Geometry-induced wave-function collapse Article Swipe
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· 2022
· Open Access
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· DOI: https://doi.org/10.1103/physreva.106.022207
· OA: W4290888404
When a quantum particle moves in a curved space, a geometric potential can\narise. In spite of a long history of extensive theoretical studies, to\nexperimentally observe the geometric potential remains to be a challenge. What\nare the physically observable consequences of such a geometric potential?\nSolving the Schrodinger equation on a truncated conic surface, we uncover a\nclass of quantum scattering states that bear a strong resemblance with the\nquasi-resonant states associated with atomic collapse about a Coulomb impurity,\na remarkable quantum phenomenon in which an infinite number of quasi-resonant\nstates emerge. A characteristic defining feature of such collapse states is the\ninfinite oscillations of the local density of states (LDOS) about the zero\nenergy point separating the scattering from the bound states. The emergence of\nsuch states in the curved (Riemannian) space requires neither a relativistic\nquantum mechanism nor any Coulomb impurity: they have zero angular momentum and\ntheir origin is purely geometrical - henceforth the term geometry-induced\nwavefunction collapse. We establish the collapsing nature of these states\nthrough a detailed comparative analysis of the behavior of the LDOS for both\nthe zero and finite angular-momentum states as well as the corresponding\nclassical picture. Potential experimental schemes to realize the\ngeometry-induced collapse states are articulated. Not only has our study\nuncovered an intrinsic connection between the geometric potential and atomic\ncollapse, it also provides a method to experimentally observe and characterize\ngeometric potentials arising from different subfields of physics. For example,\nin nanoscience and nanotechnology, curved geometry has become increasingly\ncommon. Our finding suggests that wavefunction collapse should be an important\nfactor of consideration in designing and developing nanodevices.\n
