On the hydrodynamics of unstable excitations
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Springer
Received: June 3, 2020 Accepted: August 9, 2020 Published: September 7, 2020
On the hydrodynamics of unstable excitations
a
Department of Mathematics, City, University of London, 10 Northampton Square EC1V 0HB, U.K. b Department of Mathematics, King’s College London, Strand WC2R 2LS, U.K. c Dipartimento di Fisica e Astronomia, Universit` a di Bologna, Via Irnerio 46, I-40126 Bologna, Italy d INFN, Sezione di Bologna, Via Irnerio 46, I-40126 Bologna, Italy
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The generalized hydrodynamic (GHD) approach has been extremely successful in describing the out-of-equilibrium properties of a great variety of integrable many-body quantum systems. It naturally extracts the large-scale dynamical degrees of freedom of the system, and is thus a particularly good probe for emergent phenomena. One such phenomenon is the presence of unstable particles, traditionally seen via special analytic structures of the scattering matrix. Because of their finite lifetime and energy threshold, these are especially hard to study. In this paper we apply the GHD approach to a model possessing both unstable excitations and quantum integrability. The largest family of relativistic integrable quantum field theories known to have these features are the homogeneous sine-Gordon models. We consider the simplest non-trivial example of such theories and investigate the effect of an unstable excitation on various physical quantities, both at equilibrium and in the non-equilibrium state arising from the partitioning protocol. The hydrodynamic approach sheds new light onto the physics of the unstable particle, going much beyond its definition via the analytic structure of the scattering matrix, and clarifies its effects both on the equilibrium and out-of-equilibrium properties of the theory. Crucially, within this dynamical perspective, we identify unstable particles as finitely-lived bound states of co-propagating stable particles of different types, and observe how stable populations of unstable particles emerge in large-temperature thermal baths. Keywords: Field Theories in Lower Dimensions, Integrable Field Theories ArXiv ePrint: 2005.11266
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)045
JHEP09(2020)045
Olalla A. Castro-Alvaredo,a Cecilia De Fazio,a Benjamin Doyonb and Francesco Ravaninic,d
Contents 1
2 Introducing the model and main techniques 2.1 The model 2.2 Thermodynamic Bethe Ansatz for generalized Gibbs ensembles 2.3 Out-of-equilibrium steady states
4 4 6 9
3 Equilibrium physics with unstable particles 3.1 Energy current and energy density 3.2 Effective velocities 3.3 Spectral densities 3.4 Scattering, spectral densities and the unstable particle 3.5 Particle currents
10 10 11 14 15 17
4 Out-of-equilibrium dynamics with unstable particles 4.1 Energy currents and energy densities 4.2 Effective velocities 4.3 Spectral densities 4.4 Particle currents
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