arXiv subjects

Lucas Sá

Publications and source records attributed to Lucas Sá.

At least 19 recordsLinked to original sources

arXiv2026

Dissipation-Induced Threshold on Integrability Footprints

The presence of a dissipative environment substantially disrupts unitary evolution. Nevertheless, key features of the evolution, such as its integrable or chaotic nature, are not immediately erased by dissipation. To understand this, we model environment-induced dissipation as a convex combination of unitary evolution and a random Kraus map, and examine how signatures of integrability gradually fade with increasing dissipation strength. Our analysis shows that in the weakly dissipative regime, the complex eigenvalue spectrum organizes into well-defined, high-density clusters. We estimate the critical dissipation threshold beyond which these clusters disappear, rendering the dynamics indistinguishable from chaotic evolution. This threshold depends only on the number of spectral clusters and the rank of the Kraus map. To characterize this transition, we introduce the eigenvalue angular velocity as a diagnostic of integrability loss. We illustrate our findings using several integrable quantum circuits, including the dissipative quantum Fourier transform. Our results provide a quantitative picture of how noise gradually erases the footprints of unitary integrability in open quantum systems.

quant-ph↗

arXiv2026

Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems

In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large-$N$ limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.

cond-mat.stat-mech↗

arXiv2026

Many-Body Quantum Chaos At All Time Scales

We describe the dynamics of many-body quantum chaotic systems at all time scales by studying the Green's and out-of-time order correlation (OTOC) functions of the four-body, $N$-Majorana Sachdev-Ye-Kitaev model. By combining the scramblon formalism and random-matrix-theory techniques, we obtain analytical expressions for these functions at all times. The early exponential growth of the OTOC is followed by an exponential decay at a rate governed by that of the Green's function (the real part of the leading complex Ruelle-Pollicott resonances). For late times that scale exponentially with $N$, both functions have a dip-ramp-plateau pattern for $N \mathrm{mod}8 = 2, 6$ that deviates substantially from the ergodic prediction due to local-in-energy correlations of matrix elements and eigenvalues, even after the Heisenberg time.

hep-th↗

arXiv2026

What We Talk About When We Talk About Dissipative Quantum Chaos

Dissipative quantum chaos is an emerging theory that is expected to extend the ideas, concepts, and methodology of conventional Hamiltonian quantum chaos from coherent evolution to open quantum dynamics. The new theory should provide a set of tools to distinguish chaotic open quantum systems from integrable ones, as well as quantitative measures of their chaoticity (or, conversely, integrability). The foundations of this theory were laid in the late 1980s, and from the very start it was clear that, like its Hamiltonian predecessor, it had to be based on the spectral properties of the operators governing open quantum evolution. After these first steps, the field remained relatively quiet for many years and it is only over the last decade that the development of dissipative quantum chaos has received a strong boost, as confirmed by a large number of publications on this topic and, very recently, the first experiments performed to test its theoretical predictions. In this chapter, we review these recent developments and outline the basic foundations of dissipative quantum chaos.

quant-ph↗

arXiv2026

Randomised measurements of a disorder-induced entanglement transition in a neutral atom quantum processor

The development and spread of entanglement in complex quantum systems is central to exploring many-body phenomena out of equilibrium. Measuring entanglement dynamics can shed light on information scrambling and thermalisation, namely on transitions from many-body quantum chaos to localisation in disordered, interacting systems. In quantum computing systems, entanglement entropy and other nonlinear functions of the density matrix have been recently measured, in particular by using the randomised measurement toolbox. However, it is difficult to implement the required arbitrary unitary rotations on specific subsystems without universal local control. Here we devise and demonstrate the measurement of entanglement entropy in a programmable analogue quantum simulator using a randomised measurement protocol that leverages local energy tuning together with a global field to bypass the need for local gate control. We implement this on a commercially available neutral-atom quantum simulator, QuEra's Aquila, and use it to show how programmable disorder in the local Hamiltonian parameters leads to a transition from chaotic to localised entanglement dynamics. Given current decoherence times, we clearly resolve disorder-specific, time-dependent entanglement spreading in small systems. Our work extends the utility of programmable analogue quantum simulators, and opens further opportunities for wider randomised measurement toolboxes in a range of other analogue systems.

