrum of spin-orbit Hamiltonian…
We study the symmetry properties of the Hubbard model with spin-orbit interactions of Rashba and Dresselhaus type. These interactions break the rotational symmetry in spin space, so that the magnetic order cannot be excluded by using the…
We describe a new class of atom-laser coupling schemes which lead to spin-orbit coupled Hamiltonians for ultra-cold neutral atoms. By properly setting the optical phases, a pair of degenerate pseudospin states emerge as the lowest energy…
We have described electron spin dynamics in the presence of the spin-orbit interaction and disorder using the spin-density matrix method. Exact solution is obtained for an arbitrary 2D spin-orbit Hamiltonian and arbitrary smoothness of the…
We put forward a new approach based on Green's function formalism to evaluate precisely persistent charge and spin currents in an Aharonov-Bohm ring subjected to Rashba and Dresselhaus spin-orbit interactions. Unlike conventional methods…
The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin…
In a series of recent papers it was shown that, when the attractive s-wave interaction is dominant, the spin-orbit coupled fermions form a bound state. Attributed to a convenient momentum representation, it became a common condition of…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…
In this work, we focus on the multiplicity of singular spectrum for operators of the form $A^\omega=A+\sum_{n}\omega_n C_n$ on a separable Hilbert space $\mathcal{H}$, for a self-adjoint operator $A$ and a countable collection $\{C_n\}_{n}$…
In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.
We prove that translationally invariant Hamiltonians of a chain of $n$ qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $n\rightarrow\infty$ we show that any translationally…
We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of Rashba and linear Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling…
We investigate the spin dynamics and relaxation in remotely-doped two dimensional electron systems where the dopants lead to random fluctuations of the Rashba spin-orbit coupling. Due to the resulting random spin precession, the spin…
We study quasi-periodic eigenvalue problems that arise in the stability analysis of periodic traveling wave solutions to Hamiltonian PDEs. We establish bounds on regions in the complex plane when the eigenvalues may deviate from the…
We provide sufficient conditions to have at least one $N$-particle bound state below the essential spectrum of a large class of $N$-particle discrete Schr\"odinger operators $H(K),$ $K\in \mathbb{T}^d,$ $d\ge1,$ associated to the…
We investigate the properties of persistent charge current driven by magnetic flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we work out individual…
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…
The spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin-orbit interaction is studied numerically. We find that the spin Hall conductance is very sensitive to the transverse measuring location, the…
We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have…
An alternating electric field, applied to a quantum dot, couples to the electron spin via the spin-orbit interaction. We analyze different types of spin-orbit coupling known in the literature and find two efficient mechanisms of spin…