Abstract
Spontaneous symmetry breaking (ssb) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate ssb has been independently understood for Schrödinger operators with double well potential in the classical limit (Jona-Lasinio et al, 1981; Simon, 1985) and for quantum spin systems in the thermodynamic limit (Anderson, 1952; Tasaki, 2019). We relate these to each other in the context of the Curie–Weiss model, establishing a remarkable relationship between this model (for finite NN) and a discretized Schrödinger operator with double well potential.
Highlights
Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit
We have established a link between the quantum Curie–Weiss Hamiltonian and a 1d
Schrödinger operator describing a particle in a symmetric double well potential for ħ h > 0, where ħ h = 1/N
Summary
Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schrödinger operators with double well potential in the classical limit [1, 2] and for quantum spin systems in the thermodynamic limit [3, 4]. We relate these to each other in the context of the Curie–Weiss model, establishing a remarkable relationship between this model (for finite N) and a discretized Schrödinger operator with double well potential
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
