Reservoir engineering can stabilize states inaccessible to unitary dynamics. Directed particle-conserving dissipation creates Lindbladian skin states, where Pauli exclusion turns edge accumulation into a many-body density imbalance. In a monitored fermion chain with tunable hopping range, we identify, within a Gaussian trajectory approximation, two finite-size scaling regimes: short-range hopping is consistent with complete skin accumulation and area-law entanglement, whereas sufficiently long-range hopping produces a finite bulk tail and effective algebraic sub-volume-law entanglement. Dissipation and coherent hopping thus jointly control skin localization and quantum entanglement, highlighting their close interconnection.

We show that an out-of-equilibrium percolation transition occurs after quenching ferromagnetic Ising-like systems across their magnetic first-order transitions. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature first-order transition line by a quench of the magnetic field h from h_i<0 to h>0. In the thermodynamic limit and for finite values of h, the post-quench evolution under a purely relaxational dynamics is characterized by a dynamic transition at a finite critical time t_c(h) from the metastable negatively magnetized phase to the positive one, marked by the percolation of the largest clusters of positive and negative spins. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on h. We also show that the percolation critical behavior is related to the spinodal-like behavior of the magnetization in the small-h limit, which implies that the percolation time t_c(h) exhibits a spinodal-like exponential dependence on h.

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse (g) and longitudinal (h) magnetic fields. This model exhibits a continuous quantum transition (CQT) at g = g(c) and h = 0, and first-order quantum transitions (FOQTs) driven by h along the line h = 0 (g < g(c)). In the integrable limit h = 0, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value h(i )< 0 to a positive value h(f )> 0. We focus on values of hf such that the spectrum of the post-QQ Hamiltonian H(g, h(f)) lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of g, finding qualitatively distinct behaviors for g> g(c) (where the chain is in the disordered phase), for g = g(c) (QQ across the CQT), and for g < g(c) (QQ across the FOQT line).

We study the out-of-equilibrium spinodal-like dynamics of three-dimensional q-state Potts systems driven across their thermal first-order transition in the thermodynamic limit, by a relaxational (heat-bath) dynamics. During the evolution, the inverse temperature β increases linearly with time, as δβ(t)≡β(t)-β_{fo}∼t/t_{s}, where β_{fo} is the inverse temperature at the transition point, t is the time, and t_{s} is a timescale. The dynamics starts at t_{i}<0 from an ensemble of disordered configurations equilibrated at an inverse temperature β(t_{i})<β_{fo} and ends at positive values of t, corresponding to β(t)>β_{fo} in the ordered phase (this is analogous to a standard Kibble-Zurek protocol). The time-dependent energy density shows an out-of-equilibrium scaling behavior in the large-t_{s} limit, in terms of the scaling variable σ≡t(lnt)^{κ}/t_{s}. The exponent κ turns out to be consistent with κ=3/2 (with good accuracy), which is the value obtained by assuming that the initial nucleation of ordered regions is the relevant mechanism providing the largest timescale. This scaling behavior implies a spinodal-like phenomenon close to the transition point: the passage from the disordered to the ordered phase, composed of large ordered regions of different color, occurs at δβ(t)=δβ_{*}>0, which decreases as δβ_{*}∼(lnt_{s})^{-κ} in the large-t_{s} limit.

We analyze the quantum states of an isolated composite system consisting of two stacked quantum Ising (SQI) subsystems, coupled by a local Hamiltonian term that preserves the Z2 symmetry of each subsystem. The coupling strength is controlled by an intercoupling parameter w, with w = 0 corresponding to decoupled quantum Ising subsystems. We focus on the quantum correlations of one of the two SQI subsystems, S, in the ground state of the global system and study their dependence on both the state of the weakly coupled complementary part E and the intercoupling strength. We concentrate on regimes in which S develops critical long-range correlations. The most interesting physical scenario arises when both SQI subsystems are critical. In particular, for identical SQI subsystems, the global system is equivalent to the quantum Ashkin-Teller model, characterized by an additional Z2 interchange symmetry between the two subsystem operators. In this limit, one-dimensional SQI systems exhibit a peculiar critical line along which the length-scale critical exponent nu varies continuously with w, while two-dimensional systems develop quantum multicritical behaviors characterized by an effective enlargement of the symmetry of the critical modes, from the actual discrete Z2 (R) Z2 symmetry to an effective continuous O(2) symmetry.

