TY - JOUR

T1 - Geometry-induced wave-function collapse

AU - Ye, Li Li

AU - Han, Chen Di

AU - Huang, Liang

AU - Lai, Ying Cheng

N1 - Funding Information:
We thank Dr. H.-Y. Xu for discussions during the initial stage of this work. The work at Arizona State University was supported by AFOSR Grant No. FA9550-21-1-0186. The work at Lanzhou University was supported by National Natural Science Foundation of China under Grants No. 12175090 and No. 12047501.
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/8

Y1 - 2022/8

N2 - 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 a challenge. What are the physically observable consequences of such a geometric potential? Solving the Schrödinger equation on a truncated conic surface, we uncover a class of quantum scattering states that bear a strong resemblance to the quasiresonant states associated with atomic collapse about a Coulomb impurity, a remarkable quantum phenomenon in which an infinite number of quasiresonant 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, hence the term "geometry-induced wave-function 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 does our paper uncover 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 wave-function collapse should be an important factor of consideration in designing and developing nanodevices.

AB - 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 a challenge. What are the physically observable consequences of such a geometric potential? Solving the Schrödinger equation on a truncated conic surface, we uncover a class of quantum scattering states that bear a strong resemblance to the quasiresonant states associated with atomic collapse about a Coulomb impurity, a remarkable quantum phenomenon in which an infinite number of quasiresonant 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, hence the term "geometry-induced wave-function 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 does our paper uncover 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 wave-function collapse should be an important factor of consideration in designing and developing nanodevices.

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U2 - 10.1103/PhysRevA.106.022207

DO - 10.1103/PhysRevA.106.022207

M3 - Article

AN - SCOPUS:85135916982

VL - 106

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 2

M1 - 022207

ER -