Related papers: Krylov Complexity in early universe
Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time…
We consider the recursion method applied to a generic 2pt function of a quantum system and show, in full generality, that the temperature dependence of the corresponding Lanczos coefficients is governed by integrable dynamics. After an…
A model of magnetic universe based on nonlinear electrodynamics has been introduced by Kruglov. This model describes an early inflation era followed by a radiation era. We show that this model is related to our model of universe based on a…
The inflationary cosmology is analyzed from the point of view of squeezed quantum states. As noted by Grishchuk and Sidorov, the amplification of quantum fluctuations into macroscopic perturbations which occurs during cosmic inflation is a…
We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans…
We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
The growing cosmological interest of different entropy functions (like the Tsallis entropy, the R\'{e}nyi entropy, the Barrow entropy, the Sharma-Mittal entropy, the Kaniadakis entropy and the Loop Quantum gravity entropy) naturally raises…
Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for…
We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to…
The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide an efficient description of quantum evolution and…
We analyze constraints on parameters characterizing the pre-inflating universe in an open inflation model with a present slightly open $\Lambda$CDM universe. We employ an analytic model to show that for a broad class of inflation-generating…
We study the evolution of spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe for chaotic and Starobinsky potentials in the framework of modified loop quantum cosmologies. These models result in a non-singular bounce as in loop…
In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density…
We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds…
We investigate a generalized entropic cosmology obtained by applying the gravity-thermodynamics conjecture to the Universe horizon using Kaniadakis statistics, namely a relativistic extension of the standard Boltzmann--Gibbs formalism. The…
Solving short and long time dynamics of closed quantum many-body systems is one of the main challenges of both atomic and condensed matter physics. For locally interacting closed systems, the dynamics of local observables can always be…
Methods and concepts for the study of phase transitions mediated by a time-dependent order-parameter field in curved spacetimes are discussed. A practical example is the derivation of an effective (quasi-)potential for the description of…
We propose a new four-parameter entropy function that generalizes the Tsallis, R\'{e}nyi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies for suitable limits of the parameters. Consequently, we address the early and…