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We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.

During the three decades from 1930 to 1960 J. L. Doob was, with the possible exception of Kolmogorov, the man most responsible for the transformation of the study of probability to a mathematical discipline. His accomplishments were recognized by both probabilists and other mathematicians in that he is the only person ever elected to serve as president of both the IMS and the AMS. This article is an attempt to discuss his contributions to two areas in which his work was seminal, namely, the foundations of continuous parameter stochastic processes and probabilistic potential theory.

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: St Stephen College Library Delhi Date Accessioned: 10/1/2015 20:31 The Digital Library of India was a project under the auspices of the Government of India.

Book Source: Digital Library of India Item 2015.82199 dc.contributor.other: Fao dc.date.accessioned: 2015-06-30T17:24:42Z dc.date.available: 2015-06-30T17:24:42Z dc.date.copyrightexpirydate: 0000-00-00 dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1929 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2020050019283 dc.identifier.origpath: /data7/upload/0166/913 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/82199 dc.description.numberedpages: 384 dc.description.numberedpages: 13 dc.description.scanningcentre: RMSC, IIIT-H dc.description.slocation: IIIT, Hyderabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 398 dc.description.vendor: par dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Frederick Ungar Publishing Company dc.rights: Out_of_copyright dc.source.library: None dc.subject.classification: Language. Linguistics. Literature dc.title: Foundations Of Potential Theory dc.rights.holder: Oliver Dimon Kellogg

Book Source: Digital Library of India Item 2015.82199 dc.contributor.other: Fao dc.date.accessioned: 2015-06-30T17:24:42Z dc.date.available: 2015-06-30T17:24:42Z dc.date.copyrightexpirydate: 0000-00-00 dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1929 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2020050019283 dc.identifier.origpath: /data7/upload/0166/913 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/82199 dc.description.numberedpages: 384 dc.description.numberedpages: 13 dc.description.scanningcentre: RMSC, IIIT-H dc.description.slocation: IIIT, Hyderabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 398 dc.description.vendor: par dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Frederick Ungar Publishing Company dc.rights: Out_of_copyright dc.source.library: None dc.subject.classification: Language. Linguistics. Literature dc.title: Foundations Of Potential Theory dc.rights.holder: Oliver Dimon Kellogg

Book Source: Digital Library of India Item 2015.82199 dc.contributor.other: Fao dc.date.accessioned: 2015-06-30T17:24:42Z dc.date.available: 2015-06-30T17:24:42Z dc.date.copyrightexpirydate: 0000-00-00 dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1929 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2020050019283 dc.identifier.origpath: /data7/upload/0166/913 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/82199 dc.description.numberedpages: 384 dc.description.numberedpages: 13 dc.description.scanningcentre: RMSC, IIIT-H dc.description.slocation: IIIT, Hyderabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 398 dc.description.vendor: par dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Frederick Ungar Publishing Company dc.rights: Out_of_copyright dc.source.library: None dc.subject.classification: Language. Linguistics. Literature dc.title: Foundations Of Potential Theory dc.rights.holder: Oliver Dimon Kellogg

Book Source: Digital Library of India Item 2015.82199 dc.contributor.other: Fao dc.date.accessioned: 2015-06-30T17:24:42Z dc.date.available: 2015-06-30T17:24:42Z dc.date.copyrightexpirydate: 0000-00-00 dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1929 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2020050019283 dc.identifier.origpath: /data7/upload/0166/913 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/82199 dc.description.numberedpages: 384 dc.description.numberedpages: 13 dc.description.scanningcentre: RMSC, IIIT-H dc.description.slocation: IIIT, Hyderabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 398 dc.description.vendor: par dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Frederick Ungar Publishing Company dc.rights: Out_of_copyright dc.source.library: None dc.subject.classification: Language. Linguistics. Literature dc.title: Foundations Of Potential Theory dc.rights.holder: Oliver Dimon Kellogg