PhilSci Archive

Spontaneous Symmetry Breaking in Finite Quantum Systems: a decoherent-histories approach

Wallace, David (2018) Spontaneous Symmetry Breaking in Finite Quantum Systems: a decoherent-histories approach. [Preprint]

[img]
Preview
Text
ssbfinite.pdf

Download (378kB) | Preview

Abstract

Spontaneous symmetry breaking (SSB) in quantum systems, such as ferromagnets, is normally described as (or as arising from) degeneracy of the ground state; however, it is well established that this degeneracy only occurs in spatially infinite systems, and even better established that ferromagnets are not spatially infinite. I review this well-known paradox, and consider a popular solution where the symmetry is explicitly broken by some external field which goes to zero in the infinite-volume limit; although this is formally satisfactory, I argue that it must be rejected as a physical explanation of SSB since it fails to reproduce some important features of the phenomenology. Motivated by considerations from the analogous classical system, I argue that SSB in finite systems should be understood in terms of the approximate decoupling of the system's state space into dynamically-isolated sectors, related by a symmetry transformation; I use the formalism of decoherent histories to make this more precise and to quantify the effect, showing that it is more than sufficient to explain SSB in realistic systems and that it goes over in a smooth and natural way to the infinite limit.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Wallace, Daviddmwallac@usc.edu
Subjects: Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: David Wallace
Date Deposited: 29 Aug 2018 00:21
Last Modified: 29 Aug 2018 00:21
Item ID: 14983
Subjects: Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Specific Sciences > Physics > Symmetries/Invariances
Date: August 2018
URI: http://philsci-archive.pitt.edu/id/eprint/14983

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item