arXiv subjects

Aleksandra A. Ziolkowska

Publications and source records attributed to Aleksandra A. Ziolkowska.

5 recordsLinked to original sources

arXiv2026

Permutation-symmetric quantum trajectories

We show how one may perform a stochastic unravelling which respects weak permutation symmetry for general models of $N$ emitters coupled to a common system (e.g. a cavity mode). Our work extends prior work by Zhang et al. [2018 New J. Phys. 20 112001] which provided an efficient quantum jump approach for a restricted subset of such problems. For problems involving $2$-level emitters, such an unravelling reduces the computational cost from $\mathcal{O}(N^5)$ to $\mathcal{O}(N^2)$, and with additional refinements, allows reduction to $\mathcal{O}(N)$. This significantly increases the range of system sizes for which one can model exact quantum dynamics of such systems. We further show how the method can also be applied to $d$-level systems, with computational effort scaling as $\mathcal{O}(N^{d(d-1)/2})$, and we show it allows large-$N$ simulations for $d=3$.

quant-ph↗

arXiv2026

Is Lindblad for me?

The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new research areas including open quantum many-body systems, non-equilibrium condensed matter, and the possibility to test its limits in driven-open quantum simulators, call for a critical revision of its regimes of applicability. In this pedagogical review, we re-examine the folklore surrounding its three standard approximations (Born, Markov, and Rotating Wave Approximation), as we build our narrative by employing a series of examples and case studies accessible to any reader with a solid background on the fundamentals of quantum mechanics. As a synthesis of our work, we offer a checklist that contrasts common lore with refined expectations, offering a practical guideline for assessing the breakdown of the Lindblad framework in the problem at hand.

quant-ph↗

arXiv2026

Quantum fluctuations and chaos in fully connected spin models

We investigate beyond-mean-field dynamics in a fully connected $\mathrm{SU}(3)$ spin-exchange model, focusing on the interplay between chaotic dynamics and quantum fluctuations. Using the two-particle irreducible (2PI) effective action formalism, we derive equations of motion that systematically account for higher-order correlations generated by interactions, and demonstrate how quantum fluctuations can regularize chaotic dynamics displayed by macroscopic observables. Our results show that an accurate treatment of fluctuations is essential for describing macroscopic dynamics in quantum many-body systems and promote 2PI as a robust framework for connecting microscopic correlations to macroscopic nonequilibrium phenomena.

cond-mat.stat-mech↗

arXiv2025

The deep Hilbert space of all-to-all interacting SU(3) atoms: from quantum to classical

We study the emergence of chaos in multilevel atoms with all-to-all interactions, inspired by cavity QED. Focusing on a 3-level Tavis-Cummings model in a far detuned limit, we detail its deep Hilbert space structure -- i.e. we enumerate all distinct dynamical sectors, beyond the totally symmetric subspace -- by using the Schur-Weyl duality, which is applicable thanks to the permutation symmetry in the all-to-all Hamiltonian. Strong Hilbert space fragmentation ensues from the non-abelian nature of the symmetry, with some sectors displaying regular dynamics and others being chaotic. We uncover that many permutation symmetry sectors contribute to the dynamics in the classical limit, in addition to the commonly studied totally symmetric subspace. To elucidate the dynamical responses in each of the symmetry sectors, we propose a semiclassical description in terms of spin coherent states, which is also able to explain the origin of chaotic or regular dynamics with a simple geometrical argument. Our work contributes to the study of the quantum-classical correspondence in chaotic systems, and uncovers a rich structure in multilevel all-to-all interacting models.

quant-ph↗

arXiv2019

Yang-Baxter integrable Lindblad equations

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.

cond-mat.stat-mech↗