Finite-size Systems Research Articles

Finite-size correction and variance of the mutual information of random linear estimation with non-Gaussian priors: A replica calculation.

Random linear vector channels have been known to increase the transmission of information in several communications systems. For Gaussian priors, the statistics of a key metric, namely, the mutual information, which is related to the free energy of the system, have been analyzed in great detail for various types of channel randomness. However, for the realistic case of non-Gaussian priors, only the average mutual information has been obtained in the asymptotic limit of large channel matrices. In this paper, we employ methods from statistical physics, namely, the replica approach, to calculate the finite-size correction and the variance of the mutual information with non-Gaussian priors, both for the case of correlated Gaussian and uncorrelated non-Gaussian channel matrices in the same asymptotic limit. Furthermore, using the same methodology, we show that higher order cumulants of the mutual information should vanish in the large-system-size limit. In addition, we obtain closed-form expressions for the minimum mean-square error finite-size corrections and variance for both Gaussian and non-Gaussian channels. Finally, we provide numerical verification of the results using numerical methods on finite-sized systems.

Persistent homology and topological statistics of hyperuniform point clouds

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity only utilizes information at the largest scales, hyperuniform configurations have distinctive local characteristics. However, the influence of global hyperuniformity on local structure has remained largely unexplored; establishing this connection can help uncover long-range interaction mechanisms and detect hyperuniform traits in finite-size systems. Here, we study the topological properties of hyperuniform point clouds by characterizing their persistent homology and the statistics of local graph neighborhoods. We find that varying the structure factor results in configurations with systematically different topological properties. Moreover, these topological properties are conserved for subsets of hyperuniform point clouds, establishing a connection between finite-sized systems and idealized reference arrangements. Comparing distributions of local topological neighborhoods reveals that the hyperuniform arrangements lie along a primarily one-dimensional manifold reflecting an order-to-disorder transition via hyperuniform configurations. The results presented here complement existing characterizations of hyperuniform phases of matter, and they show how local topological features can be used to detect hyperuniformity in size-limited simulations and experiments. Published by the American Physical Society 2024

Complexified synchrony.

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost five decades of research, many questions remain open, in particular, for finite-size systems. Here, we generalize recent work [Thümler et al., Phys. Rev. Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state variables analytically continued to the complex domain and also complexify its system parameters. Intriguingly, systems of two units with purely imaginary coupling do not actively synchronize even for arbitrarily large magnitudes of the coupling strengths, |K|→∞, but exhibit conservative dynamics with asynchronous rotations or librations for all |K|. For generic complex coupling, both traditional phase-locked states and asynchronous states generalize to complex locked states, fixed points off the real subspace that exist even for arbitrarily weak coupling. We analyze a new collective mode of rotations exhibiting finite, yet arbitrarily large rotation numbers. Numerical simulations for large networks indicate a novel form of discontinuous phase transition. We close by pointing to a range of exciting questions for future research.

A constructal perception of the electromagnetic field

As a law of physics, the Constructal Law (CL) encompasses the electromagnetic field (EMF). Undoubtedly, CL manifests in the functioning principles or in improving the design of machines, engines, and systems where EMF is part of the energy–work–heat conversion chains. Moreover, the EMF constructal design empowers the designer with the freedom to develop more efficient engineered constructs through its actions, controllable by the project and energizing strategy, to adjust, adapt to, or alleviate constraints. In all these instances, EMF fluxes interact, merge, influence, and are influenced by other flows and fluxes.A vacuum system is hypothesized here as a state of extreme rarefaction of matter. EMF's constructal nature extends the CL construal from material and heat flows to fluxes that detach from their source and evolve in space and time (propagate) in ponderable or imponderable systems. Consistently to CL's perception scale (finite-size flow system, not infinitesimal, one particle, or sub-particle), the couplings and interactions between the electric and magnetic fields are assumed to be modeled by Maxwell-Hertz's laws. If ponderable matter occurs, it participates in this evolutionary process. It morphs and flows together with the fluxes.Constructal law may predict fluxes and flows, whether material or not.

