CRM WorkshopPub Date : 2003-12-17DOI: 10.1090/crmp/033/09
H. Lefebvre-Brion
{"title":"Multichannel quantum defect study of the control in the frequency domain: Example of HI","authors":"H. Lefebvre-Brion","doi":"10.1090/crmp/033/09","DOIUrl":"https://doi.org/10.1090/crmp/033/09","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125453818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 2003-12-17DOI: 10.1090/CRMP/033
A. Bandrauk, M. Delfour, C. Bris
{"title":"Quantum Control - Mathematical and Numerical Challenges: CRM Workshop, Montreal, Canada, October 6-11, 2002","authors":"A. Bandrauk, M. Delfour, C. Bris","doi":"10.1090/CRMP/033","DOIUrl":"https://doi.org/10.1090/CRMP/033","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131850639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 2003-03-26DOI: 10.1090/crmp/033/05
G. Chen, D. Church, B. Englert, M. Zubairy
{"title":"Mathematical models of contemporary elementary quantum computing devices","authors":"G. Chen, D. Church, B. Englert, M. Zubairy","doi":"10.1090/crmp/033/05","DOIUrl":"https://doi.org/10.1090/crmp/033/05","url":null,"abstract":"Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any n-bit unitary operation can be carried out by concatenations of 1-bit and 2-bit elementary quantum gates. \u0000Three contemporary quantum devices--cavity QED, ion traps and quantum dots--have been widely regarded as perhaps the most promising candidates for the construction of elementary quantum gates. In this paper, we describe the physical properties of these devices, and show the mathematical derivations based on the interaction of the laser field as control with atoms, ions or electron spins, leading to the following: (i) the 1-bit unitary rotation gates; and (ii) the 2-bit quantum phase gates and the controlled-not gate. This paper is aimed at providing a sufficiently self-contained survey account of analytical nature for mathematicians, physicists and computer scientists to aid interdisciplinary understanding in the research of quantum computation.","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116298370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 2002-12-19DOI: 10.1090/crmp/033/01
O. Atabek, C. Dion
{"title":"Molecular alignment and orientation: From laser-induced mechanisms to optimal control","authors":"O. Atabek, C. Dion","doi":"10.1090/crmp/033/01","DOIUrl":"https://doi.org/10.1090/crmp/033/01","url":null,"abstract":"Genetic algorithms, as implemented in optimal control strategies, are currently successfully exploited in a wide range of problems in molecular physics. In this context, laser control of molecular alignment and orientation remains a very promising issue with challenging applications extending from chemical reactivity to nanoscale design. We emphasize the complementarity between basic quantum mechanisms monitoring alignment/orientation processes and optimal control scenarios. More explicitly, if on one hand we can help the optimal control scheme to take advantage of such mechanisms by appropriately building the targets and delineating the parameter sampling space, on the other hand we expect to learn, from optimal control results, some robust and physically sound dynamical mechanisms. We present basic mechanisms for alignment and orientation, such as pendular states accommodated by the molecule-plus-field effective potential and the \"kick\" mechanism obtained by a sudden excitation. Very interestingly, an optimal control scheme for orientation, based on genetic algorithms, also leads to a sudden pulsed field bearing the characteristic features of the kick mechanism. Optimal pulse shaping for very efficient and long-lasting orientation, together with robustness with respect to temperature effects, are among our future prospects.","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125772499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 1900-01-01DOI: 10.1090/crmp/033/12
E. Zuazua
{"title":"Remarks on the controllability of the Schrödinger equation","authors":"E. Zuazua","doi":"10.1090/crmp/033/12","DOIUrl":"https://doi.org/10.1090/crmp/033/12","url":null,"abstract":"In this paper we present some results on the controllability of the Schrodinger equation. We first discuss the controllability of the linear equation with a control distributed along a subdomain or subset of the boundary of the domain where the equation holds. We also analyze some possible extensions to semilinear equations in which the nonlinearity involves the state equation but the control enters linearly in the system. Finally we study the model bilinear control problem arising in Quantum Chemistry and some issues related with the numerical approximation of the controls.","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122602085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 1900-01-01DOI: 10.1090/crmp/033/11
Xiao-Gang Wang, T. Carrington
{"title":"Using contracted basis functions to solve the Schrödinger equation","authors":"Xiao-Gang Wang, T. Carrington","doi":"10.1090/crmp/033/11","DOIUrl":"https://doi.org/10.1090/crmp/033/11","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133518296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 1900-01-01DOI: 10.1090/crmp/033/07
R. Illner, H. Lange, Holger Teismann
{"title":"A note on the exact internal control of nonlinear Schrödinger equations","authors":"R. Illner, H. Lange, Holger Teismann","doi":"10.1090/crmp/033/07","DOIUrl":"https://doi.org/10.1090/crmp/033/07","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130855981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 1900-01-01DOI: 10.1090/crmp/033/06
M. Delfour
{"title":"Addendum and remarks on doubly conservative numerical schemes for the nonlinear Schrödinger equation and its control","authors":"M. Delfour","doi":"10.1090/crmp/033/06","DOIUrl":"https://doi.org/10.1090/crmp/033/06","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115602264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 1900-01-01DOI: 10.1090/crmp/033/02
A. Auger, A. Yedder, Marc Schoenauer
{"title":"Overview and software guide of evolutionary algorithms; A case study in quantum control","authors":"A. Auger, A. Yedder, Marc Schoenauer","doi":"10.1090/crmp/033/02","DOIUrl":"https://doi.org/10.1090/crmp/033/02","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116865721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CRM WorkshopPub Date : 1900-01-01DOI: 10.1090/crmp/033/10
Y. Ohtsuki, H. Rabitz
{"title":"Development of solution algorithms for quantum optimal control equations in product spaces","authors":"Y. Ohtsuki, H. Rabitz","doi":"10.1090/crmp/033/10","DOIUrl":"https://doi.org/10.1090/crmp/033/10","url":null,"abstract":"","PeriodicalId":122689,"journal":{"name":"CRM Workshop","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115417414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}