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We study the flat spacetime dynamics of a classical field configuration corresponding to an ensemble of sine-Gordon kinks and antikinks, semiclassically coupled to a quantum field. This coupling breaks the integrability of the sine-Gordon model resulting in the background’s decay into quantum radiation as kink-antikink pairs annihilate. We find evidence that, on average, the energy of the ensemble scales as with and independent of the coupling strength or the mass of the quantum field. The generalization of this result to domain wall networks in higher spacetime dimensions could be relevant to particle production in the early universe.
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Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation
Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.
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- Award ID(s):
- 2104255
- PAR ID:
- 10338491
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 119
- Issue:
- 18
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2201804119
