Replica Method Research Articles

Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54

Abstract Symmetry resolved entanglement and entanglement asymmetry are two measures of quantum correlations sensitive to symmetries of the system. Here we discuss their non-equilibrium dynamics in the Rule 54 cellular automaton, a simple, yet interacting, integrable model. Both quantities can be expressed in terms of the more analytically tractable “charged moments”, i.e. traces of powers of a suitably deformed density matrix, via a replica trick. We express them in terms of a tensor network, which we contract in space using a system of local algebraic relations. This gives the asymptotic form for the charged moments, valid in the regime of large but finite time that is shorter than all the relevant subsystem sizes. In this regime the charge moments decay exponentially with the rate given by the leading solution to a cubic equation.

Influence of nanodiamond on compressive and dry-sliding wear behaviors of Al2O3–Al interpenetrating-phase composites

In this research, the effects of nanodiamond (ND) addition at different loadings on the compressive and wear properties of the interpenetrating phases hybrid aluminum/alumina (Al/Al2O3) composite were investigated. The samples were fabricated in a two-step process. First, the Al2O3-ND preforms were fabricated via the replica method. Second, the squeeze casting route was employed to infiltrate the molten pure Al. The ceramic preforms were made by immersing a polyurethane foam with 17 ppi pores in a slurry containing α-Al2O3 powder (1 μm), ND particles (0–10 vol%), and natural egg white. After sintering at 1500 °C for 4 h, the preheated preforms were infiltrated with molten Al. The microstructural evaluations of the preforms and composites revealed a proper distribution of the ND particles in the preform, as well as the formation of the ND agglomerates at higher volume percentages. Also, the hardness of the samples enhanced with an increase in the ND loading, reaching a maximum of 263.8 Vickers for the 10 vol% ND-loaded composite. The compressive strength of the samples enhanced up to 3 vol% ND addition and then decreased due to the agglomeration. The wear test results indicated that the best behavior was related to the 3 vol% ND-loaded composite. Embedding the 3 vol% ND decreased the weight rate and friction coefficient of the interpenetrating phases hybrid Al/Al2O3 composite by 16 % (from 8.2396×10−3 to 6.9269×10−3 mm3/m) and 12 % (0.8165 to 0.7238), respectively. The study of the worn surfaces of the samples after wear testing revealed that the dominant wear mechanisms were abrasive and adhesive for the higher and lower volume fractions of the ND, respectively.

Replica method for computational problems with randomness: principles and illustrations

Replica method for computational problems with randomness: principles and illustrations

Precision tests of bulk entanglement entropy

We consider linear superpositions of single particle excitations in a scalar field theory on AdS3 and evaluate their contribution to the bulk entanglement entropy across the Ryu-Takayanagi surface. We compare the entanglement entropy of these excitations obtained using the Faulkner-Lewkowycz-Maldacena formula to the entanglement entropy of linear superposition of global descendants of a conformal primary in a large c CFT obtained using the replica trick. We show that the closed form expressions for the entanglement entropy in the small interval expansion both in gravity and the CFT precisely agree. The agreement serves as a non-trivial check of the FLM formula for the quantum corrections to holographic entanglement entropy as well as the methods developed in the CFT to evaluate entanglement entropy of descendants. Our checks includes an example in which the state is time dependent and spatially in-homogenous as well another example involving a coherent state with a Bañados geometry as its holographic dual.

Learning curves for deep structured Gaussian feature models*

Abstract In recent years, significant attention in deep learning theory has been devoted to analyzing when models that interpolate their training data can still generalize well to unseen examples. Many insights have been gained from studying models with multiple layers of Gaussian random features, for which one can compute precise generalization asymptotics. However, few works have considered the effect of weight anisotropy; most assume that the random features are generated using independent and identically distributed Gaussian weights, and allow only for structure in the input data. Here, we use the replica trick from statistical physics to derive learning curves for models with many layers of structured Gaussian features. We show that allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental. Our results shed light on how weight structure affects generalization in a simple class of solvable models.

Scaling properties of (2+1) directed polymers in the low-temperature limit

Abstract In terms of the replica method, we consider the low-temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows us to compute the scaling exponent θ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that θ = 1 / 4 , which is slightly different to the zero-temperature numerical value that is close to 0.241.

Effect of different sintering procedures on marginal and internal fit, color, and fracture load of monolithic zirconia fixed partial prostheses.

