{"paper":{"title":"Stochastic mechanics, trace dynamics, and differential space - a synthesis","arxiv_id":"quant-ph/0602211","primary_cat":"quant-ph","submitted_at":"2006-02-25T17:56:02+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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diffusions.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.56,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.31,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.69,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.31}},{"i":2,"p":0.98,"id":"s2","own":true,"role":"contribution","text":"A new variational approach to stochastic mechanics based on trace dynamics is introduced.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.92,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}},{"i":3,"p":0.64,"id":"s3","own":true,"role":"result","text":"It is shown that Yasue's method and Guerra and Morato's method can both be generalized to allow for any diffusion constant in a stochastic model of Schrodinger's equation, and that they can all also describe dissipative diffusion.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.76,"main_claim_p":0.17,"quantitative":false,"quantitative_p":0.27,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.64,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.35,"interpretation":0.0}},{"i":4,"p":0.81,"id":"s4","own":true,"role":"result","text":"Then it is shown that the trace dynamical theory seems to only describe dissipative diffusion unless an extra quantum mechanical potential term is added to the Hamiltonian.","hedge":{"p":0.73,"label":"hedged_possibility"},"own_p":0.82,"main_claim_p":0.26,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.81,"background":0.0,"limitation":0.19,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.83,"id":"s5","own":true,"role":"contribution","text":"The differential space theory of Wiener and Siegel is reconsidered as a useful tool in this framework, and is generalized to stochastic 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