Manifestations of projection-induced memory: General theory and the tilted single file.

Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous phenomenological approaches emerged, which can more or less successfully reproduce or account for experimental observations in condensed matter, biological and/or single-particle systems. However, as far as their predictions are concerned these approaches are not unique, often build on conceptually orthogonal ideas, and are typically employed on an ad hoc basis. It therefore seems timely and desirable to establish a systematic, mathematically unifying and clean approach starting from more fine-grained principles. Here we analyze projection-induced ergodic non-Markovian dynamics, both reversible as well as irreversible, using spectral theory. We investigate dynamical correlations between histories of projected and latent observables that give rise to memory in projected dynamics, and rigorously establish conditions under which projected dynamics is Markovian or renewal. A systematic metric is proposed for quantifying the degree of non-Markovianity. As a simple, illustrative but non-trivial example we study single file diffusion in a tilted box, which, for the first time, we solve exactly using the coordinate Bethe ansatz. Our results provide a solid foundation for a deeper and more systematic analysis of projection-induced non-Markovian dynamics and anomalous diffusion

Melting of B12P2 boron subphosphide under pressure

Melting of boron subphosphide (B12P2) to 26 GPa has been studied by in situ synchrotron X-ray powder diffraction in a laser-heated diamond anvil cell, and by quenching and electrical resistance measurements in a toroid-type high-pressure apparatus. B12P2 melts congruently, and the melting curve has a positive slope of 23(6) K/GPa. No solid-state phase transition was observed up to the melting in the whole pressure range under study

Equation of state of cubic boron nitride at high pressures and temperatures

We report accurate measurements of the equation of state (EOS) of cubic boron nitride by x-ray diffraction up to 160 GPa at 295 K and 80 GPa in the range 500-900 K. Experiments were performed on single-crystals embedded in a quasi-hydrostatic pressure medium (helium or neon). Comparison between the present EOS data at 295 K and literature allows us to critically review the recent calibrations of the ruby standard. The full P-V-T data set can be represented by a Mie-Gr\"{u}neisen model, which enables us to extract all relevant thermodynamic parameters: bulk modulus and its first pressure-derivative, thermal expansion coefficient, thermal Gr\"{u}neisen parameter and its volume dependence. This equation of state is used to determine the isothermal Gr\"{u}neisen mode parameter of the Raman TO band. A new formulation of the pressure scale based on this Raman mode, using physically-constrained parameters, is deduced.Comment: 8 pages, 7 figure

Effect of nanostructuration on compressibility of cubic BN

Compressibility of high-purity nanostructured cBN has been studied under quasi-hydrostatic conditions at 300 K up to 35 GPa using diamond anvil cell and angle-dispersive synchrotron X-ray powder diffraction. A data fit to the Vinet equation of state yields the values of the bulk modulus B0 of 375(4) GPa with its first pressure derivative B0' of 2.3(3). The nanometer grain size (\sim20 nm) results in decrease of the bulk modulus by ~9%

The high-pressure phase of boron, {\gamma}-B28: disputes and conclusions of 5 years after discovery

{\gamma}-B28 is a recently established high-pressure phase of boron. Its structure consists of icosahedral B12 clusters and B2 dumbbells in a NaCl-type arrangement (B2){\delta}+(B12){\delta}- and displays a significant charge transfer {\delta}~0.5- 0.6. The discovery of this phase proved essential for the understanding and construction of the phase diagram of boron. {\gamma}-B28 was first experimentally obtained as a pure boron allotrope in early 2004 and its structure was discovered in 2006. This paper reviews recent results and in particular deals with the contentious issues related to the equation of state, hardness, putative isostructural phase transformation at ~40 GPa, and debates on the nature of chemical bonding in this phase. Our analysis confirms that (a) calculations based on density functional theory give an accurate description of its equation of state, (b) the reported isostructural phase transformation in {\gamma}-B28 is an artifact rather than a fact, (c) the best estimate of hardness of this phase is 50 GPa, (d) chemical bonding in this phase has a significant degree of ionicity. Apart from presenting an overview of previous results within a consistent view grounded in experiment, thermodynamics and quantum mechanics, we present new results on Bader charges in {\gamma}-B28 using different levels of quantum-mechanical theory (GGA, exact exchange, and HSE06 hybrid functional), and show that the earlier conclusion about significant degree of partial ionicity in this phase is very robust

BetheSF: Efficient computation of the exact tagged-particle propagator in single-file systems via the Bethe eigenspectrum

Single-file diffusion is a paradigm for strongly correlated classical stochastic many-body dynamics and has widespread applications in soft condensed matter and biophysics. However, exact results for single-file systems are sparse and limited to the simplest scenarios. We present an algorithm for computing the non-Markovian time-dependent conditional probability density function of a tagged-particle in a single-file of particles diffusing in a confining external potential. The algorithm implements an eigenexpansion of the full interacting many-body problem obtained by means of the coordinate Bethe ansatz. While formally exact, the Bethe eigenspectrum involves the generation and evaluation of permutations, which becomes unfeasible for single-files with an increasing number of particles . Here we exploit the underlying exchange symmetries between the particles to the left and to the right of the tagged-particle and show that it is possible to reduce the complexity of the algorithm from the worst case scenario down to . A C++ code to calculate the non-Markovian probability density function using this algorithm is provided. Solutions for simple model potentials are readily implemented including single-file diffusion in a flat and a ‘tilted’ box, as well as in a parabolic potential. Notably, the program allows for implementations of solutions in arbitrary external potentials under the condition that the user can supply solutions to the respective single-particle eigenspectra

Toolbox for quantifying memory in dynamics along reaction coordinates

Memory effects in time series of experimental observables are ubiquitous, have important consequences for the interpretation of kinetic data, and may even affect the function of biomolecular nanomachines such as enzymes. Here we propose a set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate. The toolbox is general, robust, easy to use, and does not rely on any underlying microscopic model. As a proof of concept we apply it to the analysis of memory in the dynamics of the end-to-end distance of the analytically solvable Rouse-polymer model, an experimental time series of extensions of a single DNA hairpin measured by optical tweezers, and the fraction of native contacts in a small protein probed by atomistic molecular dynamics simulations

BetheSF V2: 3-point propagator and additional external potentials

In a recent paper (Comput. Phys. Commun. 258 (2021) 107569) we obtained exactly the tagged-particle propagator in a single-file with N particels diffusing in a generic confining potential via the coordinate Bethe-Ansatz. A naïve implementation of this solution requires a non-polynomial algorithm. To speed-up the computation we implemented a more efficient algorithm that exploits the particle exchange-symmetry. In this new version we expand the code-base to allow for the computation of the three point Green's function. The latter is required e.g. in the analysis of the breaking of time-translational invariance. In addition we include the support for two canonical potentials of general interest: one presenting an energy barrier and one featuring an asymmetric potential landscape

Faster uphill relaxation in thermodynamically equidistant temperature quenches

We uncover an unforeseen asymmetry in relaxation: for a pair of thermodynamically equidistant temperature quenches, one from a lower and the other from a higher temperature, the relaxation at the ambient temperature is faster in the case of the former. We demonstrate this finding on hand of two exactly solvable many-body systems relevant in the context of single-molecule and tracer-particle dynamics. We prove that near stable minima and for all quadratic energy landscapes it is a general phenomenon that also exists in a class of non-Markovian observables probed in single-molecule and particle-tracking experiments. The asymmetry is a general feature of reversible overdamped diffusive systems with smooth single-well potentials and occurs in multiwell landscapes when quenches disturb predominantly intrawell equilibria. Our findings may be relevant for the optimization of stochastic heat engines