arXiv subjects

Alessandro Laio

Publications and source records attributed to Alessandro Laio.

60 records · Page 4Linked to original sources

arXiv2009

Calculating Thermodynamics Properties of Quantum Systems by a non-Markovian Monte Carlo Procedure

We present a history-dependent Monte Carlo scheme for the efficient calculation of the free-energy of quantum systems, inspired by the Wang-Landau sampling and metadynamics method. When embedded in a path integral formulation, it is of general applicability to a large variety of Hamiltonians. In the two-dimensional quantum Ising model, chosen here for illustration, the accuracy of free energy, critical temperature, and specific heat is demonstrated as a function of simulation time, and successfully compared with the best available approaches, particularly the Wang-Landau method over two different Monte Carlo procedures.

cond-mat.stat-mech↗

arXiv2008

Optimal Langevin modelling of out-of-equilibrium molecular dynamics simulations

We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin dynamics are expressed as explicit averages over the input trajectories. The proposed strategy is applicable to cases when the input trajectories are generated by subjecting the system to a external time-dependent force (as opposed to canonically-equilibrated trajectories). Secondly, it provides an explicit control on the statistical uncertainty of the drift and diffusion profiles. These features lend to the possibility of designing the external force driving the system so to maximize the accuracy of the drift and diffusions profile throughout the phase space of interest. Quantitative criteria are also provided to assess a posteriori the satisfiability of the requisites for applying the method, namely the Markovian character of the stochastic dynamics of the collective variables.

cond-mat.stat-mech↗

arXiv2008

Equilibrium free energies from non-equilibrium metadynamics

In this paper we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to a model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes such as Wang-Landau sampling.

cond-mat.stat-mech↗

arXiv2005

Are structural biases at protein termini a signature of vectorial folding?

Experimental investigations of the biosynthesis of a number of proteins have pointed out that part of the native structure can be acquired already during translation. We carried out a comprehensive statistical analysis of some average structural properties of proteins that have been put forward as possible signatures of this progressive buildup process. Contrary to a widespread belief, it is found that there is no major propensity of the amino acids to form contacts with residues that are closer to the N terminus. Moreover, it is found that the C terminus is significantly more compact and locally-organized than the N one. Also this bias, though, is unlikely to be related to vectorial effects, since it correlates with subtle differences in the primary sequence. These findings indicate that even if proteins aquire their structure vectorially no signature of this seems to be detectable in their average structural properties.

q-bio.BM↗

arXiv2004

Reconstructing the Density of States by History-Dependent Metadynamics

We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free energy profile of a canonical system to be recovered within a pre-assigned accuracy,[A. Laio and M. Parrinello, PNAS 2002]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50x50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.

cond-mat.stat-mech↗

arXiv1998

Interacting hard-core bosons and surface preroughening

The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered flat (DOF) phase, is formulated in terms of interacting steps. Finite terraces play a crucial role in the formulation. We start by mapping the statistical mechanics of interacting (up and down) steps onto the quantum mechanics of two species of one-dimensional hard-core bosons. The effect of finite terraces translates into a number-non-conserving term in the boson Hamiltonian, which does not allow a description in terms of fermions, but leads to a two-chain spin problem. The Heisenberg spin-1 chain is recovered as a special limiting case. The global phase diagram is rich. We find the DOF phase is stabilized by short-range repulsions of like steps. On-site repulsion of up-down steps is essential in producing a DOF phase, whereas an off-site attraction between them is favorable but not required. Step-step correlation functions and terrace width distributions can be directly calculated with this method.

cond-mat↗