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General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry.
E. Cartan, Bull. Soc. Math. France 41
1913
Earlier work this paper cites.
P. Jordan, E. Wigner, Z. Phys. 47
1928
Earlier work this paper cites.
R. Brauer, H. Weyl, Amer. J. Math. 57
1935
Earlier work this paper cites.
L.K. Hua, Amer. J. Math. 66
1944
Earlier work this paper cites.
A. Borel, J. De Siebenthal, Comment. Math. Helv. 23
1949
Earlier work this paper cites.
A.I. Malcev, Amer. Math. Soc. Transl. 33
1950
Earlier work this paper cites.
H. Weyl, The Classical Groups: Their Invariants and Representations , 2nd edn. (Princeton University Press, Princeton, 1953)
1953
Earlier work this paper cites.
Reprinted in [ 89 ]
E.B. Dynkin, Amer. Math. Soc. Transl. Ser. 2 6 · 1957
Earlier work this paper cites.
Reprinted in [ 89 ]
E.B. Dynkin, Amer. Math. Soc. Transl. Ser. 2 6 · 1957
Earlier work this paper cites.
M. Obata, Trans. Amer. Math. Soc. 87
1958
Earlier work this paper cites.
E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 18
1961
Earlier work this paper cites.
F.A. Berezin, The Method of Second Quantization (Academic Press, New York, 1966)
1966
Earlier work this paper cites.
H. Boerner, Darstellungen von Gruppen , Die Grundlehren der mathematischen Wissenschaften , vol. 74, 2nd edn. (Springer, Berlin, 1967)
1967
Earlier work this paper cites.
R. Kalman, P.L. Falb, M.A. Arbib, Topics in Mathematical System Theory (McGraw-Hill, New York, 1969)
1969
Earlier work this paper cites.
A.K. Bose, J. Patera, J. Math. Phys. 11
1970
Earlier work this paper cites.
S. Sakai, C ∗ C^{*} -Algebras and W ∗ W^{*} -Algebras (Springer, Berlin, 1971)
1971
Earlier work this paper cites.
R.W. Brockett, SIAM J. Control 10
1972
Earlier work this paper cites.
H. Sussmann, V. Jurdjevic, J. Diff. Equat. 12
1972
Earlier work this paper cites.
V. Jurdjevic, H. Sussmann, J. Diff. Equat. 12
1972
Earlier work this paper cites.
Pure and Applied Mathematics (Academic Press, London, 1972)
W. Miller, Symmetry Groups and Their Applications · 1972
Earlier work this paper cites.
D.P. Želobenko, Compact Lie Groups and Their Representations (American Mathematical Society, Providence, 1973)
1973
Earlier work this paper cites.
R.W. Brockett, SIAM J. Appl. Math. 25
1973
Earlier work this paper cites.
B.G. Wybourne, Classical Groups for Physicists (John Wiley & Sons, New York, 1974)
1974
Earlier work this paper cites.
C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, 1976)
1976
Earlier work this paper cites.
H. Primas, U. Müller-Herold, Adv. Chem. Phys. 38
1978
Earlier work this paper cites.
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic Press, New York, 1978)
1978
Earlier work this paper cites.
W.M. Boothby, E.N. Wilson, SIAM J. Control Optim. 17
1979
Earlier work this paper cites.
N. Jacobson, Lie Algebras (Dover, New York, 1979)
1979
Earlier work this paper cites.
W.G. MacKay, J. Patera, Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras (Marcel Dekker, New York, 1981)
1981
Earlier work this paper cites.
J. Dixmier, Von Neumann Algebras (North Holland, Amsterdam, 1981)
1981
Earlier work this paper cites.
H.V. Henderson, S.R. Searle, Lin. Multilin. Alg. 9
1981
Earlier work this paper cites.
R.P. Feynman, Int. J. Theor. Phys. 21
1982
Earlier work this paper cites.
F. Wilczek, A. Zee, Phys. Rev. D 25
1982
Earlier work this paper cites.
J.F. Cornwell, Group Theory in Physics , vol. 2 (Academic Press, London, 1984)
1984
Earlier work this paper cites.
J.P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (The MIT Press, Cambridge, 1986)
1986
Earlier work this paper cites.
D.H. Sattinger, O.L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics , Applied Mathematical Sciences , vol. 61 (Springer, New York, 1986)
1986
Earlier work this paper cites.
A. Peirce, M. Dahleh, H. Rabitz, Phys. Rev. A 37
1987
Earlier work this paper cites.
W. Ledermann, Introduction to Group Characters , 2nd edn. (Cambridge University Press, Cambridge, 1987)
1987
Earlier work this paper cites.
No. 365 in Mem. Amer. Math. Soc. (American Mathematical Society, Providence, 1987)
G.M. Seitz, The Maximal Subgroups of Classical Algebraic Groups · 1987
Earlier work this paper cites.
No. 390 in Mem. Amer. Math. Soc. (American Mathematical Society, Providence, 1988)
D.M. Testerman, Irreducible Subgroups of Exceptional Algebraic Groups · 1988
Earlier work this paper cites.
H.B. Lawson, M.L. Michelson, Spin Geometry (Princeton University Press, NJ, 1989)
1989
Earlier work this paper cites.
H. Samelson, Notes on Lie Algebras , 2nd edn. (Springer, New York, 1990)
1990
Earlier work this paper cites.
R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 1991)
1991
Earlier work this paper cites.
W. Fulton, J. Harris, Representation Theory: A First Course (Springer, New York, 1991)
1991
Earlier work this paper cites.
G. Stuck, Isr. J. Math. 76
1991
Earlier work this paper cites.
Encyclopaedia of Mathematical Sciences Vol. 41
V.V. Gorbatsevich, A.L. Onishchik, E.B. Vinberg, Lie Groups and Lie Algebras III (Springer, Berlin, 1994), chap. Structure of Lie Groups and Lie Algebras, pp. 1–244 · 1994
Earlier work this paper cites.
R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (Krieger Publishing Company, Florida, 1994)
1994
Earlier work this paper cites.
V. Ramakrishna, H. Rabitz, Phys. Rev. A 54
1995
Cited alongside, same era.
V. Ramakrishna, M. Salapaka, M. Daleh, H. Rabitz, A. Peirce, Phys. Rev. A 51
1995
Cited alongside, same era.
A. Barenco, C.H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P.W. Shor, T. Sleator, J.A. Smolin, H. Weinfurter, Phys. Rev. A 52
1995
Cited alongside, same era.
R.P. Feynman, Feynman Lectures on Computation (Perseus Books, Reading, MA., 1996)
1996
Cited alongside, same era.
S. Lloyd, Science 273
1996
Cited alongside, same era.
V.F. Krotov, Global Methods in Optimal Control (Marcel Dekker, New York, 1996)
1996
Cited alongside, same era.
N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, S.J. Glaser, J. Magn. Reson. 172
2005
Later among the works it cites.
T. Schulte-Herbrüggen, A.K. Spörl, N. Khaneja, S.J. Glaser, Phys. Rev. A 72
2005
Later among the works it cites.
J.P. Keating, F. Mezzadri, Phys. Rev. Lett. 94
2005
Later among the works it cites.
F.H.L. Essler, H. Frahm, F. Göhmann, A. Klümper, V.E. Korepin, The One-Dimensional Hubbard Model (Cambridge University Press, Cambridge, 2005)
2005
Later among the works it cites.
A.N. Minchenko, Trans. Moscow. Math. Soc. 2006
2006
Later among the works it cites.
R. Somma, H. Barnum, G. Ortiz, E. Knill, Phys. Rev. Lett. 97
2006
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
R.C. King, B.G. Wybourne, J. Phys. A 29
1996
Cited alongside, same era.
R. Cleve, H. Buhrman, Phys. Rev. A 59
1997
Cited alongside, same era.
V. Jurdjevic, Geometric Control Theory (Cambridge University Press, Cambridge, 1997)
1997
Cited alongside, same era.
W. Bosma, J.J. Cannon, C. Playoust, J. Symbolic Comput. 24
1997
Cited alongside, same era.
T. Schulte-Herbrüggen, Aspects and Prospects of High-Resolution NMR (PhD Thesis, Diss-ETH 12752, Zürich, 1998)
1998
Cited alongside, same era.
E. Sontag, Mathematical Control Theory (Springer, New York, 1998)
1998
Cited alongside, same era.
G. Dirr, U. Helmke, K. Hüper, M. Kleinsteuber, Y. Liu, J. Global Optim. 35
2006
Later among the works it cites.
C.V. Kraus, M.M. Wolf, J.I. Cirac, Phys. Rev. A. 75
2007
Later among the works it cites.
A.K. Spörl, T. Schulte-Herbrüggen, S.J. Glaser, V. Bergholm, M.J. Storcz, J. Ferber, F.K. Wilhelm, Phys. Rev. A 75
2007
Later among the works it cites.
S. Bose, Contemp. Phys. 48
2007
Later among the works it cites.
H. Yuan, S.J. Glaser, N. Khaneja, Phys. Rev. A 76
2007
Later among the works it cites.
M.R. Sepanski, Compact Lie Groups (Springer, New York, 2007)
2007
Later among the works it cites.
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80
2008
Later among the works it cites.
R. Blatt, D. Wineland, Nature (London) 453
2008
Later among the works it cites.
Applied Mathematics and Nonlinear Science Series (Chapman & Hall/CRC, Boca Raton, 2008)
D. D’Alessandro, Introduction to Quantum Control and Dynamics · 2008
Later among the works it cites.
D. Burgarth, S. Bose, C. Bruder, V. Giovanetti, Phys. Rev. A 79
2008
Later among the works it cites.
S.G. Schirmer, I.C.H. Pullen, P.J. Pemberton-Ross, Phys. Rev. A 78
2008
Later among the works it cites.
A. Kay, Phys. Rev. A 78
2008
Later among the works it cites.
H. Yuan, R. Zeier, N. Khaneja, Phys. Rev. A 77
2008
Later among the works it cites.
N. Bourbaki, Elements of Mathematics, Lie Groups and Lie Algebras, Chapters 4–6 (Springer, Berlin, 2008)
2008
Later among the works it cites.
N. Bourbaki, Elements of Mathematics, Lie Groups and Lie Algebras, Chapters 7–9 (Springer, Berlin, 2008)
2008
Later among the works it cites.
G. Dirr, U. Helmke, GAMM-Mitteilungen 31
2008
Later among the works it cites.
H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2009)
2009
Later among the works it cites.
P. Rebentrost, I. Serban, T. Schulte-Herbrüggen, F.K. Wilhelm, Phys. Rev. Lett. 102
2009
Later among the works it cites.
T. Polack, H. Suchowski, D.J. Tannor, Phys. Rev. A 79
2009
Later among the works it cites.
S.G. Schirmer, P.J. Pemberton-Ross, Phys. Rev. A 80
2009
Later among the works it cites.
M. Ying, Y. Feng, IEEE Trans. Comp. 58
2009
Later among the works it cites.
D. Elliott, Bilinear Control Systems: Matrices in Action (Springer, London, 2009)
2009
Later among the works it cites.
R. Goodman, N.R. Wallach, Symmetry, Representations, and Invariants (Springer, Dordrecht, 2009)
2009
Later among the works it cites.
I. Buluta, F. Nori, Science 326
2009
Later among the works it cites.
M.J. O’Hara, D.P. O’Leary, Phys. Rev. A 79
2009
Later among the works it cites.
L. Carr (ed.), Understanding Quantum Phase Transitions (CRC Press, Boca Raton, 2010)
2010
Closest in time.
T. Heinosaari, M.M. Wolf, J. Math. Phys. 51
2010
Closest in time.
A. Kay, Int. J. Quant. Inf. 8
2010
Closest in time.
D. Burgarth, K. Maruyama, S. Montangero, T. Calarco, F. Noi, M. Plenio, Phys. Rev. A 81
2010
Closest in time.
A. Kay, P. Pemberton-Ross, Phys. Rev. A 81
2010
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Lists all simple irreducible subalgebras of 𝔰 𝔲 ( N ) \mathfrak{su}(N) with N ≤ 2 15 N\leq 2^{15} . Please refer to arXiv:
R. Zeier, T. Schulte-Herbrüggen, Supplementary Material for “Symmetry Principles in Quantum Systems Theory” (2010) · 2010
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Ph.D. thesis, Technische Universiteit Eindhoven (2010)
D.A. Roozemond, Algorithms for Lie Algebras of Algebraic Groups · 2010
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R. Zeier, U. Sander, T. Schulte-Herbrüggen, in Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS), 2010, Budapest, Hungary (2010), pp. 2341–2348
2010
Closest in time.
U. Sander, Numerical and Algebraic Studies for the Control of Quantum Systems (PhD Thesis, Technical University of Munich, 2010)
2010
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F. Assaad, G. Dirr, F. Goth, U. Helmke, in Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS), 2010, Budapest, Hungary (2010), pp. 547–551
2010
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A. Altland, B. Simons, Condensed Matter Field Theory , 2nd edn. (Cambridge University Press, Cambridge, 2010)
2010
Closest in time.
E.B. Dynkin, A.N. Minchenko, Transform. Groups 15
2010
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P.J. Pemberton-Ross, A. Kay, Phys. Rev. Lett. 106
2011
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T. Huckle (2011) · 2011
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2011
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