quant-ph↗

arXiv2026

Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems

We study the dynamics of Loschmidt echoes in noisy quantum many-body systems without conservation laws. We first show that the operator Loschmidt echo in noisy unitary dynamics is equivalent to the operator norm of the corresponding dissipative dynamics upon noise averaging. We then analyze this quantity in two complementary ways, revealing universal dynamical behavior. First, we develop a heuristic picture for generic Floquet systems that connects Loschmidt echoes, out-of-time-order correlators, and operator growth, which is valid at any dissipation strength. We assert that the Loschmidt echo has two dynamical regimes depending on the time $t$ and the strength of the noise $p$: Gaussian decay for $pt\ll1$ and exponential decay (with a noise-independent decay rate) for $pt\gg1$. Lastly, we rigorously prove all our results for a solvable chaotic many-body quantum circuit, the dissipative random phase model -- thus providing exact insight into dissipative quantum chaos.

cond-mat.stat-mech↗

arXiv2026

Lindblad many-body scars

Quantum many-body scars have received much recent attention for being both intriguing non-ergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with $N$ fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify $N/2+1$ scars for complex fermions due to the $U(1)$ symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for non-scarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.

quant-ph↗

arXiv2026

Universality, Robustness, and Limits of the Eigenstate Thermalization Hypothesis in Open Quantum Systems

The eigenstate thermalization hypothesis (ETH) underpins much of our modern understanding of the thermalization of closed quantum many-body systems. Here, we investigate the statistical properties of observables in the eigenbasis of the Lindbladian operator of a Markovian open quantum system. We demonstrate the validity of a Lindbladian ETH ansatz through extensive numerical simulations of several physical models. To highlight the robustness of Lindbladian ETH, we consider what we dub the dilute-click regime of the model, in which one postselects only quantum trajectories with a finite fraction of quantum jumps. The average dynamics are generated by a non-trace-preserving Liouvillian, and we show that the Lindbladian ETH ansatz still holds in this case. On the other hand, the no-click limit is a singular point at which the Lindbladian reduces to a doubled non-Hermitian Hamiltonian and Lindbladian ETH breaks down.

cond-mat.stat-mech↗

arXiv2025

Localization and Delocalization of Quantum Trajectories in the Liouvillian Spectrum

We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a quasiprobability distribution that characterizes the degree of localization of the trajectories in the Liouvillian eigenbasis. Contrary to the common wisdom that late-time dynamics are governed solely by the steady state and the slowest-decaying modes, we show that trajectories can remain well spread over transient eigenstates deep within the bulk of the Liouvillian spectrum even at late times. We demonstrate this explicitly using numerical simulations of interacting spin chains and bosonic systems. Moreover, we find that the delocalization of the trajectory strongly correlates with the purity of the trajectory-averaged steady state, establishing a further link between the trajectory and ensemble pictures of open quantum dynamics.

quant-ph↗

arXiv2025

Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model

The growth of information scrambling, captured by out-of-time-order correlation functions (OTOCs), is a central indicator of the nature of many-body quantum dynamics. Here, we compute analytically the complete time dependence of the OTOC for an integrable Sachdev-Ye-Kitaev (SYK) model, $N$ Majoranas with random two-body interactions of infinite range, coupled to a Markovian bath at finite temperature. In the limit of no coupling to the bath, the time evolution of scrambling experiences different stages. For $t \lesssim \sqrt{N}$, after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At $t \sim \sqrt{N}$, the OTOC reverses trend and starts to decrease linearly in time. The reason for this linear decrease is that, despite being a subleading $1/N$ effect, the OTOC in this region is governed by the spectral form factor of the antisymmetric couplings of the SYK model. The linear decrease stops at $t \sim 2N$, the Heisenberg time, where saturation occurs. The effect of the environment is an overall exponential decay of the OTOC for times longer than the inverse of the coupling strength to the bath. The oscillations at $t \lesssim \sqrt{N}$ indicate lack of thermalization -- a desired feature for a better performance of quantum information devices.

hep-th↗

arXiv2025

Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems

We study the dissipative dynamics of a class of interacting ``gamma-matrix'' spin models coupled to a Markovian environment. For spins on an arbitrary graph, we construct a Lindbladian that maps to a non-Hermitian model of free Majorana fermions hopping on the graph with a background classical $\mathbb{Z}_2$ gauge field. We show, analytically and numerically, that the steady states and relaxation dynamics are qualitatively independent of the choice of the underlying graph, in stark contrast to the Hamiltonian case. We also show that the exponentially many steady states provide a concrete example of mixed-state topological order, in the sense of strong-to-weak spontaneous symmetry breaking of a one-form symmetry. While encoding only classical information, the steady states still exhibit long-range quantum correlations. Afterward, we examine the relaxation processes toward the steady state by numerically computing decay rates, which we generically find to be finite, even in the dissipationless limit. However, we identify symmetry sectors where fermion-parity conservation is enhanced to fermion-number conservation, where we can analytically bound the decay rates and prove that they vanish in the limits of both infinitely weak and infinitely strong dissipation. Finally, we show that while the choice of coherent dynamics is very flexible, exact solvability strongly constrains the allowed form of dissipation. Our work establishes an analytically tractable framework to explore nonequilibrium quantum phases of matter and the relaxation mechanisms toward them.

