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Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated. <\/jats:p>","DOI":"10.1142\/s1230161218500142","type":"journal-article","created":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T08:04:37Z","timestamp":1544429077000},"page":"1850014","source":"Crossref","is-referenced-by-count":67,"title":["Non-Markovian Evolution: a Quantum Walk Perspective"],"prefix":"10.1142","volume":"25","author":[{"given":"N. Pradeep","family":"Kumar","sequence":"first","affiliation":[{"name":"The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India"}]},{"given":"Subhashish","family":"Banerjee","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Jodhpur, Jodhpur 342011, India"}]},{"given":"R.","family":"Srikanth","sequence":"additional","affiliation":[{"name":"Poornaprajna Institute of Scientific Research, Bangalore- 560 080, India"}]},{"given":"Vinayak","family":"Jagadish","sequence":"additional","affiliation":[{"name":"Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa"},{"name":"National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, South Africa"}]},{"given":"Francesco","family":"Petruccione","sequence":"additional","affiliation":[{"name":"Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa"},{"name":"National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, South Africa"}]}],"member":"219","published-online":{"date-parts":[[2018,12,10]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.022316"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.78.052316"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.062109"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/45\/014"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.109.183602"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.91.052309"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1038\/nature12802"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.91.012324"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/77\/9\/094001"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.89.015001"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/s003400000460"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.99.140403"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.143002"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.84.012114"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.032106"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms8606"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(88)90023-3"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.47.1576"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.056120"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.042105"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.210401"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.88.021002"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.82.042107"},{"key":"p_25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.105.050403"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.83.052128"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.080407"},{"key":"p_28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.118.120501"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.062340"},{"key":"p_31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.89.052330"},{"key":"p_33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.70.010304"},{"key":"p_35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.36.823"},{"key":"p_36","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2009.10.042"},{"key":"p_37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.066120"},{"key":"p_38","first-page":"541","volume":"11","author":"Chakrabarty I.","year":"2011","journal-title":"Quant. 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