Extending J walking to quantum systems: Applications to atomic clusters

Abstract

The J-walking (or jump-walking) method is extended to quantum systems by incorporating it into the Fourier path integral Monte Carlo methodology. J walking can greatly reduce systematic errors due to quasiergodicity, or the incomplete sampling of configuration space in Monte Carlo simulations. As in the classical case, quantum J walking uses a jumping scheme ,to overcome configurational barriers. It couples the usual Metropolis sampling to a distribution generated at a higher temperature where the sampling is sufficiently ergodic. The J-walker distributions used in quantum J walking can be either quantum or classical, with classical distributions having the advantage of lower storage requirements, but the disadvantage of being slightly more computationally intensive and having a more limited useful temperature range. The basic techniques are illustrated first on a simple onedimensional double well potential based on a quartic polynomial. The suitability of J walking for typical multidimensional quantum Monte Carlo systems is then shown by applying the method to a multiparticle cluster system consisting of rare gas atoms bound by pairwise Lennard-Jones potentials. Different degrees of quantum behavior are considered by examining both argon and neon clusters. Remarkable improvements in the convergence rate for the cluster energy and heat capacity, analogous to those found in classical systems, are found for temperatures near the cluster transition regions.

Stochastic potential switching algorithm for Monte Carlo simulations of complex systems

“…In form described above, the SPS idea is conceptually related to J-walking [5,6,7], parallel tempering [10,11,12,13], and the "approximate potential" method [16]. In J-walking, the simulation is stochastically switched to a configuration sampled from a highertemperature (T ′ ) simulation of the same potential with properly chosen transition probabilities.…”

“…But the procedure has to follow a carefully constructed algorithm to guarantee that detailed balance with respect to the original potential is maintained, so that the correct statistics are produced. An idea similar to this has been exploited in a number of previously proposed Monte Carlo methods, such as J-walking [5,6,7], simulated tempering [8,9], parallel tempering [10,11,12,13], catalytic tempering [14], multicanonical J-walking [15] and the approximate potential method [16]. But we will show that when generalized to multidimensional systems, the present method provides flexibilities and potential advantages that are not available with these previous methods and establishes a theoretical framework for the design of possibly more efficient algorithms for simulating complex systems.…”

Magic number behavior for heat capacities of medium-sized classical Lennard-Jones clusters

“…This poor convergence is a consequence of quasiergodicity, or the incomplete sampling of configuration space. 18 Various methods have been developed in recent years to reduce the systematic errors resulting from quasiergodicity, including histogram methods, 20 jumpwalking methods (J-walking), [21][22][23][24][25][26][27][28] smart walking methods (S-walking), 29 and parallel tempering methods. [30][31][32] Many of these methods are based on the coupling of configurations obtained from ergodic higher-temperature simulations to the quasiergodic lower-temperature simulations.…”

Thermodynamics and equilibrium structure of Ne38 cluster: Quantum mechanics versus classical

“…However, it has long been known that the Ne clusters exhibit strong quantum effects, not only in the low temperature regime, but also in liquid phase [4]. Still, perhaps because 7 and 13 are magic numbers, the quantum effects do not essentially change the structural or thermodynamic properties of the respective Ne clusters.…”