Quantum turbulence is a far-from-equilibrium process characterized by high nonlinearity. Holographic duality provides a systematic framework for simulating the decaying (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional quantum turbulence by numerically solving the dual Abelian-Higgs theory in a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>4</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional black hole background. We reveal that different types of decay behavior of the total vortex line density <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> emerge depending on the initial vortex line density, ranging from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>∼</mo><msup><mi>t</mi><mrow><mo>−</mo><mn>1.5</mn></mrow></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>L</mi><mo>∼</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, similar to the experimental observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mn>3</mn></mmultiscripts></mrow></math> in Bradley et al. [<a href="http://dx.doi.org/10.1103/PhysRevLett.96.035301">Phys. Rev. Lett. 96, 035301 (2006)</a>], and of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mn>4</mn></mmultiscripts></mrow></math> in Stalp et al. [<a href="http://dx.doi.org/10.1103/PhysRevLett.82.4831">Phys. Rev. Lett. 82, 4831 (1999)</a>] and in Walmsley and Golov [<a href="http://dx.doi.org/10.1103/PhysRevLett.118.134501">Phys. Rev. Lett. 118, 134501 (2017)</a>]. Furthermore, by measuring the energy flux at the black hole horizon, we determine that the energy dissipation rate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>t</mi></math> is proportional to the square of the total vortex line density, consistent with the vortex line decay equation proposed by W. F. Vinen and also the experimental measurement in <a href="http://dx.doi.org/10.1038/nphys1963">Nat. Phys. 7, 473 (2011)</a>.

China

Hua-Bi Zeng

Chuan-Yin Xia

Japan

Wei-Can Yang

Yu Tian

Makoto Tsubota

Dissipation and Decay of Three-Dimensional Holographic Quantum Turbulence

In the framework of the AdS/CFT correspondence, we find a neutral complex scalar field dynamics in a <math><mn>2</mn><mo>+</mo><mn>1</mn></math>-dimensional black hole background which can provide a scheme for studying the pattern formation process in <math><mn>1</mn><mo>+</mo><mn>1</mn></math>-dimensional reaction-diffusion systems. The patterns include plane wave, defect turbulence, phase turbulence, spatiotemporal intermittency where defect chaos coexists with a stable plane wave, and coherent structures. A phase diagram is obtained by studying the linear instability of the plane wave solutions to determine the onset of the holographic version of the Benjamin-Feir-Newell instability. Near the critical temperature, the holographic model is dual to the one-dimensional complex Ginzburg-Landau equation (CGLE), which has been studied extensively in reaction-diffusion systems, while at low temperature the holographic theory is different from CGLE.

Pattern formation from gauge/gravity duality

We study the interface dynamics in immiscible binary superfluids using its holographic description, which naturally consists of an inviscid superfluid component and a viscous normal fluid component. We give the first theoretical realization of interface instability for two superfluid components moving with identical velocity, providing a quantum analog to the flapping of flags that is common in daily life. This behavior is in sharp contrast to the one from Gross-Pitaevskii equation for which no such co-flow instability develops in an isolated uniform system because of Galilean invariance. The real time evolution triggered by the dynamical instability exhibits intricate nonlinear patterns leading to quantum turbulence reminiscent of the quantum Kelvin-Helmholtz instability. Moreover, we show that such interface dynamics is essentially different from the Landau instability for which the frictionless flow becomes thermodynamically unstable above a critical superfluid velocity. Our study uncovers the rich interface dynamics of quantum fluids and the emergence of complex flow phenomena.