quant-ph↗

arXiv2025

Theory of Irreversibility in Quantum Many-Body Systems

We address the longstanding challenge in quantum many-body theory of reconciling unitary dynamics with irreversible relaxation. In classical chaos, the unitary evolution operator develops Ruelle-Pollicott (RP) resonances inside the unit circle in the continuum limit, leading to mixing. In the semiclassical limit, chaotic single-particle quantum systems relax with the same RP resonances. In contrast, the theory of quantum many-body RP resonances and their link to irreversibility remain underdeveloped. Here, we relate the spectral form factor to the sum of autocorrelation functions and, in generic many-body lattice systems without conservation laws, argue that all quantum many-body RP resonances converge inside the unit disk, highlighting the role of nonunitary and the thermodynamic limit. While we conjecture this picture to be general, we analytically prove the emergence of irreversibility in the random phase model (RPM), a paradigmatic Floquet quantum circuit model, in the limit of large local Hilbert space dimension. To this end, we couple it to local environments and compute the exact time evolution of autocorrelation functions, the dissipative form factor, and out-of-time-order correlation functions (OTOCs). Although valid for any dissipation strength, we then focus on weak dissipation to clarify the origin of irreversibility in unitary systems. When the dissipationless limit is taken after the thermodynamic limit, the unitary quantum map develops an infinite tower of decaying RP resonances -- chaotic systems display so-called anomalous relaxation. We also show that the OTOC in the RPM can undergo a two-stage relaxation and that during the second stage, the approach to the stationary value is again controlled by the leading RP resonance. [See the paper for the full abstract.]

cond-mat.stat-mech↗

arXiv2025

Integrability versus chaos in the steady state of many-body open quantum systems

The Lindblad description of an open quantum system gives rise to two types of integrability, since the nonequilibrium steady state can be integrable independently of the Liouvillian. Taking boundary-driven and dephasing spin chains as a representative example, we discriminate Liouvillian and steady-state chaos by combining level spacing statistics and an extension of the eigenstate thermalization hypothesis to open quantum systems. Moreover, we analyze the structure of the steady states by expanding it in the basis of Pauli strings and comparing the weight of strings of different lengths. We show that the natural expectation that integrable steady states are "simple" (i.e., built from few-body local operators) does not hold: the steady states of both chaotic and integrable models have relevant contributions coming from Pauli strings of all possible lengths, including long-range and many-body interactions. Nevertheless, we show that one can effectively use the operator-size distribution to distinguish chaotic and integrable steady states.

cond-mat.stat-mech↗

arXiv2025

Experimental Detection of Dissipative Quantum Chaos

More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures -- such as level repulsion and eigenstate thermalization -- that serve as cornerstones in our understanding of complex quantum dynamics. The emerging field of dissipative quantum chaos explores how these properties manifest in open quantum systems, where interactions with the environment play an essential role. We report the first experimental detection of dissipative quantum chaos and integrability by measuring the complex spacing ratios (CSRs) of open many-body quantum systems implemented on a high-fidelity superconducting quantum processor. Employing gradient-based tomography, we retrieve a ``donut-shaped'' CSR distribution for chaotic dissipative circuits, a hallmark of level repulsion in open quantum systems. For an integrable circuit, spectral correlations vanish, evidenced by a sharp peak at the origin in the CSR distribution. As we increase the depth of the integrable dissipative circuit, the CSR distribution undergoes an integrability-to-chaos crossover, demonstrating that intrinsic noise in the quantum processor is a dissipative chaotic process. Our results reveal the universal spectral features of dissipative many-body systems and establish present-day quantum computation platforms, which are predominantly used to run unitary simulations, as testbeds to explore dissipative many-body phenomena.