The aim of the present in vitro study was to investigate the effects of different sintering procedures on the fit, color parameters, and fracture load of monolithic fixed partial prostheses (FPPs). A metal master model was scanned and FPPs were designed. Groups were created by fabricating FPPs using four different sintering procedures (n = 10): Prettau-Standard (PST); Prettau-Slow (PSL); Ice-Speed (ISP); Ice-Standard (IST). PST-PSL (Group P; N = 20) and ISP-IST (Group I; N = 20) were colored with different coloring liquids. The marginal and internal fit were measured using the silicone replica method. CIELAB values of the samples were measured using a spectrophotometer. Then, for each sample, the die was obtained from polymethyl methacrylate. The specimens were cemented into dies and tested in a universal testing machine for fracture load. One-way ANOVA was performed to assess the effect of the sintering procedure on the marginal and internal fit; fracture load; and ∆E00, ∆L', ∆C', and ∆H' values of the FPPs. The PSL and PST groups showed significantly smaller internal and marginal fit values compared with the ISP group. Additionally, the internal fit values of the IST group were significantly higher than those of Group P. Sintering time reduction led to a decrease in ∆E00 values. Fracture load values were not statistically significantly affected by the different sintering procedures for both brands. Different sintering procedures did not have a clinically significant effect on fit and fracture load. Different sintering procedures were found to have an impact on the color change of monolithic zirconia restorations.

Silver Nanoparticles and Simvastatin-Loaded PLGA-Coated Hydroxyapatite/Calcium Carbonate Scaffolds.

The need to develop synthetic bone substitutes with structures, properties, and functions similar to bone and capable of preventing microbial infections is still an ongoing challenge. This research is focused on the preparation and characterization of three-dimensional porous scaffolds based on hydroxyapatite (HA)-functionalized calcium carbonate loaded with silver nanoparticles and simvastatin (SIMV). The scaffolds were prepared using the foam replica method, with a polyurethane (PU) sponge as a template, followed by successive polymer removal and sintering. The scaffolds were then coated with poly(lactic-co-glycolic) acid (PLGA) to improve mechanical properties and structural integrity, and loaded with silver nanoparticles and SIMV. The scaffolds were characterized by X-ray powder diffraction (XRD), field emission scanning electron microscopy (FE-SEM), ATR FT-IR, and silver and SIMV loading. Moreover, the samples were analyzed by Brillouin and Raman microscopy. Finally, in vitro bioactivity, SIMV and silver release, and antimicrobial activity against Staphylococcus aureus and Staphylococcus epidermidis were evaluated. From the Brillouin spectra, samples showed characteristics analogous to those of bone tissue. They exhibited new hydroxyapatite growth, as evidenced by SEM, and good antimicrobial activity against the tested bacteria. In conclusion, the obtained results demonstrate the potential of the scaffolds for application in bone repair.

Fitting an Ellipsoid to Random Points: Predictions Using the Replica Method

Fitting an Ellipsoid to Random Points: Predictions Using the Replica Method

An optimization-based equilibrium measure describes fixed points of non-equilibrium dynamics: application to edge of chaos

Abstract Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient of a potential. These features make analytic studies very challenging. The common tool is the path integral approach or dynamical mean-field theory, but the drawback is that one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed form solutions in general. From the aspect of associated Fokker-Planck equation, the steady state solution is generally unknown. Here, we treat searching for the steady states as an optimization problem, and construct an approximate potential related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running an approximate stochastic gradient dynamics or Langevin dynamics. Only in the zero temperature limit, the distribution of the original steady states can be achieved. The resultant stationary state of the dynamics follows exactly the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method, which leads naturally to order parameters for the non-equilibrium steady states. Our theory reproduces the well-known result of edge-of-chaos, and further the order parameters characterizing the continuous transition are derived, and the order parameters are explained as fluctuations and responses of the steady states. Our method thus opens the door to analytically study the steady state landscape of the deterministic or stochastic high dimensional dynamics.

Geometric Landscape Annealing as an Optimization Principle Underlying the Coherent Ising Machine

Given the fundamental importance of combinatorial optimization across many diverse domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. However, a theoretical understanding of their performance remains elusive. We develop such understanding for the case of the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. We focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain of this system is annealed, the CIM interpolates between gradient descent on coupled soft spins to descent on coupled binary spins. By combining the Kac-Rice formula, the replica method, and supersymmetry breaking, we develop a detailed understanding of the evolving geometry of the high-dimensional energy landscape of the CIM as the laser gain increases, finding several phase transitions in the landscape, from flat to rough to rigid. Additionally, we develop a novel cavity method that provides a geometric interpretation of supersymmetry breaking in terms of the reactivity of a rough landscape to specific external perturbations. Our energy landscape theory successfully matches numerical experiments, provides geometric insights into the principles of CIM operation, and yields optimal annealing schedules. Published by the American Physical Society 2024

Temperature fluctuations in a relativistic gas: Pressure corrections and possible consequences in the deconfinement transition

In this work, we study the effects of random temperature fluctuations on the partition function of a quantum system by means of the . This picture provides a conceptual model for a quantum nonequilibrium system, depicted as an ensemble of subsystems at different temperatures, randomly distributed with respect to a given mean value. We then assume the temperature displays stochastic fluctuations T=T0+δT with respect to its ensemble average value T0, with zero mean δT¯=0 and standard deviation δT2¯=Δ. By means of the replica method, we obtain the average grand canonical potential, leading to the equation of state and the corresponding excess pressure caused by these fluctuations with respect to the equilibrium system at a uniform temperature. Our findings reveal an increase in pressure as the system’s ensemble average temperature T0 rises, consistently exceeding the pressure observed in an equilibrium state. We applied our general formalism to three paradigmatic physical systems; the relativistic Fermi gas, the ideal gas of photons, and a gas of non-Abelian gauge fields (gluons) in the noninteracting limit. Finally, we explore the implications for the deconfinement transition in the context of the simple bag model, where we show that the critical temperature decreases. Published by the American Physical Society 2024

The Effect of Noisy Magnetic Fields on Electrons

Abstract In this work, we study the behavior of an electron in the presence of a constant and uniform magnetic field, which is subjected to white noise fluctuations with an autocorrelation of magnitude Δ B . Starting from the Schwinger representation for a propagator in the presence of a constant magnetic field, we use the method of replicas to determine the effect of the magnetic noise on the shape of the renormalized quasi-particle parameters. Leading to an effective charge and an effective refraction index that depend not only on the energy scale, as usual, but also on the magnitude of the noise ΔB and the average field B.

Open-cell ceramic foam filters for melt filtration: Processing, characterization, improvement and application

Open-cell ceramic foams are widely used as filters for the purification of molten metals due to their high permeability and high efficiency for capturing non-metallic inclusions. With the consideration of manufacture and filtration behaviour, most filters are produced by replica methods. The intrinsic multiscale porous structure requires the ceramic foams to have sufficient strength. As a consequence, different processing approaches, material compositions and characterizations are investigated. Meanwhile, to further enhance the filtration performance, the functionalization of ceramic foam filters is often conducted with surface coating. This review summarizes the processing and characteristics of ceramic foam filters (CFFs), the nature and formation of non-metallic inclusions (NMIs), the filtration mechanism and applications of CFFs. The characterization of mechanical and filtration performance, as well as the corresponding strengthening and functionalization methods are also presented.

Comparison of the Marginal and Internal Fit of Ceramic Laminate Veneers Fabricated with Four Different Computer-Aided Manufacturing Techniques.

Purpose: The improvement of computer-aided design and computer-aided manufacturing (CAD/CAM) has changed the methods of fabricating laminate veneers. The objectives of this study were to evaluate the marginal and internal fit of ceramic veneers manufactured with different CAD/CAM techniques. Materials and methods: A metal die was made by copying a prepared plastic maxillary central right incisor and scanned for designing a laminate veneer. One hundred laminate veneers were made with four different CAD/CAM techniques (n=25), including milled lithium disilicate (MLD), heat-pressed lithium disilicate with 3-dimensional (3D) printed wax patterns (PLD), milled zirconia (MZ), and 3Dprinted zirconia (PZ). The virtual marginal and internal fit of fabricated veneers was evaluated with digital crown fitting software. The actual marginal and internal fit was measured with the silicone replica method under a digital microscope. The measured data were analyzed using the one-way analysis of variance and the Turkey test. Results: There were significant differences in marginal and internal fit (P < 0.001) among manufacturing techniques. Both the virtual and actual marginal and internal gaps were higher in the PLD and PZ groups compared to the MLD and MZ groups. Conclusion: All four CAD/CAM techniques of manufacturing veneers, that is, milled lithium disilicate, heat-pressed lithium disilicate with 3D-printed wax patterns, milled zirconia, and 3D-printed zirconia, have clinically acceptable marginal and internal fit. Milled zirconia and lithium disilicate veneers demonstrated superior marginal and internal fit compared to 3D-printed zirconia and heat-pressed lithium disilicate veneers with 3D-printed wax patterns.

