When a minimum on the potential energy surface is surrounded by multiple saddle points with similar energy barriers, the transition pathways with greater prefactors are more important than those that have similar energy barriers but smaller prefactors. In this paper, we present a theoretical formulation for the prefactors, computing the probabilities for transition paths from a minimum to its surrounding saddle points. We apply this formulation to a system of 2 degrees of freedom and a system of 14 degrees of freedom. The first is Brownian motion in a two-dimensional potential whose global anharmonicities play a dominant role in determining the transition rates. The second is a Lennard-Jones (LJ) cluster of seven particles in two dimensions. Low lying transition states of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics nor of the product states they lead to. The probabilities are computed for paths going from an equilibrium ensemble of states near a given minimum to the surrounding transition states. These probabilities are directly related to the prefactors in the rate formula. This determination of the rate prefactors includes all anharmonicities, near or far from transition states, which are pertinent in the very sophisticated energy landscape of LJ clusters and in many other complex systems.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1063/1.2188943 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Defect Conformal Field Theory from Sachdev-Ye-Kitaev Interactions.
Phys Rev Lett
December 2024
Tulane University, Department of Physics and Engineering Physics, New Orleans, Louisiana 70118, USA.
The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling N Majorana chains with SYK_{q} interactions at the defect. Our analysis reveals that the interaction with q=2 constitutes a new marginal defect.
View Article and Find Full Text PDFProbing Critical States of Matter on a Digital Quantum Computer.
Phys Rev Lett
December 2024
Quantinuum, 303 S. Technology Court, Broomfield, Colorado 80021, USA.
Although quantum mechanics underpins the microscopic behavior of all materials, its effects are often obscured at the macroscopic level by thermal fluctuations. A notable exception is a zero-temperature phase transition, where scaling laws emerge entirely due to quantum correlations over a diverging length scale. The accurate description of such transitions is challenging for classical simulation methods of quantum systems, and is a natural application space for quantum simulation.
View Article and Find Full Text PDFNematic versus Kekulé Phases in Twisted Bilayer Graphene under Hydrostatic Pressure.
Phys Rev Lett
December 2024
Instituto de Ciencia de Materiales de Madrid, CSIC, E-28049 Madrid, Spain.
We address the precise determination of the phase diagram of magic angle twisted bilayer graphene under hydrostatic pressure within a self-consistent Hartree-Fock method in real space, including all the remote bands of the system. We further present a novel algorithm that maps the full real-space density matrix to a 4×4 density matrix based on a SU(4) symmetry of sublattice and valley degrees of freedom. We find a quantum critical point between a nematic and a Kekulé phase, and show also that our microscopic approach displays a strong particle-hole asymmetry in the weak coupling regime.
View Article and Find Full Text PDFOrientation selectivity properties for the affine Gaussian derivative and the affine Gabor models for visual receptive fields.
J Comput Neurosci
January 2025
Computational Brain Science Lab, Division of Computational Science and Technology, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden.
This paper presents an in-depth theoretical analysis of the orientation selectivity properties of simple cells and complex cells, that can be well modelled by the generalized Gaussian derivative model for visual receptive fields, with the purely spatial component of the receptive fields determined by oriented affine Gaussian derivatives for different orders of spatial differentiation. A detailed mathematical analysis is presented for the three different cases of either: (i) purely spatial receptive fields, (ii) space-time separable spatio-temporal receptive fields and (iii) velocity-adapted spatio-temporal receptive fields. Closed-form theoretical expressions for the orientation selectivity curves for idealized models of simple and complex cells are derived for all these main cases, and it is shown that the orientation selectivity of the receptive fields becomes more narrow, as a scale parameter ratio , defined as the ratio between the scale parameters in the directions perpendicular to vs.
View Article and Find Full Text PDFBy utilizing the time inversion of radiation from spatial dipole arrays, we propose a method for constructing the spatial lattice-type skyrmion arrays under 4 focusing conditions, including Néel-, Bloch-, and Anti-skyrmions/merons. The Richards-Wolf vector diffraction theory is applied to analyze the radiation field emitted by dipole arrays, aiming to determine the incident field required under a high numerical aperture (NA=0.95).
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!