Non-Markovian trajectories involving future in semi-classical path integral expression
European Journal of Physics, ISSN: 1361-6404, Vol: 42, Issue: 1
2021
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Article Description
Semi-classical path integral expression for a quantum system coupled to a harmonic bath is derived based on the stationary phase condition. It is discovered that the system path is non-Markovian. Most strikingly, the system path not only couples to its past, but also to its future, i.e. the equation of motion for the system is an integro-differential equation that involves all times. Numerical examples are given at the end. Because of the future-non-Markovian nature of the equation, the numerical solution cannot be obtained by iterative methods. Instead, root search algorithms must be employed.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85099125995&origin=inward; http://dx.doi.org/10.1088/1361-6404/abb7e3; https://iopscience.iop.org/article/10.1088/1361-6404/abb7e3; https://dx.doi.org/10.1088/1361-6404/abb7e3; https://validate.perfdrive.com/9730847aceed30627ebd520e46ee70b2/?ssa=31210f15-e7f5-4e61-b64a-5b7fe6b339a3&ssb=89702234296&ssc=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F1361-6404%2Fabb7e3&ssi=cd3fc9f4-cnvj-41de-a96b-16123cfd1e22&ssk=botmanager_support@radware.com&ssm=75284640181808950199811456339731310&ssn=535c0451929db56589f65e414921fbf35c9611e4fc9b-fb87-4f4d-9ebd8a&sso=00593121-2d7afa72fb70fe0fdaba58dcaf6cb15a439226fb4d7ec256&ssp=01778440561727208565172754014909250&ssq=29947072554579455939389217638067397134901&ssr=NTIuMy4yMTcuMjU0&sst=com.plumanalytics&ssu=&ssv=&ssw=&ssx=eyJ1em14IjoiN2Y5MDAwNTVmODk4Y2YtYWZlOS00YThjLWIxZjEtZWFmODE3MTQ1NzM3NC0xNzI3Mjg5MjE3MzMwMjM2MzI4MjA4LWEyZmEwMWY1ZDE5ZmUxOTcxOTk4MSIsIl9fdXptZiI6IjdmNjAwMDdmNTZkOWViLTQ0ODgtNDJiZi1iMjIxLTA5Y2Y5MmRiNTYyZDE3MjcyODkyMTczMzAyMzYzMjgyMDgtNDBjN2Y1NThmN2JmYTMwMDE5OTgxIiwicmQiOiJpb3Aub3JnIn0=
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