Langevin Dynamics With General Kinetic Energies

Dynamics of Langevin Simulations

This chapter reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite stepsize algorithms, Fourier acceleration, and the relation of the Langevin equation to hybrid stochastic algorithms and hybrid Monte Carlo. Invited chapter to appear in the special supplement “Stochastic Quantiza...

Mirrored Langevin Dynamics

We generalize the Langevin Dynamics through the mirror descent framework for first-order sampling. The näıve approach of incorporating Brownian motion into the mirror descent dynamics, which we refer to as Symmetric Mirrored Langevin Dynamics (S-MLD), is shown to connected to the theory of Weighted Hessian Manifolds. The S-MLD, unfortunately, contains the hard instance of Cox–Ingersoll–Ross pro...

Dimensional enhancement of kinetic energies

The intensity of light radiated from independent dipoles is the number, N , of dipoles times the intensity of a single one. However, when the dipoles are located within a wavelength of the radiation the total intensity is N times the intensity of a single dipole [1]. This superradiance effect is due to constructive interference between the individual dipoles. In the present article, we propose ...

Kinetic energies in quantum solids.

Smoothed Langevin Dynamics of Highly Oscillatory Systems Smoothed Langevin Dynamics of Highly Oscillatory Systems

In this paper we generalize a result by Rubin and Ungar on Hamiltonian systems containing a strong constraining potential to Langevin dynamics. Such highly oscillatory systems arise, for example, in the context of molecular dynamics. We derive constrained equations of motion for the slowly varying solution components. This includes in particular the derivation of a correcting force-term that st...