Abstract
Feynman’s path integral approach to time-dependent quantum mechanics1 has found wide application in many areas of physics. Its most celebrated successes include situations where the effects of a dissipative environment on the system of interest can be adequately represented via a bath of harmonic oscillators. Due to its Gaussian character, the multidimensional bath can be integrated out,2 giving rise to reduced-dimension descriptions of the dynamics which in simple cases are amenable to a host of analytic approximations. Another major field where path integral ideas have proven extremely useful is quantum statistical mechanics.3 Expressing equilibrium averages of many-body systems in path integral form allows, after appropriate discretization, numerical evaluation via stochastic integration schemes.4 By contrast, the use of numerical methods to compute real-time path integral expressions of many-particle systems has not been met with success. The reason behind the failure of numerical schemes lies in the oscillatory nature of the quantum mechanical propagator which renders stochastic integration methods inappropriate.5
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Makri, N. (1997). Path Integral Simulation of Long-Time Dynamics in Quantum Dissipative Systems. In: DeWitt-Morette, C., Cartier, P., Folacci, A. (eds) Functional Integration. NATO ASI Series, vol 361. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0319-8_7
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