An open source MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs

This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian matrix describing its energy, and a spectral distribution function and temperature describing the environment's influence on it, in addition to the open quantum system's intial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all (or some) moments specified by that grid of times. This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time-propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integal actually becomes the rate limiting step for most cases tested so far. The overhead of transfrring information from the CPU to the GPU and back seems to have negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU.Comment: 8 pages, 2 figures, 1 table, 22 reference

Convection in nanofluids with a particle-concentration-dependent thermal conductivity

Thermal convection in nanofluids is investigated by means of a continuum model for binary-fluid mixtures, with a thermal conductivity depending on the local concentration of colloidal particles. The applied temperature difference between the upper and the lower boundary leads via the Soret effect to a variation of the colloid concentration and therefore to a spatially varying heat conductivity. An increasing difference between the heat conductivity of the mixture near the colder and the warmer boundary results in a shift of the onset of convection to higher values of the Rayleigh number for positive values of the separation ratio psi>0 and to smaller values in the range psi<0. Beyond some critical difference of the thermal conductivity between the two boundaries, we find an oscillatory onset of convection not only for psi<0, but also within a finite range of psi>0. This range can be extended by increasing the difference in the thermal conductivity and it is bounded by two codimension-2 bifurcations.Comment: 13 pages, 11 figures; submitted to Physical Review

Anomalous diffusion in viscosity landscapes

Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation in limiting cases confirm our results. For an ensemble of particles starting at a spatial minimum (maximum) of the viscous damping we find subdiffusive (superdiffusive) motion. Superdiffusion occurs also for a monotonically varying viscosity profile. We suggest different substances for related experimental investigations.Comment: 15 page