相关论文: Quantum Parabolic Sombrero
We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular…
We introduce the two-particle probability density $X(x)$ of $x=\bm{r}_{12}\cdot\bm{p}_{12}=\left(\bm{r}_1-\bm{r}_2\right) \cdot \left(\bm{p}_1-\bm{p}_2\right)$. We show how to derive $X(x)$, which we call the Posmom intracule, from the…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
We obtain the exact solution to the Dirac equation with the Poschl-Teller double ring-shaped Coulomb (PTDRSC) potential for any spin-orbit quantum number K. The relativistic scattering amplitude for spin 1/2 particles in the field of this…
We present the general form of potentials with two given energy levels $E_{1}$, $E_{2}$ and find corresponding wave functions. These entities are expressed in terms of one function $\xi (x)$ and one parameter $\Delta E=E_{2}$-$E_{1}$. We…
Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range…
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the…
Within the framework of Relativistic Schroedinger Theory (an alternative form of quantum mechanics for relativistic many-particle systems) it is shown that a general N-particle system must occur in one of two forms: either as a ``positive''…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $\langle r^\alpha \rangle$ and $\left\langle p^\alpha \right\rangle$, respectively. These…
We investigate the properties of a quantum walk which can simulate the behavior of a spin $1/2$ particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup…
We consider quantum dots with a parabolic confining potential. The qualitative features of such mesoscopic systems as functions of the total number of electrons N and their total angular momentum J, e.g. magic numbers, overall symmetries…
Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…
We consider a charged quantum particle in a random magnetic field with Gaussian, delta-correlated statistics. We show that although the single particle properties are peculiar, two particle quantities such as the diffusion constant can be…
We study the dynamics of a quantum particle coupled to dissipative (ohmic) environments, such as an electron liquid. For some choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular…
The hydrodynamic equations of an ideal fluid formed by a dilute quantum gas in a parabolic trapping potential are studied analytically and numerically. Due to the appearance of internal modes in the fluid stratified by the trapping…
The quantum free particle on the sphere $S_\kappa^2$ ($\kappa>0$) and on the hyperbolic plane $H_\kappa^2$ ($\kappa<0$) is studied using a formalism that considers the curvature $\k$ as a parameter. The first part is mainly concerned with…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
The Schrodinger motion of a charged quantum particle in an electromagnetic potential can be simulated by the paraxial dynamics of photons propagating through a spatially inhomogeneous medium. The inhomogeneity induces geometric effects that…
A classical representation for quantum eigenstates of a particle bound in $\lambda z^{2m}$ $(\lambda >0, m=1,2,...)$ potentials is developed. It is represented by ensembles of classical trajectories with energy distributions that can take…