### Citations

243 |
Introduction to electrodynamics
- Griffiths
- 1999
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Citation Context ...7]). To avoid this, it is easier to work in the Lorentz gauge, where the ’absolute time’ t in the Coulomb integral must be replaced by the retarded time tr = t − |x−x ′| c integrated over all sources =-=[78, 77]-=-. Then, one can observe that for ρ(x, t) = β(t)ρ(x) the 1c -contributions unexpectedly simplify, resembling the effect noticed by Griffiths [78]. The amplitude β does not even need to be analytic; if ... |

97 |
Quantum mechanics for Hamiltonians defined as quadratic forms
- Simon
- 1971
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Citation Context ... variables (we put for simplicity the mass m = 1). In the next few sections we shall not consider any higher space dimensions, nor the deeper Hilbert space problems (carefully reviewed by Barry Simon =-=[12]-=-). The only challenge we attend is strictly combinatorial: how should one program the oscillations of the c-number amplitude β(t), to generate some useful quantum control operations? On purely mathema... |

59 |
Chemistry, Quantum Mechanics and Reductionism
- Primas
- 1983
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Citation Context ...earity of basic laws at the cost of multiplying the number of variables. Some doubts, though, persist. Can indeed all ’gedanken states’, represented by vectors in Hilbert spaces be physically created =-=[1]-=-? Moreover, can all unitary operations be achieved (or at least approximated) by physical evolution? In the recent research a lot of attention is dedicated to the finite-dimensional spin states (qubit... |

20 |
Geometric Optics on Phase Space
- Wolf
- 2004
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Citation Context ...τ is now the z-distance between the source and the image, while (14) describes the action of a thin optical lens placed on the bench, the amplitude a meaning the (positive or negative) lens curvature =-=[51]-=-). Both interpretations have certain gaps and advantages. Thus, what in the dynamical language is an evolution loop (convenient for the dynamical manipulations), in optical terms is the simple reprodu... |

2 |
Phys.Today 51
- Haroche
- 1998
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Citation Context .... What could help are the exact solutions, though they seldom exist. Yet, in certain areas, there appear some windows in ’perturbative clouds’. This happened e.g. in works on bound state manipulation =-=[3, 4]-=- (Nobel Prize 2012 for S. Haroche and D. Wineland), in macroscopic superpositions of Leggett [5], then in works on ”quantum tomography” [6, 7, 8, 9]; last not least, in the duality links between the q... |

2 |
Found.Phys
- Mancini, Man’ko, et al.
- 1996
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Citation Context .... This happened e.g. in works on bound state manipulation [3, 4] (Nobel Prize 2012 for S. Haroche and D. Wineland), in macroscopic superpositions of Leggett [5], then in works on ”quantum tomography” =-=[6, 7, 8, 9]-=-; last not least, in the duality links between the quantum quark and classical string dynamics [10, 11]. The purpose of this study is to show that even the well known and modest case of classical-quan... |

2 |
Operaciones magnéticas: ¿Una ventana a la geometŕıa no conmutativa? PhD. Thesis. Centro de Investigación y de Estudios Avanzados del IPN
- Ramı́rez
- 2008
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Citation Context ...aching the same effects by softly varying, differentiable fields (without any steps) was considered in [62, 35], then elaborated in computer studies for charged particles submerged in harmonic pulses =-=[63, 64, 65]-=-. As subsequently found, the control operations are significantly simplified if the field amplitude β(t) is symmetric with respect to the center of the operation interval [60, 66, 67]. This can make i... |

1 |
arXiv:1001.0084v1 [gr-qc
- Barbosa-Cendejas, Reyes
- 2009
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Citation Context ...instability mechanisms of Avron-Simon type in our reconstruction of the early universe (or its distant future), usually neglected in the cosmological ’slow roll ’ models [24] (see also discussions in =-=[25, 26]-=-). While the cosmic parameters can be studied (but not manipulated), our purpose below will be to discuss the parallel chapters of quantum control, which can suggest the laboratory operations. 4 The e... |

1 |
Kielanowski et al
- C
- 2012
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Citation Context ...ibility of driving the quantum states by δ(t)-pulses of the external fields was considered by Lamb Jr.[33]. An extremely simple class of exact though formal solutions of (1) in L2(R) was described in =-=[14, 34, 35, 36, 37]-=- by considering two methods of stimulating the elementary operations: the intervals of free evolution and the sharp pulses of the oscillator potential. Each free evolution incident in any interval [t0... |

1 |
C Master Thesis, Depto de Fisica
- Herrera
- 1987
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Citation Context ...cluding the squeezing, distorted free evolution, etc. [34, 35, 36, 61]). The possibility of approaching the same effects by softly varying, differentiable fields (without any steps) was considered in =-=[62, 35]-=-, then elaborated in computer studies for charged particles submerged in harmonic pulses [63, 64, 65]. As subsequently found, the control operations are significantly simplified if the field amplitude... |

1 |
Operaciones selectivas de control cuantico
- C
- 1999
(Show Context)
Citation Context ...aching the same effects by softly varying, differentiable fields (without any steps) was considered in [62, 35], then elaborated in computer studies for charged particles submerged in harmonic pulses =-=[63, 64, 65]-=-. As subsequently found, the control operations are significantly simplified if the field amplitude β(t) is symmetric with respect to the center of the operation interval [60, 66, 67]. This can make i... |

1 |
Rev.Mod.Phys 74
- Gisin, Ribordy, et al.
- 2002
(Show Context)
Citation Context ...pollution, usually neglected in the trap descriptions. The cases of dynamical transformations generated with some precision are indeed not many. The results for the spin (qubit) states seem promising =-=[69, 70, 71, 72]-=- though usually limited to finite dimensional Hilbert spaces. A notable success was achieved by techniques of inducing the Rabi rotations between the pairs of bound states of hydrogen-like atoms (the ... |

1 |
et al Phys.Rev.Lett
- Campbell
- 2010
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Citation Context ...pollution, usually neglected in the trap descriptions. The cases of dynamical transformations generated with some precision are indeed not many. The results for the spin (qubit) states seem promising =-=[69, 70, 71, 72]-=- though usually limited to finite dimensional Hilbert spaces. A notable success was achieved by techniques of inducing the Rabi rotations between the pairs of bound states of hydrogen-like atoms (the ... |

1 |
Geometric Methods
- Przanowski, Skulimowski, et al.
- 2012
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Citation Context ...ined probability distribution excluded the interference of both (left and right) components at the detection point against the basic principles of quantum theory (the difficulty discovered by Leavens =-=[83, 84, 85, 86, 87, 88, 89]-=-). In spite of subsequent works on POV measures and some new but still partial results [90, 91, 92], it turns obvious that the idea of time operator has too many gaps to grant the time-energy uncertai... |

1 |
Gustavsson and L.P. Hugston J.Phys. A
- Brody, T
- 2010
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Citation Context ...ts are just the linear combinations of much wider ones (the Fourier transforms, wavelets, etc.). So, if the evolution laws are indeed linear (the discussions seem not yet concluded; see [69] but also =-=[97]-=-) and if only the most insignificant squeezing q → κq, p → 1κp, |κ| < 1 could be performed (and, of course repeated) it would violate any limits of the wave packets compression and similarly, abolish ... |