{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:51:10Z","timestamp":1760241070436,"version":"build-2065373602"},"reference-count":68,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T00:00:00Z","timestamp":1574640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schr\u00f6dinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction (linked to the corresponding Bohmian trajectory) as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of freedom. As an example of the practical utility of these states, we present a time-dependent quantum Monte Carlo algorithm to describe electron transport in open quantum systems under general (Markovian or non-Markovian) conditions. By making the most of trajectory-based and wavefunction methods, the resulting simulation technique extends to the quantum regime, the computational capabilities that the Monte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.<\/jats:p>","DOI":"10.3390\/e21121148","type":"journal-article","created":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T05:52:58Z","timestamp":1574661178000},"page":"1148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Stochastic Schr\u00f6dinger Equations and Conditional States: A General Non-Markovian Quantum Electron Transport Simulator for THz Electronics"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0349-6913","authenticated-orcid":false,"given":"Devashish","family":"Pandey","sequence":"first","affiliation":[{"name":"Departament d\u2019Enginyeria Electr\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrique","family":"Colom\u00e9s","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Electr\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Albareda","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Electr\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra (Barcelona), Spain"},{"name":"Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany"},{"name":"Institute of Theoretical and Computational Chemistry, Universitat de Barcelona, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xavier","family":"Oriols","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Electr\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1103\/RevModPhys.55.645","article-title":"The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials","volume":"55","author":"Jacoboni","year":"1983","journal-title":"Rev. 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