Mastodawn

On March 17-19, there will be a hybrid #HUBerlin /online workshop on theoretical #physics with a special emphasis on fostering collaboration with Ukrainian researchers. Topics are #quantumFieldTheory, #integrability, and #mathematics in theoretical physics. There are several rather high-profile speakers, it could be interesting to watch online even if you can't make it in person. Registration ends today.
Schedule: https://indico.desy.de/event/52099/
Signup : https://forms.cloud.microsoft/pages/responsepage.aspx?id=aTCtyIa26kCyIS9CnXNlGeD0AooaoWlIoGxvStWJhz5UMlI1OFBPSlA1SklBUlNCVEo5VlZVU0pBWS4u&route=shorturl

KMPB-Ukraine Workshop

DESY-Konferenzverwaltung (Indico)

Claudio Conti Oct 6, 2024

Observation of 2D dam break flow and a gaseous phase of solitons in a photon fluid

https://arxiv.org/abs/2409.18738

#solitons #opticalsolitons #integrability #quantumfluids #physics

arXiv:2409.18738

We report the observation of a two-dimensional dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to two-dimensional (2D) nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D solitons gas in integrable systems. We measure the statistical features of this gaseous-like phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.

[complexlight.org](https://www.newcomplexlight.org/observation-of-2d-dam-break-flow-and-a-gaseous-phase-of-solitons-in-a-photon-fluid/)

[PhysRevLett.133.183801](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.183801)

Observation of 2D dam break flow and a gaseous phase of solitons in a photon fluid

We report the observation of a two-dimensional dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to two-dimensional (2D) nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D solitons gas in integrable systems. We measure the statistical features of this gaseous-like phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.

arXiv.org

katch wreck Aug 22, 2024

`Kakutani's theorem is a fundamental result on the equivalence or mutual singularity of countable product measures. It gives an "if and only if" characterisation of when two such measures are equivalent, and hence it is extremely useful when trying to establish change-of-measure formulae for measures on function spaces.`

https://en.wikipedia.org/wiki/Kakutani's_theorem_(measure_theory)

#measureTheory #math #mathematics #integrability

Kakutani's theorem (measure theory) - Wikipedia

Markus Heyl Nov 29, 2023

Identifying Quantum Many-Body Integrability and Chaos Using Eigenstate Trace Distances

While the concept of quantum many-body integrability is of fundamental relevance for the understanding of quantum matter, its precise definition has remained open so far. Here, we introduce an alternative indicator, which signals the expected behavior also for models such as the celebrated kicked top, where other established indicators face limitations.

https://link.aps.org/doi/10.1103/PhysRevLett.131.216701

#quantum #chaos #integrability

Identifying Quantum Many-Body Integrability and Chaos Using Eigenstate Trace Distances

While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this Letter, we introduce an alternative indicator for quantum many-body integrability and chaos, which is based on the statistics of eigenstates by means of nearest-neighbor subsystem trace distances. We show that this provides us with a faithful classification through extensive numerical simulations for a large variety of paradigmatic model systems including random matrix theories, free fermions, Bethe-ansatz solvable systems, and models of many-body localization. While existing indicators, such as those obtained from level-spacing statistics, have already been utilized with great success, they also face limitations. This concerns, for instance, the quantum many-body kicked top, which is exactly solvable but classified as chaotic in certain regimes based on the level-spacing statistics, while our introduced indicator signals the expected quantum many-body integrability. We discuss the universal behaviors we observe for the nearest-neighbor trace distances and point out that our indicator might be useful also in other contexts such as for the many-body localization transition.

Physical Review Letters

Erwin Schrödinger Institute Sep 5, 2023

It's a pleasure to announce that a new article has just been published by our recent research fellows Prof Sako and Prof Grosse as an outcome of their Research in Teams Project at @ESIVienna. 📑

🔵 Harald Grosse, Akifumi Sako: #Integrability of Φ
4 Matrix Model
as N-body Harmonic Oscillator System 🔵

Check out the article on https://arxiv.org/pdf/2308.11523.pdf

(Permission is given by the authors for using their figure from the paper for this post)

#MathematicalPhysics #HighEnergyPhysics
@univienna

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Stijn De Baerdemacker Dec 7, 2022

@j_bertolotti Interesting! Limiting scattering channels is something I associate with integrable systems (Bethe Ansatz). To some extent, factorizable interactions can be regarded as integrable, hence ... Would you happen to have a list of those reflectionless potentials? #BetheAnsatz #InfeldHull #integrability

Stijn De Baerdemacker Dec 2, 2022

Faribault and collaborators succeed in deriving Richardson-Gaudin 2RDMs in the Eigenvalue-based formalism, *without* the need of computing rapidities .... removing an important bottleneck in Richardson-Gaudin Geminal theory

https://doi.org/10.1063/5.0123911

#theochem #compchem #integrability #geminalttheory

Reduced density matrices/static correlation functions of Richardson–Gaudin states without rapidities

Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson–Gaudin states stand out as they are eigenvectors of a model Hamilt...

AIP Publishing