Cumulant Expansion Research Articles

Advances in EXAFS studies of thermodynamic properties and anharmonic effects based on Debye-Waller factors. Applications to semiconductors

This paper presents the advances in EXAFS studies of the thermodynamic properties and anharmonic effects based on Debye-Waller factors presented in terms of cumulant expansion. The advances are succeeded based on the generalized anharmonic correlated Einstein model (GACEM) derived for all material structures including complex systems and separated for each structure by its anharmonic effective potential parameters contained in the derived analytical expressions of three first EXAFS cumulants and thermal coefficient. Many-body effects are accounted in the present one-dimensional model based on the first-shell near-neighbor contributions to the vibrations between absorber and backscatterer atoms. Morse potential is assumed to describe single-pair atomic interaction. The method created in this GACEM has the advantage of using it all considered quantities are provided based on only the calculation or measurement of second cumulants. The advanced studies are successfully applied to semiconductors. The results calculated using the present theory and those obtained by the created method for Ge and Si having diamond structure are found to be in good and reasonable agreement with experiment and with those of other theories.

Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. II. Semiclassical-to-quantum boundary

We numerically study the dynamics and stationary states of a spin ensemble strongly coupled to a single-mode resonator subjected to loss and external driving. Employing a generalized cumulant expansion approach we analyze finite-size corrections to a semiclassical description of amplitude bistability, which is a paradigm example of a driven-dissipative phase transition. Our theoretical model allows us to include inhomogeneous broadening of the spin ensemble and to capture in which way the quantum corrections approach the semiclassical limit for increasing ensemble size $N$. We set up a criterion for the validity of the Maxwell-Bloch equations and show that close to the critical point of amplitude bistability even very large spin ensembles consisting of up to $10^4$ spins feature significant deviations from the semiclassical theory.

Charge Mobility Prediction in Organic Semiconductors: Comparison of Second-Order Cumulant Approximation and Transient Localization Theory

In the last years, several theoretical models for the simulation of charge transfer in organic semiconductors have been developed. Two particularly interesting approaches, because of their low computational cost and high accuracy, are the transient localization theory (TLT) and the second-order cumulant expansion of the density matrix (SOC). In this work, we apply these models for the evaluation of charge carrier mobility of four prototypical molecules, that is, tetracene, pentacene, picene, and rubrene. Their relative performances in reproducing experimental data are discussed, and their predictions are compared with the outcomes of semiclassical Marcus theory. We focus on a simplified framework for the SOC model, resorting to constant transfer integrals and time-averaged kinetic constants, showing that, despite the rather severe approximations introduced, the results are in good agreement with the TLT approach and experimental data. The temperature dependence of the mobility is also analyzed for pentace...

Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions

We study a numerical instability of direct simulations with truncated equation chains for the “circular cumulant” representation and two approaches to its suppression. The approaches are tested for a chimera-bearing hierarchical population of coupled oscillators. The stabilization techniques can be efficiently applied without significant effect on the natural system dynamics within a finite vicinity of the Ott-Antonsen manifold for direct numerical simulations with up to 20 cumulants; with increasing deviation from the Ott-Antonsen manifold the stabilization becomes more problematic.

Range-wide population structure and dynamics of a serotinous conifer, knobcone pine (Pinus attenuata L.), under an anthropogenically-altered disturbance regime

There is growing concern that populations of fire-adapted species around the world are at risk of extirpation due to 20th century fire exclusion (i.e. senescence risk). Concurrently, increasing fire activity in many regions is prompting concern that repeated, short-interval fire poses a risk to young stands before trees reach reproductive maturity (i.e. immaturity risk). Conceptual models assessing vulnerability to both risks exist, yet there is a lack of empirically-based studies that assess the effects of anthropogenically-altered fire regimes across the entire range of a fire-adapted species. We used geospatial data on fire occurrence (1900–2015) and a systematic sample of recently re-measured (∼2005–2015) forest inventory plots across the range of a serotinous conifer, knobcone pine (Pinus attenuata), in California and southwestern Oregon, U.S.A. to assess the relative threat of immaturity and senescence risk. We base our assessment on: (1) recent trends in area burned, (2) geographic variability and changes in stand-scale population structure, and (3) patterns of local colonization, extirpation, and population change. The area burned across the species range was lowest during the early and mid-20th century and increased in the early 1980s. Approximately 39% of the range burned between 1984 and 2015 and fire rotation was 81 years for the 25-year period ending in 2015. During this period, approximately 6% of the range of knobcone pine experienced repeated fire, and only 4% of the reburned area (∼0.25% of the entire range) experienced multiple fires at an interval less than 10 years. Most populations of knobcone pine currently exist in a mature or decadent state and we found evidence of recent senescence-related extirpation across approximately 15% of its range. However, we also observed a cumulative expansion of knobcone pine during the last decade, and the rate of colonization (less than half of which was associated with fire) was almost double that of extirpation. Despite high rates of colonization and expansion of knobcone pine in response to recent fires, vulnerability to extirpation varies geographically and remains high in some parts of the species range where wildfire activity has been low. This study provides a rare empirically-based look at the contribution of extirpation and colonization to the range-wide dynamics of a serotinous tree. Our findings underlie the importance of recognizing the different temporal and spatial scales at which contemporary disturbance regimes threaten fire-adapted species, and highlight the potential for alternative pathways of persistence and expansion of serotinous species.

Comparative analysis of anatomy, gene expression of Vaccinium corymbosum cyclins and cyclin dependent kinases during the flower bud and fruit ontogeny

Cell-cycle system controls flower and fruit growth, size and mass precisely, accompanied by cumulative cell proliferation and cell expansion. Vaccinium corymbosum shows significant variation in berry size, but its underlying anatomical and molecular mechanisms are poorly known. In this study, single fruit mass and cell layers of Southern highbush blueberry cultivars 'O'Neal' and 'Bluerain' were analyzed, and 12 cell-cycle related genes were isolated and detected its expression tendency. The results showed that blueberry flower buds had a lower contribution to mature fruit mass, and fruit growth exhibited a double-sigmoid pattern. Ovary wall (or pericarp) was the vital component for final fruit size, and approximately 70% cell layers of pericarp were produced before anthesis. Cell division in the blueberry fruit was arrested at pre- and post-anthesis. The sequences of Vccyclins and VcCDKs were relatively conserved, and its expression tendency followed flower bud and fruit developmental pattern, while VcCycA2L, VcCycB2L, VcCycD3;1L, VcCycT1;4L, VcCDKB2;2, VcCDKC1L and VcCDKE1 might be directly involved in cell proliferation and cell expansion. However, the difference of expression pattern between two cultivars was not quite significant, indicated that isolated Vccyclins and VcCDKs were not the key factors for blueberry fruit size. Collectively, this study expands our understanding of the complex cell division and cell expansion mechanisms, and cell-cycle regulatory mechanisms were involved in V. corymbosum flower and fruit during ontogeny.

INFLATION, ECONOMIC GROWTH AND UNEMPLOYMENT

The main characteristic of today's inflation is its universality, durability and the power of rapid spread and transmission. Тhere is not more reliable and more sophisticated way of breaking down the existing foundations of society from the depreciation of its currency. That process on the side of the destruction connects all the hidden forces of economic flows. Тhere is not generally accepted inflation theory that would satisfy and would give the greatest number of responses to the complex phenomenon of inflationary disorder, while at the same time giving the economic policy makers reliable indicators for conducting an efficient stabilization policy. Economic theory is faced with new questions, even when defining the problem itself . Inflation does not repeat in the same form, it further expresses the complexity of this problem, although it always binds its external manifestation to a steady and rapid increase in prices. Today, there can be inflation without price growth (controlled inflation). Inflation is no longer explained as a disproportion between supply and demand, i.e. excess demand over the supply of goods and services. The theory of inflation is more pre-tasking to explain the initial impulse and the mechanism of their cumulative expansion. The relation to the causes and types of inflation is changing. The question is how to ensure a high rate of economic growth with technological stability of prices and possible full employment. In connection with the previous one, other questions are asked, how growth is justified, with a growing appreciation of the need for introducing a new distribution system. The distribution system often has a crucial effect on the formation of accumulation and consumption and their relations. Inflation today develops under completely different conditions of various economic, political and other structures of the society as a whole. This means that there are new factors that decisively affect the production, supply and demand, prices and money in the cyclical fluctuation of modern society.

Resolving degeneracy in diffusion MRI biophysical model parameter estimation using double diffusion encoding.

PurposeBiophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, it has been shown recently that, in the general Standard Model, parameter estimation from dMRI data is ill‐conditioned even when very high b‐values are applied. We analyze this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from single diffusion encoding (SDE) to double diffusion encoding (DDE) resolves the ill‐posedness for intermediate diffusion weightings, producing an increase in accuracy and precision of the parameter estimation.MethodsWe analyze theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions.ResultsWe prove analytically that DDE provides invariant information non‐accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space.ConclusionsDDE adds additional information for estimating the model parameters, unexplored by SDE. We show, as an example, that this is sufficient to solve the previously reported degeneracies in the NODDIDA model parameter estimation.

Impurity effects in Debye–Waller factors of bcc crystals based on anharmonic correlated Einstein model

Impurity effects in Debye–Waller factors (DWFs) describing thermodynamic properties of bcc impure crystals included in X-ray absorption fine structure (XAFS) have been studied based on the anharmonic correlated Einstein model. The impurity is obtained by replacing absorber of host element by an atom of doping element. Analytical expressions of DWFs presented in terms of cumulant expansion up to the third-order and thermal expansion coefficient of impure crystals have been derived. Anharmonic effective potential of impure crystal includes interactions of absorber and backscatterer atoms with their first shell near neighbors. Morse potential is assumed to describe single-pair atomic interaction. The obtained expressions for impure crystal can also be used for calculating the considered XAFS quantities of pure material based on replacing all data of the doping atoms by those of pure host element. The advantage of using the anharmonic effective potential is shown by its possibility of defining the difference of XAFS quantities between the two inverse doping processes, which cannot be obtained by using the single-pair potential. Numerical results are found to be in good agreement with experiment for the impure Fe doped by Mo or inversely for Mo doped by Fe, as well as for pure Fe and Mo.

Onset of intermittency in stochastic Burgers hydrodynamics.

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations-the viscous instantons-are assumed to play a dominant role in modeling the left tails of velocity gradient probability distribution functions. We find, as expected on general grounds, that the field-theoretical approach becomes meaningful in practice only if the effects of fluctuations around instantons are taken into account. Working with a systematic cumulant expansion, it turns out that the integration of fluctuations yields, in leading perturbative order, to an effective description of the Burgers stochastic dynamics given by the renormalization of its associated heat kernel propagator and the external force-force correlation function.

Lessons learned about steered molecular dynamics simulations and free energy calculations.

The calculation of free energy profiles is central in understanding differential enzymatic activity, for instance, involving chemical reactions that require QM-MM tools, ligand migration, and conformational rearrangements that can be modeled using classical potentials. The use of steered molecular dynamics (sMD) together with the Jarzynski equality is a popular approach in calculating free energy profiles. Here, we first briefly review the application of the Jarzynski equality to sMD simulations, then revisit the so-called stiff-spring approximation and the consequent expectation of Gaussian work distributions and, finally, reiterate the practical utility of the second-order cumulant expansion, as it coincides with the parametric maximum-likelihood estimator in this scenario. We illustrate this procedure using simulations of CO, both in aqueous solution and in a carbon nanotube as a model system for biologically relevant nanoheterogeneous environments. We conclude the use of the second-order cumulant expansion permits the use of faster pulling velocities in sMD simulations, without introducing bias due to large dispersion in the non-equilibrium work distribution.

Joint instability and abrupt nonlinear transitions in a differentially rotating plasma

Global magnetohydrodynamic (MHD) instabilities are investigated in a computationally tractable two-dimensional model of the solar tachocline. The model’s differential rotation yields stability in the absence of a magnetic field, but if a magnetic field is present, a joint instability is observed. We analyse the nonlinear development of the instability via fully nonlinear direct numerical simulation, the generalized quasi-linear approximation (GQL) and direct statistical simulation (DSS) based upon low-order expansion in equal-time cumulants. As the magnetic diffusivity is decreased, the nonlinear development of the instability becomes more complicated until eventually a set of parameters is identified that produces a previously unidentified long-term cycle in which energy is transformed from kinetic energy to magnetic energy and back. We find that the periodic transitions, which mimic some aspects of solar variability – for example, the quasiperiodic seasonal exchange of energy between toroidal field and waves or eddies – are unable to be reproduced when eddy-scattering processes are excluded from the model.

Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems.

We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form F(t)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.

Planetary boundaries of consumption growth: Declining social discount rates

We introduce the logistic model of consumption growth, which captures a negative feedback preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount curve. The latter plays a critical role in, e.g., climate finance with benefits on current investments deferred to centuries from now. The growth rate of consumption is irregularly evolving in time, which makes estimation of an expected term-structure of consumption growth and associated social discount rates a challenging task. Nonetheless, observations show that the problem at hand is perturbative with the small parameter being the product of an average strength of fluctuations in the growth rate and its autocorrelation time. This fact permits utilization of the cumulant expansion method to derive remarkably simple expressions for the term-structure of expected consumption growth and associated discount rates in the bounded economy. We demonstrate that the dynamic effect related to the planetary resource constrains could become a dominant mechanism responsible for a declining long-term tail of a social discount curve in a distant future. The derived results can help to shape a more realistic long-term social discounting policy. Furthermore, with the obvious redefinition of the key parameters of the model, obtained results are directly applicable for description of expected long-term population growth in stochastic environments.

Linear statistics and pushed Coulomb gas at the edge of β-random matrices: Four paths to large deviations

The Airyβ point process, , describes the eigenvalues at the edge of the Gaussian β ensembles of random matrices for large matrix size . We study the probability distribution function (PDF) of linear statistics for large parameter t. We show the large deviation forms and for the cumulant generating function and the PDF. We obtain the exact rate function, or excess energy, using four apparently different methods: i) the electrostatics of a Coulomb gas, ii) a random Schrödinger problem, i.e., the stochastic Airy operator, iii) a cumulant expansion, iv) a non-local non-linear differential Painlevé-type equation. Each method was independently introduced previously to obtain the lower tail of the Kardar-Parisi-Zhang equation. Here we show their equivalence in a more general framework. Our results are obtained for a class of functions φ, the monotonous soft walls, containing the monomials and the exponential and equivalently describe the response of a Coulomb gas pushed at its edge. The small u behavior of the excess energy exhibits a change between a non-perturbative hard-wall–like regime for (third-order free-to-pushed transition) and a perturbative deformation of the edge for (higher-order transition). Applications are given, among them i) truncated linear statistics such as , leading to a formula for the PDF of the ground-state energy of non-interacting fermions in a linear plus random potential, ii) interacting spinless fermions in a trap at the edge of a Fermi gas, iii) traces of large powers of random matrices.

Evaluation of Gallium Arsenide Thermal Expansion Coefficient by Extended X-Ray Absorption Fine Structure

Negative thermal expansion of gallium arsenide has been investigated through temperature dependent Extended X-ray Absorption Fine Structure (EXAFS) measurements. The bond thermal expansion coefficient αbond has been evaluated and compared to negative expansion coefficient αtens due to tension effects. The overall thermal expansion coefficient is the sum of αbond and αtens. Below 60 K, αtens is greater than αbond yielding to a negative expansion in this temperature region. Tension effects are progressively overcome by the stretching effects in the region 60 - 300 K. The asymmetry of nearest neighbors distribution is not negligible since the gaussian approximation underestimates the bond expansion by about 0.00426 Å. This error decreases when the temperature is lowered. The accuracy in the thermal expansion evaluation and the connection between third cumulant and thermal expansion are discussed.

RANDOM MATRICES WITH SLOW CORRELATION DECAY

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajankiet al.[‘Stability of the matrix Dyson equation and random matrices with correlations’,Probab. Theory Related Fields173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.

Demonstration of resonant inelastic x-ray scattering as a probe of exciton-phonon coupling

Resonant inelastic X-ray scattering (RIXS) is a promising technique for obtaining electron-phonon coupling constants. However, the ability to extract these coupling constants throughout the Brillouin zone for crystalline materials remains limited. To address this need, we developed a Green's function formalism to capture electron-phonon contributions to core-level spectroscopies without explicitly solving the full vibronic problem. Our approach is based on the cumulant expansion of the Green's function combined with many-body theory calculated vibrational coupling constants. The methodology is applied to X-ray photoemission spectroscopy, X-ray absorption spectroscopy (XAS), and RIXS. In the case of the XAS and RIXS, we use a 2-particle exciton Green's function, which accounts implicitly for particle-hole interference effects that have previously proved difficult. To demonstrate the methodology and gain a deeper understanding of the experimental technique, we apply our formalism to small molecules, for which unambiguous experimental data exist. This comparison reveals that the vibronic coupling constant probed by RIXS is in fact related to exciton-phonon coupling rather than electron-phonon coupling, challenging the conventional interpretation of the experiment.

Shattered time: can a dissipative time crystal survive many-body correlations?

We investigate the emergence of a time crystal (TC) in a driven dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the TC formation and establish a connection between the regime where it is stable and where the system features a slow growth rate of the mutual information. This observation allows us to conclude that the TC studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the TC to single-particle dephasing. Finally, we discuss an experimental implementation using long lived dipoles in an optical cavity.

Targeted Molecular Dynamics Calculations of Free Energy Profiles Using a Nonequilibrium Friction Correction.

As standard unbiased molecular dynamics (MD) simulations become impractical for sampling rare events, "targeted MD" employs a moving distance constraint to enforce rare transitions along some reaction coordinate x. To calculate free energy profiles from these nonequilibrium simulations via Δ G( x) = W( x) - Wdiss( x), apart from the (readily obtained) work W( x) performed on the system, the dissipated work Wdiss( x) is also required. By employing a second-order cumulant expansion of Jarzynski's equality combined with an analysis within Langevin theory, the dissipated work can be expressed via a nonequilibrium friction coefficient ΓNEQ( x) that may be calculated on-the-fly from constraint force fluctuations. Adopting the ion dissociation of NaCl in water as a test system, this friction correction is shown to result in accurate free energy profiles, even for a modest number of simulations and at high constraint velocities. As a bonus, the analysis of ΓNEQ( x) may yield valuable insight into the microscopic mechanism of friction.