Related papers: Universal Hypothesis of Autocorrelation Function f…
In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…
This paper considers the problem of estimating the time auto-correlation function for a quantity that is defined in configuration space, given a knowledge of the mean-square displacement as function of time in configuration space. The…
We show in full generality that time-correlation function of a physical observable analytically continued to imaginary time is a tau-function of integrable Toda hierarchy. Using this relation we show that the singularity along the imaginary…
We study real-time local correlators $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle$ in chaotic quantum many-body systems. These correlators show universal structure at late times, determined by the dominant operator-space Feynman…
We show that Hall's exact uncertainty relation acquires a simple geometric form in the Krylov basis generated by the Liouvillian. In this canonical operator frame, the uncertainty equality implies that the operator amplitude vector evolves…
Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…
The universal quantum work relation connects a functional of an arbitrary observable averaged over the forward process to the free energy difference and another functional averaged over the time-reversed process. Here, we ask the question…
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…
Through an explicit construction, we assign to any infinite temperature autocorrelation function $C(t)$ a set of functions $\alpha^n(t)$. The construction of $\alpha^n(t)$ from $C(t)$ requires the first $2n$ temporal derivatives of $C(t)$…
We introduce a general procedure for computing higher-order moments of correlation functions in open quantum systems, extending the scope of our recent work on Memory Kernel Coupling Theory (MKCT) [W. Liu, Y. Su, Y. Wang, and W. Dou,…
The resolvent Krylov subspace method builds approximations to operator functions $f(A)$ times a vector $v$. For the semigroup and related operator functions, this method is proved to possess the favorable property that the convergence is…
This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…
We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average…
Nuclear mass autocorrelations are investigated as a function of the number of nucleons. The fluctuating part of these autocorrelations is modeled by a parameter free model in which the nucleons are confined in a rigid sphere. Explicit…
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the…
This paper presents a study of the inherent structural properties of Krylov subspaces, in particular for the self-adjoint class of operators, and how they relate with the important phenomenon of `Krylov solvability' of linear inverse…
We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional…
Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems,…