2002/11/20 by Luca Capriotti, Alessandro Cuccoli, Andrea Fubini +2
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Quantum many-body systems #Quantum, superfluid, helium dynamics #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1002/pssb.200301797
published as Phys. Stat. Sol. (b) 237, 23 (2003) · 10 pages, 5 figures, contribution to the "Festschrift" dedicated to Prof. Jozef T. Devreese
arxiv created 2002/11/20 · openalex publication_date 2003/04/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Abstract We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira–Leggett formulation, which describes the system in the path‐integral formalism through the inclusion of an influence action that is bilocal and quadratic in the system's coordinates. At a first sight the usual direct approach of discretizing the path integral could seem feasible, but complications arise when one tries to introduce a physically meaningful dissipation kernel: in particular its imaginary‐time dependence turns out to be severely singular and difficult to evaluate analytically, in spite of the simple expressions for its Matsubara components. We therefore propose to face the numerical problem using Fourier path‐integral Monte Carlo, that can be formulated in two different ways: transforming the continuous paths and then truncating the high Fourier components (with possible improvements upon the truncation procedure), or performing the Fourier transformation upon the discretized paths. The latter choice leads to a simpler formulation and allows for a better control of the extrapolation to the limit of infinite Trotter number. The method is implemented for a single nonlinear particle with Ohmic dissipation and for a ϕ 4 chain with Drude‐like dissipation.