Geometry-induced wavefunction collapse

Abstract

When a quantum particle moves in a curved space, a geometric potential can arise. In spite of a long history of extensive theoretical studies, to experimentally observe the geometric potential remains to be a challenge. What are the physically observable consequences of such a geometric potential? Solving the Schrodinger equation on a truncated conic surface, we uncover a class of quantum scattering states that bear a strong resemblance with the quasi-resonant states associated with atomic collapse about a Coulomb impurity, a remarkable quantum phenomenon in which an infinite number of quasi-resonant states emerge. A characteristic defining feature of such collapse states is the infinite oscillations of the local density of states (LDOS) about the zero energy point separating the scattering from the bound states. The emergence of such states in the curved (Riemannian) space requires neither a relativistic quantum mechanism nor any Coulomb impurity: they have zero angular momentum and their origin is purely geometrical - henceforth the term geometry-induced wavefunction collapse. We establish the collapsing nature of these states through a detailed comparative analysis of the behavior of the LDOS for both the zero and finite angular-momentum states as well as the corresponding classical picture. Potential experimental schemes to realize the geometry-induced collapse states are articulated. Not only has our study uncovered an intrinsic connection between the geometric potential and atomic collapse, it also provides a method to experimentally observe and characterize geometric potentials arising from different subfields of physics. For example, in nanoscience and nanotechnology, curved geometry has become increasingly common. Our finding suggests that wavefunction collapse should be an important factor of consideration in designing and developing nanodevices.

14 pages, 8 figures, journal

References in corpus (32)

• Substrate-induced band gap opening in epitaxial graphene
• Andreev reflection and Klein tunneling in graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Elastic scattering theory and transport in graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Geometry, mechanics and electronics of singular structures and wrinkles in graphene
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Screening of a hypercritical charge in graphene
• Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene
• Topological Phases in Graphitic Cones
• Mapping Dirac Quasiparticles near a Single Coulomb Impurity on Graphene
• Anomalies in Quantum Mechanics: the 1/r^2 Potential
• Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding
• Screening of Coulomb Impurities in Graphene
• Geometric Phases in Graphitic Cones
• Geometric potential and transport in photonic topological crystals
• Resource Letter GPP-1: Geometric Phases in Physics
• Adatoms in Graphene
• Unfamiliar trajectories for a relativistic particle in a Kepler or Coulomb potential
• On the quantum dynamics of a point particle in conical space
• On the limit cycle for the 1/r^2 potential in momentum space
• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Observing a scale anomaly and a universal quantum phase transition in graphene
• Quantum transport in a curved one-dimensional quantum wire with spin-orbit interactions
• Bound states in the dynamics of a dipole in the presence of a conical defect
• Curvature-induced bound states and coherent electron transport on the surface of a truncated cone
• Calculation of the electronic structure near the tip of a graphitic nanocone
• Constrained quantum mechanics: chaos in non-planar billiards