quant-ph↗

arXiv2025

Symmetry classes of classical stochastic processes

We perform a systematic symmetry classification of the Markov generators of classical stochastic processes. Our classification scheme is based on the action of involutive symmetry transformations of a real Markov generator, extending the Bernard-LeClair scheme to the arena of classical stochastic processes and leading to a set of up to fifteen allowed symmetry classes. We construct families of solutions of arbitrary matrix dimensions for five of these classes with a simple physical interpretation of particles hopping on multipartite graphs. In the remaining classes, such a simple construction is prevented by the positivity of entries of the generator particular to classical stochastic processes, which imposes a further requirement beyond the usual symmetry classification constraints. We partially overcome this difficulty by resorting to a stochastic optimization algorithm, finding specific examples of generators of small matrix dimensions in six further classes, leaving the existence of the final four allowed classes an open problem. Our symmetry-based results unveil new possibilities in the dynamics of classical stochastic processes: Kramers degeneracy of eigenvalue pairs, dihedral symmetry of the spectra of Markov generators, and time reversal properties of stochastic trajectories and correlation functions.

cond-mat.stat-mech↗

arXiv2025

Emergent Topology in Many-Body Dissipative Quantum Matter

The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern insulators in condensed matter, to protected states in complex photonic lattices in optics, and the structure of the QCD vacuum. Here, we introduce another playground for topology: the dissipative dynamics of pseudo-Hermitian many-body quantum systems. For that purpose, we study two different systems, the dissipative Sachdev-Ye-Kitaev (SYK) model, and a quantum chaotic dephasing spin chain. For the two different many-body models, we find the same topological features for a wide range of parameters suggesting that they are universal. In the SYK model, we identify four universality classes, related to pseudo-Hermiticity, characterized by a rectangular block representation of the vectorized Liouvillian that is directly related to the existence of an anomalous trace of the unitary operator implementing fermionic exchange. As a consequence of this rectangularization, we identify a topological index $ν$ that only depends on symmetry. Another distinct consequence of the rectangularization is the observation, for any coupling to the bath, of purely real topological modes in the Liouvillian. The level statistics of these real modes agree with that of the corresponding random matrix ensemble and therefore can be employed to characterize the four topological symmetry classes. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium, which may enable a direct path for experimental confirmation of topology in dissipative many-body quantum chaotic systems.

cond-mat.str-el↗

arXiv2024

Robustness of quantum chaos and anomalous relaxation in open quantum circuits

Dissipation is a ubiquitous phenomenon that affects the fate of chaotic quantum many-body dynamics. Here, we show that chaos can be robust against dissipation but can also assist and anomalously enhance relaxation. We compute exactly the dissipative form factor of a generic Floquet quantum circuit with arbitrary on-site dissipation modeled by quantum channels and find that, for long enough times, the system always relaxes with two distinctive regimes characterized by the presence or absence of gap-closing. While the system can sustain a robust ramp for a long (but finite) time interval in the gap-closing regime, relaxation is ``assisted'' by quantum chaos in the regime where the gap remains nonzero. In the latter regime, we prove that, if the thermodynamic limit is taken first, the gap does not close even in the dissipationless limit. We complement our analytical findings with numerical results for quantum qubit circuits.

cond-mat.stat-mech↗

arXiv2024

Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot of interest due to their relevance in research areas ranging from quantum optics and continuously monitored dynamics to Euclidean wormholes in quantum gravity and dissipative quantum chaos. While a symmetry classification of non-Hermitian systems leads to 38 universality classes, we show that, under certain conditions, PT-symmetric systems are grouped into 24 universality classes. We identify 14 of them in a coupled two-site Sachdev-Ye-Kitaev (SYK) model and confirm the classification by spectral analysis using exact diagonalization techniques. Intriguingly, in 4 of these 14 universality classes, AIII$_ν$, BDI$^\dagger_ν$, BDI$_{++ν}$, and CI$_{--ν}$, we identify a basis in which the SYK Hamiltonian has a block structure in which some blocks are rectangular, with $ν\in \mathbb{N}$ the difference between the number of rows and columns. We show analytically that this feature leads to the existence of $ν$ robust purely \emph{real} eigenvalues, whose level statistics follow the predictions of Hermitian random matrix theory for classes A, AI, BDI, and CI, respectively. We have recently found that this $ν$ is a topological invariant, so these classes are topological. By contrast, nontopological real eigenvalues display a crossover between Hermitian and non-Hermitian level statistics. Similarly to the case of Lindbladian dynamics, the reduction of universality classes leads to unexpected results, such as the absence of Kramers degeneracy in a given sector of the theory. Another novel feature of the classification scheme is that different sectors of the PT-symmetric Hamiltonian may have different symmetries.

quant-ph↗