Yu-Ping An

Li Li

Quantum analog to flapping of flags: interface instability for co-flow binary superfluids

General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants $$\beta _{n}$$ <math> <msub> <mi>β</mi> <mi>n</mi> </msub> </math> and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

Mexico

Omar Rodríguez-Tzompantzi

Faddeev–Jackiw Hamiltonian formulation for general exotic bi-gravity

We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models for Euclidean quantum gravity originally proposed by John Barrett and collaborators. A perturbative solution is found for the first twenty moments using the Schwinger-Dyson equations and properties of certain bi-colored unstable maps associated to the model. We then apply a result of Guionnet et al. to show that the perturbative and convergent solution coincide for a small neighbourhood of the coupling constants. For each model we compute an explicit expression for the free energy, critical points, and critical exponents in the large N limit. In particular, the string susceptibility is found to be γ = 1/2, hinting that the associated universality class of the model is the continuous random tree.

Canada

Masoud Khalkhali

Nathan Pagliaroli

Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

India

Siddharth Prabhu

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

We employ the Einstein-Abelian-Higgs theory to investigate the structure of vortex-antivortex lattices within a superconductor driven by spatial periodic magnetic fields. By adjusting the parameters of the external magnetic field, including the period (<math><mrow><mi>T</mi></mrow></math>) and the amplitude (<math><msub><mi>B</mi><mn>0</mn></msub></math>), various distinct vortex states emerge. These states encompass the Wigner crystallization state, the vortex cluster state, and the suppressed state. Additionally, we present a comprehensive phase diagram to demarcate the specific regions where these structures emerge, contributing to our understanding of superconductivity in complex magnetic environments.

Jia-Hao Su

Vortex-antivortex lattices in a holographic superconductor

We study the nonlinear dynamical evolution of spinodal decomposition in a first-order superfluid phase transition using a simple holographic model in the probe limit. We first confirm the linear stability analysis based on quasinormal modes and verify the existence of a critical length scale related to a gradient instability — negative speed of sound squared — of the superfluid sound mode, which is a consequence of a negative thermodynamic charge susceptibility. We present a comparison between our case and the standard Cahn-Hilliard equation for spinodal instability, in which a critical length scale can be also derived based on a diffusive instability. We then perform several numerical tests which include the nonlinear time evolution directly from an unstable state and fast quenches from a stable to an unstable state in the spinodal region. Our numerical results provide a real time description of spinodal decomposition and phase separation in one and two spatial dimensions. We reveal the existence of four different stages in the dynamical evolution, and characterize their main properties. Finally, we investigate the strength of dynamical heterogeneity using the spatial variance of the local chemical potential and we correlate the latter to other features of the dynamical evolution.

Xin Zhao

Zhang-Yu Nie

Zi-Qiang Zhao

Matteo Baggioli

Dynamical evolution of spinodal decomposition in holographic superfluids

Continuing the previous initiatives [1, 2], we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which individually generate non-orthogonal subspaces. Unlike the previously studied Arnoldi iteration, this algorithm renders the Lindbladian into a purely tridiagonal form, thus opening up a possibility to study a wide class of dissipative integrable and non-integrable systems by computing Krylov complexity at late times. Our study relies on two specific systems, the dissipative transverse-field Ising model (TFIM) and the dissipative interacting XXZ chain. We find that, for the weak coupling, initial Lanczos coefficients can efficiently distinguish integrable and chaotic evolution before the dissipative effect sets in, which results in more fluctuations in higher Lanczos coefficients. This results in the equal saturation of late-time complexity for both integrable and chaotic cases, making the notion of late-time chaos dubious.

Poland

Aranya Bhattacharya

Pratik Nandy

Pingal Nath

Himanshu Sahu

On Krylov complexity in open systems: an approach via bi-Lanczos algorithm

We study integrable deformations of two-dimensional non-linear σ-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2, ℝ) bi-Yang-Baxter model, we show that our solutions can be mapped to the known complex uniton solutions of the SU(2) bi-Yang-Baxter model. In general, our solutions are constructed from so-called Sl(2)-orbits that play a central role in the study of asymptotic Hodge theory. This provides further evidence for a close relation between integrable non-linear σ-models and the mathematical principles underlying Hodge theory. We have also included a basic introduction to the relevant aspects of asymptotic Hodge theory and have provided some simple examples.