Asymmetric nucleation processes in spontaneous mode switch of active matter

Flocking and vortical are two typical motion modes in active matter. Although it is known that the two modes can spontaneously switch between each other in a finite-size system, the switching dynamics remain elusive. In this work, by computer simulation of a two-dimensional Vicsek-like system with 1000 particles, we find from the perspective of the classical nucleation theory that the forward and backward switching dynamics are asymmetric: going from flocking to vortical is a one-step nucleation process, while the opposite is a two-step nucleation process, with the system staying in a metastable state before reaching the final flocking state.

Random matrix model of Kolmogorov-Zakharov turbulence.

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.

Coherent Phase Change in Interstitial Solutions: A Hierarchy of Instabilities.

Metal hydrides or lithium ion battery electrodes can take the form of interstitial solid solutions with a miscibility gap. This work discusses theory approaches for locating, in temperature-composition space, coherent phase transformations during the charging/discharging of such systems and for identifying the associated transformation mechanisms. The focus is on the simplest scenario, where instabilities derive from the thermodynamics of the bulk phase alone, considering strain energy as the foremost consequence of coherency and admitting for stress relaxation at free surfaces. The extension of the approach to include capillarity is demonstrated by an example. The analysis rests on constrained equilibrium phase diagrams that are informed by geometry- and dimensionality-specific mechanical boundary conditions and on elastic instabilities-again geometry-specific-as implied by the theory of open-system elasticity. It is demonstrated that some scenarios afford the analysis of chemical stability to be based entirely on a linear stability analysis of the mechanical equilibrium, which provides closed-form solutions in a straightforward manner. Attention is on the impact of the system geometry (infinitely extended or of finite size) and on the chemical (closed or open system) and mechanical (incoherent or coherent) boundary conditions. Transformation mechanism maps are suggested for documenting the findings. The maps reveal a hierarchy of instabilities, which depend strongly on each of the above characteristics. Specifically, realistic, finite-sized systems differ qualitatively from idealized systems of infinite extension. Among the transformation mechanisms exposed by the analysis are a uniform switchover to the other phase when the open system reaches its chemical spinodal, practical coherent nucleation, as well as chemo-elastically coupled spontaneous buckling modes, which may take the form of either, single-phase or dual-phasestates.

Measurement induced transitions in non-Markovian free fermion ladders

Recently there has been an intense effort to understand measurement induced transitions, but we still lack a good understanding of non-Markovian effects on these phenomena. To that end, we consider two coupled chains of free fermions, one acting as the system of interest, and one as a bath. The bath chain is subject to Markovian measurements, resulting in an effective non-Markovian dissipative dynamics acting on the system chain which is still amenable to numerical studies in terms of quantum trajectories. Within this setting, we study the entanglement within the system chain, and use it to characterize the phase diagram depending on the ladder hopping parameters and on the measurement probability. For the case of pure state evolution, the system is in an area law phase when the internal hopping of the bath chain is small, while a non-area law phase appears when the dynamics of the bath is fast. The non-area law exhibits a logarithmic scaling of the entropy compatible with a conformal phase, but also displays linear corrections for the finite system sizes we can study. For the case of mixed state evolution, we instead observe regions with both area, and non-area scaling of the entanglement negativity. We quantify the non-Markovianity of the system chain dynamics and find that for the regimes of parameters we study, a stronger non-Markovianity is associated to a larger entanglement within the system.

Disorder-induced spiky phonon transmission of harmonic lattices.

In this article, we find that impurity in a one-dimensional harmonic chain leads to spikes in the phonon transmission. Using the Langevin equationsand Green's function method (LEGF), we find the underlying mechanism of spikes, which comes from the fact that the wave energy can be transferred through uniform subchains laid between impurities without loss. Both the position and magnitude of spikes can be analytically obtained. By employing these results, we provide an analytical approach to transmission in the thermodynamic limit, thereby compensating for the limitation of LEGF that are practically confined to finite system size. Finally, we determine an expression for the localization length based on LEGF, demonstrating the equivalence between mass disorder and spatial disorder in low impurity concentration.