Exponentiation of soft quark effects from the replica trick

In this paper, we show that multiple maximally soft (anti-)quark and gluon emissions exponentiate at the level of either the amplitude or cross-section. We first show that such emissions can be captured by introducing new soft emission operators, which serve to generalise the well-known Wilson lines describing emissions of maximally soft gluons. Next, we prove that vacuum expectation values of these operators exponentiate using the replica trick, a statistical-physics argument that has previously been used to demonstrate soft-gluon exponentiation properties in QCD. The obtained results are general, i.e. not tied to a particular scattering process. We illustrate our arguments by demonstrating the exponentiation of certain real and virtual corrections affecting subleading partonic channels in deep-inelastic scattering.

Reticulated porous structures of La0.8Al0.2NiO3-δ perovskite for enhanced green hydrogen production by thermochemical water splitting

The preparation and optimisation of La0.8Al0.2NiO3-δ (LANi82) perovskite shaped as reticulated porous ceramic (RPC) structures for H2 production by thermochemical water splitting is presented for the first time. The perovskite was first synthesised in powder form following a modified Pechini method. The redox properties of the LANi82 were first tested under N2/air flow in a thermogravimetric analyser. After that, the sponge replica method for preparing RPCs was optimised in terms of slurry composition and final thermal treatment to obtain a LANi82-RPC structure with porosity and strength appropriate to enhance heat and mass transfer in further solar reactors. The optimised LANi82-RPC material showed an outstanding hydrogen production of 8.3 cm3 STP/gmaterial·cycle at isothermal conditions (800 °C). This production was increased up to 11.5 cm3 STP/gmaterial·cycle if the thermal reduction was performed at 1000 °C. Additionally, a stable activity with almost constant H2 production in consecutive cycles was obtained for the optimised LANi82-RPC in both cases. The structure of the reticulated porous materials, with open macroporosity and wide interconnected channels, enhances heat and mass transfer, leading to higher hydrogen productions of the LANi82-RPC as compared to the materials as powder form in the same experimental set-up. These facts reinforce the favourable prospects of LANi82-RPC for large-scale hydrogen production, improving the coupling to current solar thermal concentration technologies developed, such as concentrated solar power tower.

Rényi mutual information in quantum field theory, tensor networks, and gravity

We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z, the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.

Entanglement and pseudo entanglement dynamics versus fusion in CFT

The fusion rules and operator product expansion (OPE) serve as crucial tools in the study of operator algebras within conformal field theory (CFT). Building upon the vision of using entanglement to explore the connections between fusion coefficients and OPE coefficients, we employ the replica method and Schmidt decomposition method to investigate the time evolution of entanglement entropy (EE) and pseudo entropy (PE) for linear combinations of operators in rational conformal field theory (RCFT). We obtain a formula that links fusion coefficients, quantum dimensions, and OPE coefficients. We also identify two definition schemes for linear combination operators. Under one scheme, the EE captures information solely for the heaviest operators, while the PE retains information for all operators, reflecting the phenomenon of pseudo entropy amplification. Irrespective of the scheme employed, the EE demonstrates a step-like evolution, illustrating the effectiveness of the quasiparticle propagation picture for the general superposition of locally excited states in RCFT. From the perspective of quasiparticle propagation, we observe spontaneous block-diagonalization of the reduced density matrix of a subsystem when quasiparticles enter the subsystem.

Factors affecting the property of open-cell fly ash-based porous geopolymer via replica method

Fly ash (FA) is a silicate solid waste produced by coal-fired power plants, encroaching on land and polluting the soil. Aluminosilicate can be hydrated using alkali activators to form a high-strength geopolymer. Using organic foam impregnation, geopolymer slurry can be converted into lightweight, high-strength, and porous geopolymer. Herein, FA and a sodium-based alkaline activator were mixed to prepare a geopolymer slurry. Immersing a polyurethane sponge in the slurry and adjust the roller spacing yielded a porous geopolymer with a uniform structure. Different process parameters were adjusted, revealing that the modulus of the alkali activator at 1.5% and 10% water content resulted in a high-strength FA geopolymer. When the dispersant dosage was set at 1%, the slurry with an excellent slurry-hanging effect. Adjusting the roller spacing produced a porous geopolymer with a porosity of 71%, a thermal conductivity of 0.1454 W·m−1·K−1, and a strength of 1.33 MPa. This study highlights the potential for repurposing FA into environmentally friendly and versatile geopolymer materials.