Equations describing the macroscopic dynamics of complex materials are traditionally derived by a systematic symmetry-based approach. A model derived in this way usually contains a number of unknown parameters that have to be estimated from data; either from experiments or simulations. With a suitable regression method, not only the parameters, but also the dynamic equations themselves can be extracted directly from data, bypassing the need for a traditional derivation. In this talk, I will present such a method, based on the SINDy (Sparse Identification of Nonlinear Dynamics) framework, a weak formulation of the dynamics and a novel model selection measure. Using this method, we were able to extract partial differential equations governing the dynamics of a simple fluid from simulations based on a particle model — dissipative particle dynamics. These equations were the mass continuity equation and a form of the Navier-Stokes equation, the latter containing the correct pressure equation of state. The talk is based on our recently published article (https://doi.org/10.1016/j.cma.2024.117379).

I am going to talk about a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of symplectic dynamics in two orthogonal (time and space) directions. In close analogy with quantum dual-unitary circuits, one can prove that two-point dynamical correlation functions are nonvanishing only along the edges of the light cones. The dynamical correlations are exactly computable in terms of a one-site Markov transfer operator, which is generally of infinite dimensionality. The theory is tested for a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain. Remarkably, expressing these models in the form of a composition of rotations leads to a transfer operator with a block diagonal form in the basis of spherical harmonics. This allows for obtaining, analytical predictions for simple local observables. 

While the notion of quantum chaos is tied to random-matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into such eigenstate properties can be obtained by the recently introduced partial spectral form factor, which captures correlations between eigenstates. Here, we study the partial spectral form factor in chaotic dual-unitary quantum circuits. We compute the latter for a finite connected subsystem in a brickwork circuit in the thermodynamic limit, i.e., for an infinite complement. For initial times, shorter than the subsystem’s size, spatial locality and (dual) unitarity implies constant partial spectral form factor, clearly deviating from the linear ramp of the partial spectral form factor in random matrix theory. In contrast, for larger times we prove, that the partial spectral form factor follows the random matrix result up to exponentially suppressed corrections. We supplement those exact results by semi-analytic computations performed directly in the thermodynamic limit.

Many physical systems admit a simplified description of their dynamics when examined at macroscopic scales. This simplified description—generally referred to as hydrodynamics—is governed by a restricted set of macroscopic observables that includes conserved quantities, Goldstone modes, and order parameters. An outstanding challenge in quantum many-body physics is finding this hydrodynamic description in terms of the microscopic variables. I will present a method inspired by holography for constructing the effective hydrodynamic description in the form of a transfer matrix and a set of hydrodynamically-relevant variables. The method proceeds by constructing an alternative representation of the operator dynamics in the form of a local (1+1)d “bulk” theory. I will show how the properties of the auxiliary bulk encode the existence of an effective local equation of motion of a given model, allowing for the extraction of hydrodynamic parameters like diffusion constants and characteristic thermalization scales. I will show results for various qubit and fermionic systems, and compare to the known literature.

The black hole complementarity principle is a conjectured solution to the black hole information loss paradox. In this talk, we will explore how the complementarity principle can emerge in a way that is consistent with quantum information theory via explicit microscopic models that preserve unitarity and a local semi-classical description of the black hole horizon. In particular, we will consider simple toy models where simple quantum systems are coupled to a black hole and show how the initial state of the quantum system is encoded both into the late-time quantum trajectory of the quantum system as well as the late-time (non-linear) ringdown of the black hole. Such models provide insights into how information can be encoded in the interior and exterior of black holes without encountering paradoxes.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density P(I) for the single-point intensity I decays as a powerlaw for large intensities: P(I) ∼ I −(M+2), provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law P(I) ∼ exp(−I/I) which turns out to be valid only in the limit M → ∞. We also find the joint probability density of intensities I1, . . . , IL in L > 1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For L → ∞ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

I will present our on-going work on quantum time evolution after a local quench at an interface between paramagnetic and ferromagnetic regions of a transverse field Isingmodel. The two regions are related by the Kramers-Wannier duality and thus support elementary excitations with the same energy dispersion but different physical nature. For open chain geometry a novel symmetry appears, a combination of the Kramers-Wannier transformation and a reflection, which squares to the Ising Z_2 symmetry. I will also present our first numerical results of time evolution at the interface.

Large-N quantum field theories are a playground for doing non-perturbative physics. Certain large-N theories turn out to be asymptotically free in d=4 and have features like bound states, just like quantum chromodynamics (QCD) and Yang–Mills theories. Their asymptotic freedom is connected to their apparent non-Hermiticity. However, when coupled with an antilinear symmetry, in many cases referred to as PT symmetry, this non-Hermicity does not prevent such theories from having real, bounded spectra and a notion of unitarity. It’s possible to calculate equations of state, phase diagrams, and transport coefficients like shear viscosity η/s in these theories. I will talk in particular about the O(N) model, which is relevant to Higgs physics when N=4. I’ll discuss the phase structure at large N. There is a first-order phase transition at finite temperature, which has implications for cosmology. In particular, the stable vacuum is not the spontaneous symmetry broken (SSB) vacuum, as is otherwise assumed in the Standard Model of particle physics. I’ll demonstrate how one can generate “mass from nothing”, without SSB, when a massless Higgs field is coupled to a U(1) Abelian gauge field. Lastly, I’ll briefly talk about how large-N techniques in the O(N) model are analogous to a method for non-perturbative analytical calculations in QCD and Yang–Mills theories, via so-called Rn resummation methods. This analogy might allow a study of the phase structure, transport coefficients, and confinement in QCD and Yang–Mills, with applications to the quark–gluon plasma and neutron stars.