Finite system size correction to the effective coupling in ϕ4 scattering

We compute and explore numerically the finite system size correction to next-to-leading-order 2→2 scattering in massive scalar ϕ4 theory. The derivation uses “denominator regularization” (instead of the usual dimensional regularization) on a spacetime with spatial directions compactified to a torus, with characteristic lengths not necessarily of equal size. We determine a useful analytic continuation of the generalized Epstein zeta function to isolate the usual UV divergence. Self-consistently, the renormalized finite system size correction reduces to zero as the system size goes to infinity and, further, satisfies the optical theorem. One of our checks of unitarity leads to a generalization of a number-theoretic result from Hardy and Ramanujan. Precise numerical exploration of the finite system size correction to the amplitude and coupling when two spatial dimensions are finite requires the exploitation of the analytic structure of the finite system size result via a dispersion relation. We find that the finite system size scattering amplitude exhibits “geometric” bound states. Even away from these bound states, the finite system size correction to the effective coupling can be large. Published by the American Physical Society 2024

Dynamic compaction of cohesive granular materials: scaling behavior and bonding structures.

The compaction of cohesive granular materials is a common operation in powder-based manufacture of many products. However, the influence of particle-scale parameters such as bond strength on the packing structure and the general scaling of the compaction process are still poorly understood. We use particle dynamics simulations to analyze jammed configurations obtained by dynamic compaction of sticky particles under a fixed compressive pressure for a broad range of system parameter values. We show that relative porosity, representing the relative importance of porosity with respect to its minimum and maximum values, is a unique function of a modified cohesion number that combines adhesion force, confining pressure, and particle size, as well as contact stiffness, which is often assumed to be ineffective but is shown here to play an essential role in compaction. An asymmetric sigmoidal form based on two power laws provides an excellent fit to the data. The statistical properties of the bond network reveal self-balanced force structures and an exponential fall-off of the number of both tensile and compressive forces. Remarkably, the properties of the bond network depend on the cohesion number rather than the modified cohesion number, implying that similar bond network characteristics are compatible with a broad range of porosities mainly due to the effect of contact stiffness. We also discuss the origins of data points escaping the general scaling of porosity and show that they reflect either finite system size or rigid confining walls.

Orthogonality catastrophe and quantum speed limit for dynamical quantum phase transition

We investigate the orthogonality catastrophe and quantum speed limit in the Creutz model for dynamical quantum phase transitions. We show that exact zeros of the Loschmidt echo can exist in finite-size systems for specific discrete values. We highlight the role of the zero-energy mode when analyzing quench dynamics near the critical point. Additionally, we examine the behaviors of the time for the first exact zeros of the Loschmidt echo and the corresponding quantum speed limit time as the system size increases. While the bound is not tight, it can be attributed to the scaling properties of the band gap and energy variance with respect to system size. As such, we establish a link between the orthogonality catastrophe and quantum speed limit by referencing the full form of the Loschmidt echo. In addition, we reveal the potential that the quantum speed limit holds to detect static quantum phase transition point and a reduced amplitude of the noise induced behaviors of quantum speed limit.

Study on the electronic structures and optical properties of Ca-doped KH2PO4 crystal

The first-principles method has been used to investigate the impact of Ca substitution at K sites on the electrical structures and optical characteristics of KH2PO4 crystals. And we use the FNV correction approach for the finite-size system and the HSE06 hybrid functional to update the defect formation energy and fix the "band-edge" issue. The results of defect formation energy indicate that the defect CaK· is the easiest to form. Crystal properties may be more susceptible to damage. The valence band maximum (VBM) of CaK× is shifted downward and the conduction band minimum (CBM) is shifted downward. The VBM of CaK· and CaK·· is slightly shifted upward, and CBM is almost unchanged. But Ca-induced defect energy levels are responsible for bandgap reduction and conduction band bottom shift. The absorption peaks of PE-KDP and FE-KDP occur at 1.1 eV and 2.05 eV, respectively, when the electron transitions between the defect transition level and CBM. Conversely, the absorption maxima are located at 6.5 eV and 5.4 eV, correspondingly, when the electron makes a jump between the defect transition level and VBM. Stokes redshifts are 0.3 and 0.9 eV. It damages the crystal and lowers the irradiation resistance threshold by generating vibrational energy in the lattice. Avoid CaK for better KDP quality.

Non-local linear response in anomalous transport

The anomalous heat transport observed in low-dimensional classical systems is associated with super-diffusive spreading of the space–time correlation of the conserved fields in the system. This leads to a non-local linear response relation between the heat current and the local temperature gradient in the non-equilibrium steady state. This relation provides a generalization of Fourier’s law of heat transfer and is characterized by a non-local kernel operator related to the fractional operators describing super-diffusion. The kernel is essentially proportional, in an appropriate hydrodynamic scaling limit, to the time integral of the space–time correlations of local currents in equilibrium. In finite-size systems, the time integral of correlation of microscopic currents at different locations over an infinite duration is independent of the locations. On the other hand, the kernel operator is space-dependent. We demonstrate that the resolution of this apparent puzzle becomes evident when we consider an appropriate combination of the limits of a large system size and a long integration time. Our study shows the importance of properly handling these limits, even when dealing with (open) systems connected to reservoirs. In particular, we reveal how to extract the kernel operator from simulated microscopic current–current correlation data. For two model systems exhibiting anomalous transport, we provide a direct and detailed numerical verifications of the kernel operators.

Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement

. The Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L 2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters’ regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit.

Continuous phase transition induced by non-Hermiticity in the quantum contact process model

Non-Hermitian (NH) quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of NH many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-Hermiticity remains unclear. Here we study NH quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-Hermiticity in QCP. We also determine the critical exponents β of order parameter, γ of susceptibility and study the correlation and entanglement near phase transition point. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-Hermiticity endow many-body system with different singular behavior from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.

Ultrathin Fe Films Sandwiched Between Au Layers: CEMS- study

The STM studies of Fe films with thickness above 0.6 ML do not contribute significantly to the solution of the structural problems, because of the Au surface layer, which hinders details of the Fe sub-surface layers. The Mossbauer spectroscopy appears in this case as an exceptional method, which has the ability to solve structural and magnetic problems. Our discussion is based on a simplified spectrum analysis, assuming a discrete character of the spectral components. In reality, a distribution of the hyperfine magnetic field, as well as isomer shift and the quadrupole splitting is an obvious and natural consequence of the finite size system 'presented by the monolayer film. The exact fitting of all hyperfine parameters distribution is too difficult. Most of the fitting procedures treat the distributions of IS vs. Bhf and QS vs. Bhf as linearly dependent as described using the well-known Voigt-based method.

Anisotropic particle multiphase equilibria in nonuniform fields.

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1-9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid-nematic, fluid-crystal, and fluid-nematic-crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal-nematic and crystal-fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications.

Generalized phase-space techniques to explore quantum phase transitions in critical quantum spin systems

We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-12 one-dimensional spin-chain models, viz., the Ising and anisotropic XY models in a transverse field, and the XXZ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system’s single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in detecting and characterizing first-order, second-order and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method’s ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function’s utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be readily analyzed.

NLO Scattering in ϕ 4 Theory Finite System Size Corrections Self-Consistency

Previously a 2 → 2 NLO scattering amplitude for massive ϕ 4 theory with periodic boundary conditions was derived to investigate finite system size effects. This utilized new techniques and results, and as such benefited from self-consistency checks. Here we revisit the self-consistency of the derived amplitude, in order to more rigorously establish the self-consistency. Special attention is given to potentially pathological sums, which sets up for numerical evaluation investigating the finite system effects on quantities of interest, such as the effective coupling.