We investigate operator delocalization in disordered one-dimensional spin chains by introducing-besides the already known operator mass-a complementary measure of operator complexity: the operator length. Like the operator nonstabilizerness, both these quantities are defined from the expansion of time-evolved operators in the Pauli basis. They characterize, respectively, the number of sites on which an operator acts nontrivially and the spatial extent of its support. We show that both the operator mass and length can be computed efficiently and exactly within a matrix-product-state framework, providing direct access to their full probability distributions, without resorting to stochastic sampling. Applying this approach to the disordered XXZ spin-1/2 chain, we find sharply distinct behaviors in non-interacting and interacting regimes. In the Anderson-localized case, operator mass, length, and operator entanglement entropy rapidly saturate, signaling the absence of scrambling. By contrast, in the many-body localized (MBL) regime, for arbitrarily weak interactions, all quantities exhibit a robust logarithmic growth in time, consistent with the known logarithmic light cone of quantum-correlation propagation in MBL. We demonstrate that this behavior is quantitatively captured by an effective & ell;-bit model and persists across system sizes accessible via tensor-network simulations.

We study the out-of-equilibrium spinodal-like behavior of three-dimensional (3D) q-state Potts models (for q >= 3), observed when the temperature is quenched across the first-order transition (FOT) point beta(fo)=T-fo(-1). We consider a standard quench protocol, in which high-temperature configurations, thermalized at beta(i)beta(fo). We focus on the emergence of spinodal-like behaviors in the thermodynamic limit, associated with the dynamic phase change. We argue that, if the nucleation of smooth droplets is the relevant mechanism of the post-quench phase change, for sufficiently small beta(fo)-beta(i)>0, the time-dependent energy density should scale in terms of rho=(lnt)(3/2)delta, where delta=beta/beta(fo)-1, with a discontinuity at a particular value rho=rho(s)>0. This implies the emergence of a spinodal-like behavior, whose time scale tau increases exponentially as ln tau approximate to (rho(s)/delta)(2/3) in the limit delta -> 0(+). We present a numerical analysis of the quench protocol in the 3D q=6 Potts model, which supports the above spinodal-like scenario.

We study the asymptotic bipartite entanglement in various integrable and nonintegrable models of monitored fermions. We find that, for the integrable cases, the entanglement versus the system size is well fitted, over more than one order of magnitude, by a function interpolating between a linear and a power-law behavior. Up to the sizes we are able to reach, a logarithmic growth of the entanglement can be also captured by the same fit with a very small power-law exponent. We thus propose a characterization of the various entanglement phases using the fitting parameters. For the nonintegrable cases, as the staggered t-V and the Sachdev-Ye-Kitaev (SYK) models, the numerics prevents us from spanning different orders of magnitude in the size, therefore we fit the asymptotic entanglement versus the measurement strength and then look at the scaling with the size of the fitting parameters. We find two different behaviors: for the SYK we observe a volume-law growth, while for the t-V model some traces of an entanglement transition emerge. In the latter models, we study the localization properties in the Hilbert space through the inverse participation ratio, finding an anomalous delocalization with no relation with the entanglement properties. Finally, we show that our function fits very well the fermionic logarithmic negativity of a quadratic model in ladder geometry with stroboscopic projective measurements.

We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular and chaotic regimes. At finite size, we describe the system dynamics using stochastic quantum trajectories. We find that the asymptotic nonstabilizerness (alias the $magic$, a measure of quantum complexity), averaged over trajectories, mirrors to some extent the classical chaotic behavior, while the entanglement entropy has no relation with chaos in the thermodynamic limit.

