Related papers: Krylov Complexity Under Hamiltonian Deformations a…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between…
The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
In recent years, growing attention has been devoted to the possibility that theories with deformed symmetries, associated with certain models of non-commutative spacetime, may encode a fundamental form of decoherence. This effect should be…
We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…
Predicting ground state energies of quantum many-body systems is one of the central computational challenges in quantum chemistry, physics, and materials science. Krylov subspace methods, such as Krylov Quantum Diagonalization and…
Stellar streams retain a memory of their gravitational interactions with small-scale perturbations. While perturbative models for streams have been formulated in action-angle coordinates, a direct transformation to these coordinates is only…
We consider the problem of model reduction for Markovian quantum systems whose dynamics are described by a time-dependent Lindblad generator -- notably, as arising in the presence of external control. Our approach, which builds upon Krylov…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
We analyse the Krylov solvability of inverse linear problems on Hilbert space $\mathcal{H}$ where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
Ultracold quantum gases are highly controllable and, thus, capable of simulating difficult quantum many-body problems ranging from condensed matter physics to astrophysics. Although experimental realizations have so far been restricted to…
Simulating quantum systems is one of the most promising tasks where quantum computing can potentially outperform classical computing. However, the robustness needed for reliable simulations of medium to large systems is beyond the reach of…
Krylov methods have reappeared recently, connecting physically sensible notions of complexity with quantum chaos and quantum gravity. In these developments, the Hamiltonian and the Liouvillian are tridiagonalized so that…