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Operator growth in open quantum systems: lessons from the dissipative SYK
A bstract We study the operator growth in open quantum systems with dephasing dissipation
terms, extending the Krylov complexity formalism of [1]. Our results are based on the study of …
terms, extending the Krylov complexity formalism of [1]. Our results are based on the study of …
Universal chaotic dynamics from Krylov space
A bstract Krylov complexity measures the spread of the wavefunction in the Krylov basis,
which is constructed using the Hamiltonian and an initial state. We investigate the evolution …
which is constructed using the Hamiltonian and an initial state. We investigate the evolution …
Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
A bstract We use Krylov complexity to study operator growth in the q-body dissipative
Sachdev-Ye-Kitaev (SYK) model, where the dissipation is modeled by linear and random p …
Sachdev-Ye-Kitaev (SYK) model, where the dissipation is modeled by linear and random p …
Krylov complexity in quantum field theory, and beyond
A bstract We study Krylov complexity in various models of quantum field theory: free massive
bosons and fermions on flat space and on spheres, holographic models, and lattice models …
bosons and fermions on flat space and on spheres, holographic models, and lattice models …
Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
A bstract Using spread complexity and spread entropy, we study non-unitary quantum
dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the …
dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the …
Quantum dynamics in Krylov space: Methods and applications
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 …
space, known as the Krylov space. This review presents the use of Krylov subspace …
Spread and spectral complexity in quantum spin chains: from integrability to chaos
A bstract We explore spread and spectral complexity in quantum systems that exhibit a
transition from integrability to chaos, namely the mixed-field Ising model and the next-to …
transition from integrability to chaos, namely the mixed-field Ising model and the next-to …
Spread complexity as classical dilaton solutions
We demonstrate a relation between Nielsen's approach toward circuit complexity and Krylov
complexity through a particular construction of quantum state space geometry. We start by …
complexity through a particular construction of quantum state space geometry. We start by …
Dynamical actions and q-representation theory for double-scaled SYK
A bstract We show that DSSYK amplitudes are reproduced by considering the quantum
mechanics of a constrained particle on the quantum group SU q (1, 1). We construct its left …
mechanics of a constrained particle on the quantum group SU q (1, 1). We construct its left …
Krylov complexity in Lifshitz-type scalar field theories
We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar
theories, characterized by their integer dynamical exponent, at finite temperature. In this non …
theories, characterized by their integer dynamical exponent, at finite temperature. In this non …