Wallace, David (2018) Spontaneous Symmetry Breaking in Finite Quantum Systems: a decoherent-histories approach. [Preprint]
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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.
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| Item Type: | Preprint | ||||||
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| Subjects: | Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Professor 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 |
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| Date: | August 2018 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/14983 |
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