English
Related papers

Related papers: KPZ scaling from the Krylov space

200 papers

We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…

Statistical Mechanics · Physics 2014-01-14 Silvia N. Santalla , Javier Rodriguez-Laguna , Rodolfo Cuerno

Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive…

Statistical Mechanics · Physics 2021-08-11 Tianshu Song , Hui Xia

We investigate the Krylov complexity of Schr\"odinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in…

High Energy Physics - Theory · Physics 2025-03-21 Peng-Zhang He , Hai-Qing Zhang

Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the…

High Energy Physics - Theory · Physics 2022-04-20 E. Rabinovici , A. Sánchez-Garrido , R. Shir , J. Sonner

Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, 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…

Quantum Physics · Physics 2023-12-15 Aranya Bhattacharya , Pratik Nandy , Pingal Pratyush Nath , Himanshu Sahu

We study the statistical properties of the spread complexity in the Krylov space of quantum systems driven across a quantum phase transition. Using the diabatic Magnus expansion, we map the evolution to an effective one-dimensional hopping…

Quantum Physics · Physics 2026-05-26 András Grabarits , Adolfo del Campo

We study in the present article the Kardar-Parisi-Zhang (KPZ) equation $$ \partial_t h(t,x)=\nu\Delta h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta(t,x), \qquad (t,x)\in\mathbb{R}_+\times\mathbb{R}^d $$ in $d\ge 3$ dimensions in the…

Analysis of PDEs · Mathematics 2018-01-24 Jacques Magnen , Jérémie Unterberger

The term 'KPZ' stands for the initials of three physicists, namely Kardar, Parisi and Zhang, which, in 1986 conjectured the existence of universal scaling behaviours for many random growth processes in the plane. A process is said to belong…

Probability · Mathematics 2024-10-11 Pantelis Tassopoulos

In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…

High Energy Physics - Theory · Physics 2023-06-09 Kiran Adhikari , Sayantan Choudhury

We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By…

Statistical Mechanics · Physics 2024-06-17 Pritha Dolai , Aditi Simha , Abhik Basu

Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($\xi$) are the only relevant lengths determining the scaling behavior. However, in cylindrical…

Statistical Mechanics · Physics 2024-05-06 Ismael S. S. Carrasco , Tiago J. Oliveira

In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture…

High Energy Physics - Theory · Physics 2026-04-23 Arpan Bhattacharyya , S. Shajidul Haque , Jeff Murugan , Mpho Tladi , Hendrik J. R. Van Zyl

Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that…

High Energy Physics - Theory · Physics 2024-03-14 Tran Quang Loc

Krylov complexity, as a novel measure of operator complexity under Heisenberg evolution, exhibits many interesting universal behaviors and also bounds many other complexity measures. In this work, we study Krylov complexity $\mathcal{K}(t)$…

High Energy Physics - Theory · Physics 2024-01-01 Haifeng Tang

This work investigates the origin of Kardar-Parisi-Zhang (KPZ) scaling in the phase dynamics of one-dimensional and two-dimensional polariton condensates. We demonstrate that the key mechanism leading to the observed power laws for the…

Mesoscale and Nanoscale Physics · Physics 2026-04-14 Denis Novokreschenov , Alexey Kavokin

Universal behavior in far-from-equilibrium systems is driven by interactions between transport processes and noise structure. The Kardar-Parisi-Zhang (KPZ) framework predicts that extensions incorporating conserved currents or temporally…

This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM). Krylov complexity quantifies how an operator evolves over time by expanding it in a series of…

Quantum Physics · Physics 2024-10-08 Niloofar Vardian

State-of-the-art tensor networks are employed to simulate the Hamiltonian ramp in the analog-digital quantum simulation of the quantum phase transition to the quasi-long-range ordered phase of the two-dimensional square-lattice $XX$ model…

Quantum Physics · Physics 2025-10-13 Yintai Zhang , Francis A. Bayocboc , Jacek Dziarmaga

We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the…

Statistical Mechanics · Physics 2016-05-04 Pierre Le Doussal , Satya N. Majumdar , Gregory Schehr

We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ),…

Statistical Mechanics · Physics 2026-03-04 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo