Related papers: Energy landscape properties studied by symbolic se…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its Boltzmann entropy is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the…
The potential energy landscape in the Kob-Andersen Lennard-Jones binary mixture model has been studied carefully from liquid down to the supercooled regime, from T =2 down to T =0.46. One thousand of independent configurations along the…
We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multi-dimension configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy…
State-specific approximations can provide an accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of…
The aging dynamics of a simple model glass is numerically investigated observing how it takes place in the potential energy landscape $V$. Partitioning the landscape in basins of minima of $|\nabla V|^2$, we are able to elucidate some…
The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal -- an array of vortex lines which is stationary in the rotating frame. Experimental realisations of this behaviour typically show a sequence of…
In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…
We calculate the density of stationary points and minima of a $N\gg 1$ dimensional Gaussian energy landscape. We use it to show that the point of zero-temperature replica symmetry breaking in the equilibrium statistical mechanics of a…
Describing the complex landscape of infinite-dimensional free energy is generally a challenging problem. This difficulty arises from the existence of numerous minimizers and, consequently, a vast number of saddle points. These factors make…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of…
The thermodynamic and kinetic anomalies of supercooled liquids are analyzed from the perspective of energy landscapes. A mean field model, a generalized random energy model of liquids is developed, which exhibits a dynamical transition of…
A computational framework is presented for the sampling of the energy surface of magnetic systems via the systematic identification of first-order saddle points that determine connectivity of metastable states and define the mechanisms of…
All systems in thermal equilibrium exhibit a spatially variable energy landscape due to thermal fluctuations. Thus at any instant there is naturally a thermodynamically driven localization of energy in parts of the system relative to other…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square well potential,…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…
We study the 3-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial…