Related papers: Dependence of Krylov complexity on the initial ope…
Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open…
Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time…
We investigate Krylov complexity in open quantum systems using Lindblad master equations for bosonic bath models, with particular emphasis on the Caldeira--Leggett model. Krylov complexity is computed from the moments of the two-point…
In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos. However,on several occasions, it has been argued that, even in integrable systems, OTOC can grow…
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…
In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and non-integrable…
We present a framework for investigating wave function spreading in $\mathcal{PT}$-symmetric quantum systems using spread complexity and spread entropy. We consider a tight-binding chain with complex on-site potentials at the boundary…
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…
We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators…
We investigate signatures of quantum chaos in the mixed-field quantum Ising model on finite-size Erd\H{o}s-R\'enyi graphs using probes scalable on near-term quantum devices. By tuning the graph connectivity, the system exhibits a crossover…
We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
We introduce the Krylov distribution $\mathcal{D}(\xi)$, a static Krylov-space diagnostic that characterizes how inverse-energy response is organized in Hilbert space. The central object is the resolvent-dressed state…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
The asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. The long-time limit of this distribution is shown to exist and to depend on the initial…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method. The mathematics of…
In this paper, we investigate the dynamics of a non-Hermitian SSH model that arises out of the no-click limit of a monitored SSH model in the Krylov space. We find that the saturation timescale of the complexity associated with the spread…
We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian noise. We compute and analyze the quantum Krylov complexity and the spectral form factor for…
We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ Majorana fermions with $q$-body fermion interaction with $q=4,6,8$ for a range of sparse parameter $k$ that controls the number of remaining terms in…