# Entanglement of boundary conditions giving rise to spontaneous symmetry breaking in quantum mechanics

## TL;DR

This paper explores how specific boundary conditions in quantum mechanics can lead to spontaneous symmetry breaking, resulting in stable, broken-symmetry states influenced by singular potentials and external fluctuations.

## Contribution

It introduces a novel boundary condition entanglement approach to induce spontaneous symmetry breaking in quantum systems, connecting it to molecular chiral states.

## Key findings

- Existence of a stable broken-symmetry ground state.
- Boundary condition entanglement induces symmetry breaking.
- Relevance to molecular chiral states like NH3.

## Abstract

We study spontaneous symmetry breaking in one dimensional quantum mechanical problems in terms of two-point boundary problems which lead to singular potentials containing Dirac delta functions and its derivatives. We search for broken-symmetry bound states. For a particular entanglement of boundary conditions, we show the existence of a ground state, giving rise to a spontaneous symmetry breaking, stable under the phenomenon of decoherence generated from external fluctuations. We discuss the model in the context of the "chiral" broken-symmetry states of molecules like $NH_3$.