Numerical study of tunneling in a dissipative system

Semiclassical dynamics of open quantum systems: Comparing the finite with the infinite perspective

“…One possibility is to explicitly calculate their dynamics alongside the system DOFs including all interactions between the two sets. This approach has, e.g., been employed to tunneling/spin-boson problems [5][6][7][8] as well as to the interaction of (an)harmonic oscillators with a thermal bath [6,[9][10][11]7,12]. Another choice would recast the environmental influence into an alternative formalism that captures the bath dynamics implicitly.…”

Decay Rates of Metastable States in Cubic Potential by Variational Perturbation Theory

“…A particle in a one-dimensional anharmonic oscillator with a cubic potential is a popular model for tunneling processes with negligible backscattering. It has been widely used in the calculation of non-zero temperature quantum transition rates in the presence of friction 1,2]. All such studies have been restricted to the regime of high barriers, where saddle-point and instanton methods are applicable.…”

Periodic Orbit Approach to the Quantum‐Kramers‐Rate

“…This yields [28] Z , = Aldet 6'S, I ; = ! ( : , expressing A by use of (20b), one finds with n set equal to one upon the comparison of (19) with (14) where…”

“…In other words, we analytically continue the semiclassical propagator (qlexp(-iH t / h ) l q ) to complex times t = -it. The analytically continued Green's function then formally reads [28] The time integration inherent in (13) must be understood to be performed in SPA with the integration path deformed so as to go through the stationary points in the direction of steepest descent. This procedure is consistent with the use of the semiclassical approximation.…”

“…In our case, we consider the Euclidean Lagrangian for a harmonic bath coupled bilineary to the nonlinear reaction coordinate x. (17) Following the standard procedure, one finds after integrating first over the harmonic bath degrees of freedom in terms of the dissipative bounce trajectory cj(r') and the well-known non-local (Euclidean) Lagrangian LeII [S-9, 13, 141 for the trace the result [28] Tr…”