Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation

Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of the local environment (i.e., a thermal bath). In the case of classical systems, strong system-bath interaction has been successfully modelled by the Generalised Langevin Equation (GLE) formalism. Here we show that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014) can be extended to include some crucial aspects of the quantum fluctuations. In particular, the expected isotopic effect is observed along with the convergence of the quantum and classical transition rates in the strong coupling limit. Saturation of the transition rates at low temperature is also retrieved, in qualitative, yet not quantitative, agreement with the analytic predictions. The discrepancies in the tunnelling regime are due to an incorrect sampling close to the barrier top. The domain of applicability of the quasiclassical GLE is also discussed.Comment: 21 pages, 5 figures. Presented at the NESC16 conference: Advances in theory and simulation of non-equilibrium system

Applications of the Generalised Langevin Equation: towards a realistic description of the baths

The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalises toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.Comment: accepted for publication in PR

The large-scale magnetic field in the solar wind

A literature review is presented of theoretical models of the interaction of the solar wind and interplanetary magnetic fields. Observations of interplanetary magnetic fields by the IMP and OSO spacecraft are discussed. The causes for cosmic ray variations (Forbush decreases) by the solar wind are examined. The model of Parker is emphasized. This model shows the three dimensional magnetic field lines of the solar wind to have the form of spirals wrapped on cones. It is concluded that an out-of-the-ecliptic solar probe mission would allow the testing and verification of the various theoretical models examined. Diagrams of the various models are shown

Perturbative calculation of quasi-normal modes of AdS Schwarzschild black holes

We calculate analytically quasi-normal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasi-normal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic.Comment: 20 pages incl. 8 figures (using eepic and color

Nonequilibrium processes from Generalised Langevin Equations: realistic nanoscale systems connected to two thermal baths

We extend the Generalised Langevin Equation (GLE) method [Phys. Rev. B 89, 134303 (2014)] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nose-Hoover thermostats). We concentrate on the steady state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e. ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.Comment: present version accepted for publication in Phys. Rev. B (Apr 2016