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We introduce a spatial form factor (SFF) for the characterization of spatial patterns associated with point processes. Specifically, the SFF is defined in terms of the averaged even Fourier transform of the distance between any pair of points. We focus on homogeneous Poisson point processes and derive the explicit expression for the SFF in $d$-spatial dimensions. The SFF can then be found in terms of the even Fourier transform of the probability distribution for the distance between two independent and uniformly distributed random points on a $d$-dimensional ball, arising in the ball line picking problem. The relation between the SFF and the set of $n$-order spacing distributions is further established. The SFF is analyzed in detail for $d=1,2,3$ and in the infinite-dimensional case, as well as for the $d$-dimensional Coulomb gas, as an interacting point process. We also introduce a generalization of the SFF applicable to arbitrary sets in a metric space., Comment: 15 pages, 6 figures

We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through a first-order quantum phase transition. Specifically, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving fully adiabatic evolution remains challenging, necessitating high-order nonlocal terms in the expansion. Our results demonstrate that local CD strategies have limited effectiveness when crossing the extremely small gaps characteristic of NP-hard Ising problems. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which significantly increases the fidelity to the target state over the expansion method by directly addressing the gap-closing point and the associated edge states.

We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces the dependence on extensive higher-order CD terms and classical optimization techniques, rendering it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum computing.

The present work aims to measure speeds of sound $c$ in a biogas mixture of $CH_{4}$ + $N_{2}$ + $CO_{2}$ + $CO$, at $p$ = (1-12) MPa and $T$ = (273, 300 and 325) K, using a spherical acoustical resonator. The results are fitted to the virial acoustic equation of state, and the virial acoustic coefficients are obtained, $\beta_{a}$ and $\gamma_{a}$ and extrapolated to zero pressure, determining the adiabatic coefficient as perfect gas, $\gamma^{pg}$, and the isobaric and isochoric heat capacities as perfect gas, $C_{p}^{pg}$ and $C_{V}^{pg}$, respectively. The speeds of sound are acquired with a mean expanded relative uncertainty of 165 parts in $10^{6}$ ($k$ = 2) and are compared with the results predicted by the reference equation of state for this kind of mixture (natural gas-like mixtures), EoS GERG-2008. Relative deviations between experimental data and values estimated by this model were less than 700 parts in $10^{6}$ at $T$ = 325 K, and below 400 parts in $10^{6}$, and within measurement uncertainty of at $T$ = 300 K, although appreciably higher at isotherm $T$ = 273 K at the highest pressure data for this work, and even reaching values above 3 400 parts in $10^{6}$.

A new determination of the molar gas constant was performed from measurements of the speed of sound in argon at the triple point of water and extrapolation to zero pressure. A new resonant cavity was used. This is a triaxial ellipsoid whose walls are gold-coated steel and which is divided into two identical halves that are bolted and sealed with an O-ring. Microwave and electroacoustic traducers are located in the northern and southern parts of the cavity, respectively, so that measurements of microwave and acoustic frequencies are carried out in the same experiment. Measurements were taken at pressures from 600 kPa to 60 kPa and at 273.16 K. The internal equivalent radius of the cavity was accurately determined by microwave measurements and the first four radial symmetric acoustic modes were simultaneously measured and used to calculate the speed of sound. The improvements made using the new cavity have reduced by half the main contributions to the uncertainty due to the radius determination using microwave measurements which amounts to 4.7 parts in $10^{6}$ and the acoustic measurements, 4.4 parts in $10^{6}$, where the main contribution (3.7 parts in $10^{6}$) is the relative excess half-widths associated with the limit of our acoustic model, compared with our previous measurements. As a result of all the improvements with the new cavity and the measurements performed, we determined the molar gas constant $R$ = (8.314 449 $\pm$ 0.000 056) J/(K mol) which corresponds to a relative standard uncertainty of 6.7 parts in $10^{6}$. The value reported in this paper lies -1.3 parts in $10^{6}$ below the recommended value of CODATA 2014, although still within the range consistent with it.

The development of a novel technique based on a cylindrical microwave resonator for high pressure phase equilibrium determination is described. Electric permittivity or dielectric constant is a physical property that depends on temperature and pressure $\epsilon$($p$,$T$). Based on this property, a measuring technique consisting of a cylindrical resonant cavity that works in the microwave spectrum has been developed. Equilibrium data of fluid mixtures are measured at high pressure using a synthetic method, where phase transition is determined under isothermal conditions due to the change of the dielectric constant. This technique may be a more accurate alternative to conventional visual synthetic methods. The technique was validated measuring pure $CO_{2}$, and phase behaviour was then determined for two binary mixtures [$CO_{2}$ (0.6) + $CH_{4}$ (0.4)] and [$CO_{2}$ (0.4) + $CH_{4}$ (0.6)], results for which are presented. These systems are interesting for the study of biogas-like mixtures. In addition, data were compared with the equation of state used for natural gas GERG-2008, and also, they were modelled using Peng-Robinson equation of state and Wong-Sandler mixing rules, which are widely employed in chemical industries and which give good results.

