Efficient choice of colored noise in the stochastic dynamics of open quantum systems

The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

Optimization algorithm for rate equations with an application to epitaxial graphene

We describe an algorithm that searches the parameter space of rate theories to optimize the associated rate coefficients based on a fit to experimental (or any other) data. Beginning with an initial set of parameters, which may be estimated, partially calculated, or indeed random, the algorithm follows a path, calculating the error at each point, until a minimum error is reached. We illustrate our method by correcting a previously proposed rate theory for the nucleation and growth of graphene on Ru(0 0 0 1) and Ir(1 1 1) to account for the temperature dependence of the graphene island density. This quantity shows an exponential decrease as the temperature is raised, in contrast to the power law decrease predicted by conventional nucleation theory, which indicates that a qualitatively different mechanism is operative for graphene island formation. Other applications of our method are also discussed.

Phase coexistence in colloidal suspensions: an analytic Poisson-Boltzmann treatment

We solve the linearized Poisson-Boltzmann equation analytically, subject to justifiable approximations, for a suspension containing a large number of identical spherical macroions under conditions of constant surface charge and zero added salt, in order to investigate the phase behavior of charge-stabilized colloidal suspensions. Our results for the electrostatic part of the Helmholtz free energy lead to an interaction which resembles the intermolecular interaction in the theory of molecular fluids. When combined with the ideal gas free energy of the counterions, this produces a van der Waals loop in the pV diagram, indicating coexistence between phases with different densities, for certain values of the macroion radius and charge. We also derive an expression for the surface potential of the macroions, and clarify the interpretation of the Poisson-Boltzmann equation.

Mixing of atmospheric gas concentrations

Atmospheric gas concentrations were measured at 1 s intervals in the upper troposphere during a flight through and near the anvil of a storm. The observed very high correlations between the concentrations of CO and CH4 are interpreted as arising from the mixing of two distinct air masses with differing concentrations of each species, and is due to the nearly identical diffusivities of CO and CH4 in air. We find that the correlations depend on the period over which each concentration measurement was made. Correlations in measurements made over short periods decay with time, while correlations over larger scales remain high. We interpret this using a simple mixing model.

Nucleation theorems applied to the Ising model

We use Monte Carlo simulations to study a single cluster of "up" spins in a sea of "down" spins in the three-dimensional Ising model. We evaluate the growth and decay rates for clusters of different sizes, identify the critical size for which these rates are equal, and obtain the internal energy of the critical size cluster. The results of the simulations at different temperatures and magnetic fields are used together with the first and second nucleation theorems to predict how the cluster nucleation rate changes when the external magnetic field and the temperature are changed. Our results are in agreement with literature values, but our method requires significantly less computational effort than the simulations reported earlier and avoids the difficult evaluation of free energies.