相关论文: Curvature-induced bound states in quantum wires

The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…

We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…

We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…

Investigating the geometric effects resulting from the detailed behaviors of the confining potential, we consider square and circular confinements to constrain a particle to a space curve. We find a torsion-induced geometric potential and a…

Context: Due to advances in synthesizing lower dimensional materials there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently…

We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…

Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like…

We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…

Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a point particle moving on a…

Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…

We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra…

Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative…

Quantum simulators hold the promise of probing central questions of high-energy physics in tunable condensed matter platforms, for instance the physics of confinement. Local defects can be an obstacle in these setups harming their…

We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…

The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…

We consider a quantum particle constrained to a curved layer of a constant width built over an infinite smooth surface. We suppose that the latter is a locally deformed plane and that the layer has the hard-wall boundary. Under this…

We study quantum mechanics on a curved wire by approximating the physics around the curved region by three parameters coming from the boundary conditions given by the two interval Sturm-Liouville theory. Since the geometric potential on a…

Detailed account is given of the fact that the Cornell potential predicted by Lattice QCD and its exactly solvable trigonometric extension recently reported by us can be viewed as the respective approximate and exact counterparts on a…

We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the…