Quantum batteries have demonstrated remarkable charging properties, showing that a quantum advantage is possible in the realm of quantum thermodynamics. However, finding an effective strategy to store energy for long periods remains crucial in these systems. Here, we investigate different configurations of a waveguide-QED system acting as a quantum battery and show that, in this context, collective effects can slow down the self-discharging time of the battery, thus improving the storage time. Specifically, when the artificial atoms of the array are arranged randomly, the energy and ergotropy of the optical system are shown to decay at a subexponential rate over long periods, in contrast to the energy decay of a single atom in a waveguide. In the case of atoms arranged in an ordered lattice, collective effects slow down dissipative discharging only for a specific lattice spacing. Thus, in both configurations, collective effects can be used to boost the energy-protection properties of optical systems.

We consider the quantum-state-diffusion dynamics of the XXZ-staggered spin chain, also focusing on its noninteracting XX-staggered limit, and of the Sachdev-Ye-Kitaev (SYK) model. We describe the process through quantum trajectories and evaluate the nonstabilizerness (also known as "magic") along the trajectories, quantified by the stabilizer R & eacute;nyi entropy (SRE). In the absence of measurements, we find that the SYK model is the only one in which the time-averaged SRE saturates the random state bound and has a scaling with the system size that is well described by the theoretical prediction for quantum chaotic systems. In the presence of measurements, we numerically find that the steady-state SRE versus the coupling strength to the environment is well fitted by a generalized Lorentzian function. The scaling of the fitting parameters with the system size suggests that the steady-state SRE linearly increases with the system size in all the considered cases and displays no measurement-induced quantum transition, as confirmed by the curves of the steady-state SRE versus the system size.

We demonstrate a simple technique for adding controlled dissipation to Rydberg atom experiments. In our experiments we excite cold rubidium atoms in a magneto-optical trap to 70-S Rydberg states, whilst simultaneously inducing forced dissipation by resonantly coupling the Rydberg state to a hyperfine level of the short-lived 6-P state. The resulting effective dissipation can be varied in strength and switched on and off during a single experimental cycle.

In this review, we give a brief overview of quantum simulation as applied to the study of complex systems. In particular, we cover the basic ideas of quantum simulation, neuromorphic computation, the Sachdev–Ye–Kitaev model, as well as applications to quantum batteries.

We study the out-of-equilibrium dynamics of one-dimensional quantum Ising models in a transverse field g. driven by a time-dependent longitudinal field h across their magnetic first-order quantum transition at h = 0 for sufficiently small values of [g]. We consider nearest-neighbor Ising chains of size L with periodic boundary conditions. We focus on the out-of-equilibrium behavior arising from Kibble-Zurek protocol, in which h is varied linearly in time with a timescale 1,, ie, h(t)=t/t(s),. The system starts from the ground state at h(i) equivalent to h(t(i)) < 0 , where the longitudinal magnetization M is negative. Then it evolves unitarily up to positive values of h(t), where M(t) becomes eventually positive. We identify several scaling regimes characterized by a nontrivial interplay be-tween the size 1. and the timescale 1,, which can be observed when the system is close to one of the many avoided level crossings that occur for h >= 0 In the L -> infinity limit, all these crossings approach h = 0, making the study of the thermodynamic limit, defined as the limit L -> infinity keeping 1 and 1, constant, problematic. We study this limit numerically, by first determining the large-1. quantum evolution at fixed t,, and then analyzing its behavior with increasing 1,. Our analysis shows that the system switches from the initial state with to a positively magnetized state at h = h(*)(t(s)) > 0, where h(*)(t(s)) decreases with increasing t(s), apparently as h(star)similar to 1/ln t(s). This suggests the existence of a scaling behavior in terms of the rescaled time Omega = t ln t(s)/t(s). The numerical results also show that the system converges to a nontrivial stationary state in the large-t limit, characterized by an energy significantly larger than that of the corresponding homogeneously magnetized ground state.

We explore the energy content of superpositions of single-excitation current states. Specifically, we focus on the maximum energy that can be extracted from them through local unitary transformations. The figure of merit we employ is the local ergotropy. We consider an XY spin-chain model and perform a complete analysis in the whole range of the system parameters. This way, we prove that superpositions of two current states in spatially closed spin networks are characterized by specific peaks in extractable energy, generally overcoming the ergotropy of each of the two separate current states characterized by a single winding number. The many-body state dynamics entails to ergotropy evolving in a controlled fashion. The implementation we suggest is based on a Rydberg-atom platform. Optimal transformations able to extract locally the maximum possible amount of energy are sorted out.

We study the out-of-equilibrium Kibble-Zurek (KZ) dynamics in quantum Ising chains in a transverse field, driven by a time-dependent longitudinal field h(t) = t(i)/t(s) (t(s) is the timescale of the protocol), across their first-order quantum transitions (FOQTs) at h = 0. The KZ protocol starts at time t(i) < 0 from the negatively magnetized ground state for hi = t(i)/t(s) < 0. Then, the system evolves unitarily up to a time t(f )> 0, such that the magnetization of the state at time t(f) is positive. In finite-size systems, the KZ dynamics develops out-of-equilibrium finite-size scaling (OFSS) behaviors. Their scaling variables depend either exponentially or with a power law on the size, depending on the boundary conditions (BC). The OFSS functions can be computed in effective models restricted to appropriate low-energy (magnetized and/or kink) states. The KZ scaling behavior drastically changes in the thermodynamic limit (TL), defined as the infinite-size limit keeping t and ts fixed, which appears substantially unrelated with the OFSS regime, because it involves higher-energy multikink states, which are irrelevant in the OFSS limit. The numerical analyses of the KZ dynamics in the TL show the emergence of a quantum spinodal-like scaling behavior at the FOQTs for all considered BC, which is independent of the BC. The longitudinal magnetization changes sign at h(t) = & planckh;(star) > 0, where h, decreases with increasing t(s), as h(star) similar to 1/ lnts. Moreover, in the large-t(s) limit, the time dependence of the magnetization is described by a universal function of Omega = t/t(s), with t(s) = t(s)/ ln ts.

We study the performances of an imperfect quantum many-body Otto engine based on free-fermion systems. Starting from the thermodynamic definitions of heat and work along ideal isothermal, adiabatic, and isochoric transformations, we generalize these expressions in the case when the hypotheses of ideality are relaxed (i.e., nonperfect thermalization with the external baths, as well as nonperfect quantum adiabaticity in the unitary dynamic protocols). These results are used to evaluate the work and the power delivered by an imperfect quantum many-body heat engine in a finite time, whose working substance is constituted by a quantum Ising chain in a transverse field: We discuss the emerging optimal working points as functions of the various model parameters.

The coherent quantum transport of matter wave through a ring-shaped circuit attached to leads defines an iconic system in mesoscopic physics that has allowed both to explore fundamental questions in quantum science and to draw important avenues for conceiving devices of practical use. Here we study the source-to-drain transport of excitations going through a ring-network, without propagation of matter waves. We model the circuit in terms of a spin system with specific long-range interactions that are relevant for quantum technology, such as Rydberg atoms trapped in optical tweezers or ion traps. Inspired by the logic of rf- and dc-SQUIDs, we consider rings with one and two local energy offsets, or detunings. As a combination of specific phase shifts in going though the localized detunings and as a result of coherent tunneling, we demonstrate how the transport of excitations can be controlled, with a distinctive dependence on the range of interactions.

We consider a free-fermion chain undergoing dephasing, described by two different random-measurement protocols (unravelings): a quantum-state-diffusion and a quantum-jump one. Both protocols keep the state in a Slater-determinant form, allowing to address quite large system sizes. We find a bifurcation transition in the distribution of the measurement operators along the quantum trajectories, where it changes from unimodal to bimodal. The value of the measurement strength where such transition occurs is similar for the two unravelings, but the distributions and the transition have different properties reflecting the symmetries of the two measurement protocols. We also consider the scaling with the system size of the inverse participation ratio of the Slater-determinant components and find a power-law scaling that marks a multifractal behaviour, in both unravelings and for any nonvanishing measurement strength.