Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0602269

Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

Rosalind J. Allen·Daan Frenkel·Pieter Rein ten Wolde
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods, and for the statistical error in the final estimate of the rate constant, for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.

Explore related subjects

cond-mat.otherphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rosalind J. Allen, Daan Frenkel, Pieter Rein ten Wolde. 2006-02-10. Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis. https://doi.org/10.1063/1.2198827

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

THz-Driven Quantum Ionic Magnetism in a Quantum Paraelectric SrTiO3

Magnetic moments carried by rotating ionic motion in crystals are becoming recognized as an important contribution to magnetism, angular momentum transport, and optical activity. However, efficient approaches to their dynamical control are lacking. Here, we report THz-driven generation and optical detection of quantum ionic magnetism in quantum paraelectric SrTiO3. We observe an oscillatory ionic magnetization without a corresponding oscillatory polarization, contradicting from the classical relation M~PXdP/dt while its suppression above the quantum paraelectric regime points to a quantum ionic origin. Analysis shows that this effect results from the beating between quantum ionic eigenstates whose degeneracy is lifted due to the directional symmetry breaking by the THz pulse. The presented approach provides a pathway for the ultrafast control of ionic magnetization in quantum materials for spintronic and thermotronic applications.

cond-mat.other↗
arXiv2026

Resonantly Enhanced Multiphonon Scattering and Local Orbital-Phonon Coupling in Bulk and Thin Flakes of 2D Single Crystals of Antiferromagnetic (NixFe1-x)2P2S6

Orbital degrees of freedom play a pivotal role in shaping the physical properties of two-dimensional (2D) van der Waals magnetic systems, strongly influencing electron-phonon coupling and intermediate-state dynamics. In this study, we present a comprehensive temperature and thickness-dependent Raman investigation of the single crystals of 2D van der Waals antiferromagnetic series (NixFe1-x)2P2S6. Utilizing Raman spectroscopy, we explore the interplay between local orbital excitations and lattice vibrations, observing higher-order phonon modes extending up to the fourth order. We observe an anomalously high and weakly temperature-dependent intensity ratio of these higher-order modes relative to low-energy first-order phonons. Theoretical cluster calculations and Franck-Condon modelling reveal that these features originate from resonantly enhanced multiphonon scattering mediated by localized intermediate Ni 3d8 multiplet excitations. The local orbital occupancy of these intermediate states couples strongly to lattice coordinates, providing a selective enhancement mechanism for specific phonon channels. Notably, these higher-order features are absent in the end-member Fe2P2S6. This distinction reflects the charge-transfer character of Ni2P2S6, which places optical transitions in resonance with local multiplet states, contrasted with the Mott-Hubbard insulator regime in Fe-rich analogues. Our findings clarify the microscopic origin of high-frequency Raman scattering in transition metal thiophosphates and underscore the central role of local orbital-phonon interactions in 2D correlated magnets.

cond-mat.other↗
arXiv2026

Matching Rules for a Three-Dimensional Strongly Aperiodic Monotile

A recent pre-print [arXiv:2609.19214] proposed a three-dimensional (3D) strongly aperiodic monotile: a shape that tiles Euclidean space only aperiodically and which admits no symmetry of infinite order. The proof takes the 3D Chair tile identified previously by Lee and Moody, and adds geometric decorations to the faces so as to force aperiodicity (without these decorations The Chair also admits periodic tilings). Here we establish general requirements on face decorations to achieve the same end, in order to facilitate the search for physical realisations. We find that the requirements are minimal. We provide matching rules using three colours of arrow. They are not equivalent to the original rules, but force the same tiling by forcing Chairs to compose into `Superchairs' with doubled linear dimensions. In this process the matching rules themselves compose uniquely, which is the core of the earlier proof. Relaxing this constraint further we find that the same structure can be forced using only a matching rule based on the colours of squares, regardless of orientation. Any physical system encoding these rules (geometrically or otherwise) will force the strongly aperiodic monotiling. We provide simple examples.

cond-mat.other↗