相关论文: Operator growth in open quantum systems: lessons f…

Sachdev-Ye-Kitaev (SYK) model has emerged as a new paradigm of the non-Fermi-liquid behavior. Here we investigate a possibility of having a superconducting off-diagonal long-range order (ODLRO) and a pseudogap phase within the SYK…

We consider the Sachdev-Ye-Kitaev (SYK) model where interaction involves $q$ fermions at a time. We find the next order correction to the thermal two-point function in the large $q$ expansion. Using this result we find the next order…

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…

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical…

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…

We propose a way to understand the evolution of an open quantum system using a description that dispenses a continuous evolution in time, by discrete operators entangled states, in its most direct and fundamental way. We show that the…

We prove bounds on operator growth and infinite temperature out-of-time-ordered correlators in many-body systems with $N$ spin-$\frac{1}{2}$ degrees of freedom which interact via two-body all-to-all interactions. Our results parametrically…

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 high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed…

This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…

Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are prerogative of quantum chaotic systems and how they relate to more standard…

We consider operator growth for generic large-N gauge theories at finite temperature. Our analysis is performed in terms of Fourier modes, which do not mix with other operators as time evolves, and whose correlation functions are determined…

"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…

We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, $N$ fermions with a $q$-body interaction of infinite range, coupled to a Markovian environment. Close to the infinite-temperature steady state, the real-time…

We illustrate the equivalence between the non-unitary evolution of an open quantum system governed by a Markovian master equation and a process of continuous measurements involving this system. We investigate a system of two coupled modes,…

We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to…

We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N , the standard result for the q-local, all-to-all SYK,…

We study the time evolution governed by the two-sided chord Hamiltonian in the double-scaled SYK model, which induces a probability distribution over operators in the double-scaled algebra. Through the bulk-to-boundary map, this…

We consider a collection of Markov chains that model the evolution of multitype biological populations. The state space of the chains is the positive orthant, and the boundary of the orthant is absorbing representing the extinction states…

The out-of-time-ordered correlator has been proposed as an indicator of chaos in quantum systems due to its simple interpretation in the semiclassical limit. In particular, its rate of possible exponential growth at $\hbar \to 0$ is closely…