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Any realistic quantum system is coupled to its environment even if this coupling is very weak. The influence of the environment results in dissipation of energy as well as the decay of the coherences of the system. Both effects have to be taken into account to accurately describe the time evolution of an initial state prepared in the system. A typical model system for the study of
these effects is a single anharmonic oscillator, linearly coupled to a bath of harmonic oscillators at a fixed temperature. The dynamics of the heat bath is treated using the influence functional formalism [1]. We generate numerical results for the system under the influence of the heat bath using trajectory based descriptions of quantum mechanics. Examples are semiclassical techniques
in initial value representation [2] and Bohmian mechanics with complex action.
[1] Feynman, R. P. & Vernon, F. L.. "The theory of a general quantum system interacting with a linear dissipative system." Annals of Physics, no. 24 (1963): 118-173. [2] Herman, M. F. & Kluk, E.. "A semiclassical justification for the use of nonspreading wavepackets in dynamics calculations." Chemical Physics, vol. 91 (1984): 27-34 |
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