dorsal/arxiv
View SchemaPhysics of singular points in quantum mechanics
| Authors | Izumi Tsutsui, Tamas Fulop |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312028 |
| URL | https://arxiv.org/abs/quant-ph/0312028 |
Abstract
Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an unexpectedly rich structure and thereby provide a variety of physical phenomena, especially if their properties are controlled properly. Based on our recent studies, we present a brief review on the physical aspects of such quantum singularities in one dimension. Among the intriguing phenomena that the singularities admit, we mention strong vs weak duality, supersymmetry, quantum anholonomy (Berry phase), and a copying process by anomalous caustics. We also show that a partition wall as a singularity in a potential well can give rise to a quantum force which exhibits an interesting temperature behavior characteristic to the particle statistics.
{
"annotation_id": "c931865a-a180-422c-b59b-92245f9c6507",
"date_created": "2026-03-02T18:02:03.531000Z",
"date_modified": "2026-03-02T18:02:03.531000Z",
"file_hash": "5c67d7d7a9563a2c8f6478f69fbf97bada859b20c534ef53a6bae20e33b0081f",
"private": false,
"record": {
"abstract": "Defects or junctions in materials serve as a source of interactions for\nparticles, and in idealized limits they may be treated as singular points\nyielding contact interactions. In quantum mechanics, these singularities\naccommodate an unexpectedly rich structure and thereby provide a variety of\nphysical phenomena, especially if their properties are controlled properly.\nBased on our recent studies, we present a brief review on the physical aspects\nof such quantum singularities in one dimension. Among the intriguing phenomena\nthat the singularities admit, we mention strong vs weak duality, supersymmetry,\nquantum anholonomy (Berry phase), and a copying process by anomalous caustics.\nWe also show that a partition wall as a singularity in a potential well can\ngive rise to a quantum force which exhibits an interesting temperature behavior\ncharacteristic to the particle statistics.",
"arxiv_id": "quant-ph/0312028",
"authors": [
"Izumi Tsutsui",
"Tamas Fulop"
],
"categories": [
"quant-ph"
],
"title": "Physics of singular points in quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0312028"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "59c45376-57e1-4716-b890-ab187fb260e6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}