TALKS

One of the criteria for the Quantum Chaos is through the OTOC. We evaluate this in the bulk with the corresponding operators at the boundary in various geometries, and discuss the physical implication. 

TBA

TBA

The formation of topological defects during continuous phase transitions exhibits nonequilibrium universality. While the Kibble-Zurek mechanism (KZM) predicts universal scaling of point-like defect numbers under slow driving, the statistical properties of extended defects remain largely unexplored across both slow and fast protocols. We investigate vortex string formation in a three-dimensional holographic superfluid. For slow quenches, the vortex string number follows KZM scaling, while for rapid quenches, it exhibits complementary universal scaling governed by the final temperature. Beyond the vortex string number, the loop-length distribution reveals a richer structure: individual loops follow the first-return statistics of three-dimensional random walks, $P(\ell)\sim\ell^{-5/2}$ for loops of length $\ell\ll L^2$, while for longer loops, $\ell>>L^2$ it crosses over to $P(\ell)\sim\ell^{-1}$. While the total vortex length distribution remains Gaussian, its cumulants obey universal scaling laws with varying power-law exponents, and thus differ markedly from those observed in point-defect systems, indicating distinct statistical features of extended topological defects.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the AdS/CFT correspondence by solving the Einstein-Abelian-Higgs model in an AdS4 black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

TBA

TBA

TBA

TBA

TBA

Recently, together with a collaborator, I proposed a prescription for incorporating Lindblad dynamics into AdS/CFT, in which the CFT is treated as an open system with a corresponding holographic dual. Meanwhile, the Brownian motion of a probe quark in a holographic CFT is another well-known prototypical example of an open system in holography. In this talk, I will present a derivation of the Lindbladian for such a quark in the high-temperature regime and analyze operator expectation values and variances in a simple example.

TBA

Complexity is becoming an ever more popular probe of the dynamics of complex systems, with applications in high energy physics, condensed matter physics and quantum information. On the other hand quantum (random) walks are a useful tool for the investigation of quantum algorithms and their potential speed-ups, as well as the foundation for a universal model of quantum computation. As such the study of their complexity properties is a natural direction, which however has been primarily explored using more traditional quantum computing definitions.

In this talk I will show that the notion of Krylov complexity is entwined with that of quantum walks, thus uniting these two big areas of research. In particular, one can always reduce the dynamics of a walk on an arbitrary graph to a so-called Krylov chain, using a simple graphical algorithm that produces the Lanczos coefficients. The importance of this interplay is two-fold, as it allows us to assign families of graphs to well-known classes of dynamics and conversely to study graphs that naturally arise in certain complex systems. In order to illustrate the utility of this framework I will discuss how it can be used to better understand the dynamics of the SYK model and black holes. 

In this talk, we will review some recent work that can be interpreted as a time-like version of quantum entanglement. In particular, we will focus on a particular proposal, based on correlation functions of self-adjoint operators, that provides us with interesting universal results, as well as sheds light on the specific nature of the underlying dynamics. We will also offer some comments on two-dimensional CFT, where the time-like entanglement can be understood in terms of conformal transformations.

I will report on recent work on complexity in de Sitter spacetime under various different but complementary proposals for dS Holography.

TBA

TBA