Geometry-induced wavefunction collapse
- URL: http://arxiv.org/abs/2402.13980v1
- Date: Wed, 21 Feb 2024 18:09:12 GMT
- Title: Geometry-induced wavefunction collapse
- Authors: Li-Li Ye, Chen-Di Han, Liang Huang, and Ying-Cheng Lai
- Abstract summary: We find a class of quantum scattering states that bear a strong resemblance with the quasi-resonant states associated with atomic collapse.
The emergence of such states in the curved space requires neither a relativistic quantum mechanism nor any Coulomb impurity.
Our finding suggests that wavefunction collapse should be an important factor of consideration in designing and developing nanodevices.
- Score: 3.2557651446146587
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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