Nonequilibrium Dynamics and Weakly Broken Integrability

Durnin, Joseph; Bhaseen, M. J.; Doyon, Benjamin

doi:10.1103/physrevlett.127.130601

Cited by 50 publications

(35 citation statements)

References 85 publications

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“…First, it would be useful to formulate the BGR at a junction, with a minimal set of phenomenological parameters (∼ generalised resistances) which encode the transport properties of multiple conserved quantities, without the need to fully solve the dynamics. Secondly, here, we focused on the case where the bulk Hamiltonian is free and interacting-integrable bulk Hamiltonians are a natural next step to be addressed: the study of collision terms in the framework of Generalized Hydrodynamics is still at its infancy [70][71][72], but an analysis in the same spirit of our kinetic equation can be envisaged. Beside integrability, there are several ways to hinder thermalisation while retaining non-trivial transport, such as Hilbert space fragmentation [9,73] and it is natural to wonder about interfaces between fragmenting and non-fragmenting Hamiltonians.…”

Section: Discussionmentioning

confidence: 99%

“…Ref. [71]), but this approach is very costly already in the homogeneous case, hence the inhomogeneous Boltzmann equation (where the collision integral must be computed at each point on the space grid) seems out of reach. In order to tackle these technical difficulties, we devised a new algorithm presented in the next section, which can efficiently compute I k .…”

Section: B Derivation Of the Boltzmann Equationmentioning

confidence: 99%

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Transport through interacting defects and lack of thermalisation

2022

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We consider 1D integrable systems supporting ballistic propagation of excitations, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. Focusing on classical systems, we study an out-of-equilibrium protocol engineered activating the defect in an initially homogeneous and far from the equilibrium state. We find that large enough defects induce full thermalisation at their center, but nonetheless the outgoing flow of carriers emerging from the defect is non-thermal due to a generalization of the celebrated Boundary Thermal Resistance effect, occurring at the edges of the chaotic region. Our results are obtained combining ab-initio numerical simulations for relatively small-sized defects, with the solution of the Boltzmann equation, which becomes exact in the scaling limit of large, but weak defects.

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Section: Discussionmentioning

confidence: 99%

Section: B Derivation Of the Boltzmann Equationmentioning

confidence: 99%

Transport through interacting defects and lack of thermalisation

2022

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“…Secondly, from our "operatorial" GHD equation it should be possible to derive corrections to GHD [55][56][57][58][59] in a systematic fashion. Finally, our approach can be used to study the effects of general weak integrability breaking interactions [60][61][62][63][64][65][66][67]. An important goal is to investigate how, and over what time-scales, they render perturbed GHD descriptions invalid.…”

mentioning

confidence: 99%

BBGKY Hierarchy and Generalised Hydrodynamics

Bertini,

Essler,

Granet

2022

Preprint

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We consider fermions defined on a continuous one-dimensional interval and subject to weak repulsive two-body interactions. We show that it is possible to perturbatively construct an extensive number of mutually compatible conserved charges for any interaction potential. However, the contributions to the densities of these charges at second order and higher are generally non-local and become spatially localized only if the potential fulfils certain compatibility conditions. We prove that the only solution to the first of these conditions with strictly local densities of charges is the Cheon-Shigehara potential (fermionic dual to the Lieb-Liniger model), and observe numerically that the only other solutions appear to be the Calogero-Sutherland potentials. We use our construction to show how Generalized Hydrodynamics (GHD) emerges from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and argue that GHD in the weak interaction regime is robust under non-integrable perturbations.

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“…Recent kinematic approaches offer a description of integrability-breaking scattering processes consistent with Fermi's golden rule [11][12][13][14]. The description permits a particular scenario owing to the fermionic nature of the occupied rapidities: Following a scattering event, if all allowed rapidities of the out-going state are already occupied, the process becomes Pauli blocked.…”

mentioning

confidence: 99%

“…However, if the energy of a particle collision exceeds twice the transverse level spacing, a transverse excitation can occur [22]. For such integrability-breaking scattering processes one can associate the in and out states with particles and holes [11]. Here, the collision creates two particle-hole pairs, where the rapidities of the particles are much smaller than those of the holes, reflecting the gain in transverse potential energy.…”

mentioning

confidence: 99%

Emergent Pauli blocking in a weakly interacting Bose gas

Cataldini¹,

Møller²,

Tajik³

et al. 2021

Preprint

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We experimentally study the dynamics and relaxation of a single density mode in a weakly interacting Bose gas trapped in a highly elongated potential. Although both the chemical potential and thermal energy of the gas exceed the level spacing of the transverse potential, we find that the observed dynamics are accurately described by the one-dimensional, integrable theory of generalized hydrodynamics. We attribute the absence of thermalization to the suppression of three-dimensional excitations, as outgoing states of the associated scattering processes obey fermionic statitistics, thus being susceptible to the Pauli exclusion principle. The mechanisms effectively preserves onedimensionality, and hence integrability, far beyond conventional limits.

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Nonequilibrium Dynamics and Weakly Broken Integrability

Cited by 50 publications

References 85 publications

Transport through interacting defects and lack of thermalisation

Transport through interacting defects and lack of thermalisation

BBGKY Hierarchy and Generalised Hydrodynamics

Emergent Pauli blocking in a weakly interacting Bose gas

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