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. 

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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.

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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. 

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.

Recently Parity-Time reversal (PT) symmetric non-Hermitian quantum mechanics has gained greater interest, especially in non-equilibrium physics and open systems. In this talk we consider a CFT with non-Hermitian effect localized on the boundary, and its holographic dual using AdS/BCFT correspondence. Our discussion includes the spontaneous breaking of PT-symmetry, and phase transitions associated with it. We also discuss Wick rotated setup where non-Hermitian effects creates a new kind of quantum quenched states, which exhibit faster growth of entanglement entropy than that of standard Cardy states. This talk is based on arXiv: 2606.18629.

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BMN matrix quantum mechanics is a mass deformation of the BFSS matrix model that lifts the flat directions, providing a controlled setting for studying protected sectors of D0-brane holography. In this talk I will explain how protected quantities in BMN matrix quantum mechanics can be used to probe black-hole microstates. I will first review the relation between BFSS/BMN matrix quantum mechanics and D0-brane black holes, emphasizing how the BMN deformation lifts the flat directions and makes protected counting well-defined. I will then describe the finite-N BMN Witten index across vacuum sectors, where the all-sector computation exhibits an N^2 entropy signal and identifies the vacuum sectors that dominate the protected count. Finally, I will discuss why Q-cohomology contains finer information than the index, as well as a mass-flow argument showing that BMN Q-cohomology is invariant under changes of the mass parameter at nonzero mass, subject to analytic domain control. The broader goal is to use protected BMN sectors as a sharp window into the microscopic structure of holographic black holes.

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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.

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