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Nowadays, the numerical models of real-world structures are more precise, more complex and, of course, more time-consuming. Despite the growth of a computational effort, the exploration of model behaviour remains a complex task. The…
Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattice to simulate models for unsolved strongly correlated systems, so as to…
At the Institute for Thermodynamics and Thermal Process Engineering (ITT) about 100 molecular models for pure substances have been developed so far. These models reproduce vapor pressure, saturated liquid density, and enthalpy of…
The aim of this tutorial is to analyze the equilibrium properties of some simple but widely used quantum systems. The canonical ensemble is used to evaluate the required properties here.
Conventional simulations of complex systems in the canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble overcomes this difficulty by performing a random walk in potential energy space and other…
Warm dense matter systems created in the laboratory are highly dynamical. In such cases electron dynamics is often needed to accurately simulate the evolution and properties of the system. Large systems force one to make simple…
The complex Langevin method (CLM) is a promising tool to address the sign problem in quantum field theories with complex actions. However, it can converge to incorrect results even when simulations appear stable, highlighting the need for…
One popular approach to incorporating experimental data into molecular simulations is to restrain the ensemble average of observables to their experimental values. Here I derive equations for the equilibrium distributions generated by…
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…
We present an accelerated algorithm that samples correctly the thermodynamic ensemble in complex systems where the dynamics is controlled by activation barriers. The efficiency of the thermodynamically-weighted activation-relaxation…
All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties…
Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
Monte Carlo computer simulations are virtually the only way to analyze the thermodynamic behavior of a system in a precise way. However, the various existing methods exhibit extreme differences in their efficiency, depending on model…
Calculating thermodynamic potentials and observables efficiently and accurately is key for the application of statistical mechanics simulations to materials science. However, naive Monte Carlo approaches, on which such calculations are…
In this paper, we investigate the problem of assessing statistical methods and effectively summarizing results from simulations. Specifically, we consider problems of the type where multiple methods are compared on a reasonably large test…