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time-dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems., Comment: 6+13 pages, 3 figures

We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the density imbalance are analyzed using bosonization and exact diagonalization. The energy becomes complex valued, despite the instantaneous Hamiltonian having the same real spectrum throughout. The adiabatic limit is approached very slowly through damped oscillations. The decay scales with $\tau^{-1}$ with $\tau$ the ramp duration, while the oscillation period is $2L/v$ with $v$ the Fermi velocity and $L$ the system length. Yet, without the need for auxiliary controls, a shortcut to adiabaticity is found for ramp times commensurate with the period. Our work highlights the intricate interplay of adiabaticity and non-Hermitian many-body physics., Comment: 11 pages, 4 figures

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a novel framework, Non-Adiabatic Quantum Optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered non-integrable model., Comment: 24 pages, 15 figures, comments welcome

The spin-vector Monte Carlo model is widely used as a benchmark for the classicality of quantum annealers but severely restricts the time evolution. The spin-vector Langevin (SVL) model has been proposed and tested as an alternative, closely reproducing the real-time dynamics of physical quantum annealers such as D-Wave machines in the dissipative regime. We investigate the SVL annealing dynamics of classical O(2) rotors on regular graphs, identifying universal features in the nonequilibrium dynamics when changing the range of interactions and the topology of the graph. Regular graphs with low connectance or edge density exhibit universal scaling dynamics consistent with the Kibble-Zurek mechanism, which leads to a power-law dependence of the density of defects and the residual energy as a function of the annealing time. As the interaction range is increased, the power-law scaling is suppressed, and an exponential scaling with the annealing time sets in. Our results establish a universal breakdown of the Kibble-Zurek mechanism in classical systems characterized by long-range interactions, in sharp contrast with previous findings in the quantum domain.

We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The master equation governing the noise-average dynamics describes a new form of dephasing. We characterize the resulting state evolution and analyze its purity. The novel properties of such dynamics are illustrated in a stochastic dissipative qubit. Our analytical results show that adding noise allows for a rich control of the dynamics, with a greater diversity of steady states and the possibility of state purification., Comment: 4+6 pages, 3 + 4 figures, Comments are welcome!

Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The relation satisfies the Kibble-Zurek scaling shortly after the critical point. However, as time goes by, the coarsening dynamics suppresses the Kibble-Zurek scaling in favor of a universal dynamical scaling of the characteristic length and the adiabatic growth of the system. Theoretical predictions of the universal scaling laws are consistent with numerical findings in both regimes for both weak and strongly coupled systems., Comment: 9 pages, 9 figures

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter., Comment: 13 pages, 7 figures

We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erd\H{o}s-R\'enyi network. This is achieved by studying local spectral measures such as the level spacing and the level velocity statistics. A spectral form factor analysis is also performed as a global measure, probing energy level correlations at arbitrary spectral distances. Our findings show that these measures capture the breakdown of chaotic behavior upon varying the connectivity and strength of the transverse field in various regimes. We demonstrate that the level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks. The velocity statistics capture the surviving chaotic signatures in the sparse limit. However, these integrable-like regimes extend over a vanishingly small segment in the full range of connectivity.

Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. We use this insight to develop its geometrical description. In particular, we identify mutually orthogonal coherent and incoherent directions and give their physical interpretation. This understanding allows us to optimize the success rate for implementing non-Hermitian driving along prescribed trajectories. We show its significance for shortcuts to adiabaticity. We introduce the geometrical interpretation of a speed limit for non-Hermitian Hamiltonians and analyze its tightness. We derive the explicit expression that saturates such a speed limit and illustrate our results on a minimal example of a dissipative qubit.

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 methods to provide a compact and computationally efficient description of quantum evolution, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems., Comment: v2: 65 pages, 28 figures, Sec.IX.E. added, texts expanded, plots updated, references added

Shortcuts to adiabaticity (STA) make the fast preparation of many-body states possible, circumventing the limitations of adiabatic strategies. We propose a fast STA protocol for generating interacting states in the Tomonaga-Luttinger liquid by counter-diabatic driving, stirring the dynamics with an auxiliary control field. To this end, we exploit the equivalence between the time-dependent Tomonaga-Luttinger liquid and an ensemble of quantum oscillators with driven mass and frequency. We specify the closed-form expression of the counterdiabatic control and demonstrate its efficiency in suppressing excitations., Comment: 5+7, 1 figure

Within the framework of natural orbital functional theory, having a convenient representation of the occupation numbers and orbitals becomes critical for the computational performance of the calculations. Recognizing this, we propose an innovative parametrization of the occupation numbers that takes advantage of the electron-pairing approach used in Piris natural orbital functionals through the adoption of the softmax function, a pivotal component in modern deep-learning models. Our approach not only ensures adherence to the N-representability of the first-order reduced density matrix (1RDM) but also significantly enhances the computational efficiency of 1RDM functional theory calculations. The effectiveness of this alternative parameterization approach was assessed using the W4-17-MR molecular set, which demonstrated faster and more robust convergence compared to previous implementations., Comment: 13 pages, 6 Figures

Studying and controlling the properties of individual exfoliated materials is one of the first steps towards the fabrication of complex van der Waals systems. However, prolonged exposure to ambient conditions can affect the properties of very thin exfoliated materials altering their physical properties. For this reason, it is imperative to employ versatile characterization strategies compatible with reduced ambient exposure times. In this work, we demonstrate that optical microscopy and Raman spectroscopy are quick and non-invasive techniques to study flakes of the high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO-2212). The apparent color of BSCCO-2212 exfoliated flakes on SiO$_2$/Si has been studied allowing a rough and fast identification of the number of layers. Moreover, we find that thin flakes have a refractive index of around 1.7 in the visible range and 0.5 for the absorption coefficient near the maximum at 550 nm. We determine the optimal combination of illumination wavelength and substrate properties for the identification of different numbers of unit cells of BSCCO-2212. In addition, we report the hardening of the characteristic Raman modes at 116 cm$^{-1}$ and 460 cm$^{-1}$ as flake thickness decreases, possibly due to strain in the BiO and CuO$_2$ planes, respectively. Moreover, the evolution of the Raman modes establishes a second approach to determine the thickness of BSCCO-2212 thin flakes. As BSCCO-2212 is a challenging material to be due to its sensitivity to ambient conditions deriving in an insulating state, the present work provides a guide for the fabrication and characterization of complex van der Waals systems paving the way for studying heterostructures based on unconventional superconductors in the 2D limit.

Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies., Comment: 13 pages, 6 figures

Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an interaction quench, making use of the $SU(1,1)$ dynamical symmetry group and the Schr\"odinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, that cancels the final non-adiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols., Comment: 14+11 pages, 10 figures

This paper shows a systematic experimental and theoretical study on the temperature dependence of the infrared optical properties of pyrolytic boron nitride (pBN), from 390 to 1050 $^{\circ}$CC for wavelengths between 4 and 16 {\mu}m. The temperature dependence of these properties has never been analyzed before. The measured emissivity spectra were fitted to a dielectric function model and an effective medium approximation. The phonon frequencies and dielectric constants agreed well with room temperature experimental values from the literature, as well as with ab initio and first principles calculations. In addition, the phonon frequencies of the perpendicular mode and the dielectric constants of the parallel mode showed an appreciable parabolic temperature dependence, which justifies the interest of more theoretical efforts in order to explain this behavior. Finally, the results of this work demonstrate that thermal emission spectroscopy allows obtaining the values of the optical and dielectric parameters of impure ceramic materials in a simple manner as a function of temperature., Comment: 6 pages, 6 figures

The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry., Comment: 16 pages, 16 figures

In this study, 529 variables extracted from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of 922 breast cancer patients have been evaluated, focusing on distinguishing between recurrent and non-recurrent cases, as well as those with and without metastasis. Special emphasis is placed on the differences among invasive breast cancer subtypes (Luminal A, Luminal B, HER2 positive, and TNBC). The accurate identification of the subtype is crucial as it impacts both treatment and prognosis. The analysis is based on the dataset from Saha et al., highlighting key factors for predicting recurrences and metastases, providing valuable information for proper monitoring and the selection of effective treatments., Comment: 9 pages, text in Spanish

In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers., Comment: 10 pages, 6 figures

Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis., Comment: 12 pages, 7 figures, comments are welcome

In this work, we extend the Piris natural orbital functionals (PNOFs) to excited states by coupling their reconstructed second-order reduced density matrices with the extended random-phase approximation (ERPA). We have named the general implementation as PNOF-ERPA, and we refer to specific cases as PNOF-ERPA0, PNOF-ERPA1 and PNOF-ERPA2, according to how the excitation operator is built. The approaches have been tested in the first excited states of H2, HeH+, LiH and Li2, showing good results compared with the full configuration interaction (FCI) method. As expected, an increase in accuracy is observed when going from ERPA0 to ERPA1 and ERPA2. We have also studied the effect of electron correlation included by PNOF5, PNOF7 and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where PNOF7 and GNOF provide better results. This effect can already be seen in the excitation energies of the neon atom, where GNOF provides more accurate values than PNOF5 and PNOF7. Overall, the extension of PNOF to excited states has been successful, making the PNOF-ERPA method promising for further applications., Comment: 18 pages, 10 figures

The use of rare-earth-based permanent magnets is one of the critical points for the development of the current technology. On the one hand, industry of the rare-earths is highly polluting due to the negative environmental impact of their extraction and, on the other hand, the sector is potentially dependent on China. Therefore, investigation is required both in the development of rare-earth-free permanent magnets and in sintering processes that enable their greener fabrication with attractive magnetic properties at a more competitive price. This work presents the use of a cold sintering process (CSP) followed by a post-annealing at 1100 {\deg}C as a new way to sinter composite permanent magnets based on strontium ferrite (SFO). Composites that incorporate a percentage < 10% of an additional magnetic phase have been prepared and the morphological, structural and magnetic properties have been evaluated after each stage of the process. CSP induces a phase transformation of SFO in the composites, which is partially recovered by the post-thermal treatment improving the relative density to 92% and the magnetic response of the final magnets with a coercivity of up to 3.0 kOe. Control of the magnetic properties is possible through the composition and the grain size in the sintered magnets. These attractive results show the potential of the sintering approach as an alternative to develop modern rare-earth-free composite permanent magnets.

We have grown high-quality magnetite micrometric islands on ruthenium stripes on sapphire through a combination of magnetron sputtering (Ru film), high-temperature molecular beam epitaxy (oxide islands), and optical lithography. The samples have been characterized by atomic force microscopy, Raman spectroscopy, X-ray absorption and magnetic circular dichroism in a photoemission microscope. The magnetic domains on the magnetite islands can be modified by the application of current pulses through the Ru stripes in combination with magnetic fields. The modification of the magnetic domains is explained by the Oersted field generated by the electrical current flowing through the stripes underneath the magnetite nanostructures. The fabrication method is applicable to a wide variety of rock salt and spinel oxides.

The proliferation of topological defects is a common out-of-equilibrium phenomenon when a system is driven into a phase of broken symmetry. The Kibble-Zurek mechanism (KZM) provides a theoretical framework for the critical dynamics and generation of topological defects in such scenarios. One of the early applications of KZM is the estimation of heavy magnetic monopoles left behind by the cosmological phase transitions in the early universe. The scarcity of such relic monopoles, which contradicts the prediction of KZM, is one of the main motivations for cosmological inflationary theories. On the other hand, magnetic monopoles as emergent quasi-particles have been observed in spin ices, a peculiar class of frustrated magnets that remain disordered at temperatures well below the energy scale of exchange interaction. Here we study the annihilation dynamics of magnetic monopoles when spin ice is cooled to zero temperature in a finite time. Through extensive Glauber dynamics simulations, we find that the density of residual monopole follows a power law dependence on the annealing rate. A kinetic reaction theory that precisely captures the annihilation process from Monte Carlo simulations is developed. We further show that the KZM can be generalized to describe the critical dynamics of spin ice, where the exponent of the power-law behavior is determined by the dynamic critical exponent $z$ and the cooling protocol., Comment: 13 pages, 7 figures

The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black hole physics, it describes the survival probability (fidelity) of a thermofield double state under unitary time evolution. However, detailed properties of the SFF of isolated quantum systems with generic spectra are smeared out by large temporal fluctuations, whose minimization requires disorder or time averages. This requirement holds for any system size, that is, the SFF is non-self averaging. Exploiting the fidelity-based interpretation of this quantity, we prove that using filters, disorder and time averages of the SFF involve unitarity breaking, i.e., open quantum dynamics described by a quantum channel that suppresses quantum noise. Specifically, averaging over Hamiltonian ensembles, time averaging, and frequency filters can be described by the class of mixed-unitary quantum channels in which information loss can be recovered. Frequency filters are associated with a time-continuous master equation generalizing energy dephasing. We also discuss the use of eigenvalue filters. They are linked to non-Hermitian Hamiltonian evolution without quantum jumps, whose long-time behavior is described by a Hamiltonian deformation. We show that frequency and energy filters make the SFF self-averaging at long times., Comment: 12 pages, 5 figures