Quantum many-body state

We have examined two assisted adiabatic transfer schemes designed to control the dynamical evolution of a quantum many-body system. That control is achieved by active manipulation with external fields that work cooperatively with coherence and interference effects embedded in the system quantum dynamics. The schemes we have discussed are a small subset of the many that have been proposed to induce complete transfer of population from an arbitrary initial state to a selected target state of a system, yet they illuminate the generic character of the... 

CONTROL OF QUANTUM MANY-BODY DYNAMICS 0/iH + = 0,7T for zero change in the ground-state energy + = j7r for zero force... 

Thus far we have examined the determination of a field that will control the quantum many-body dynamics of a system when all that is specified is the initial and final states of the system and the constraints imposed by the equations of motion and physical limitations on the field. When posed in this fashion, the calculation of the control field is an inverse problem that has similarities to the determination of the interaction potential from scattering data. Despite the similarities, the mathematical methods used are very different. Because only the end points of the initial-to-final state transforma-... 

Two lines of inquiry will be important in future work in photochemistry. First, both the traditional and the new methods for studying photochemical processes will continue to be used to obtain information about the subtle ways in which the character of the excited state and the molecular dynamics defines the course of a reaction. Second, there will be extension and elaboration of recent work that has provided a first stage in the development of methods to control, at the level of the molecular dynamics, the ratio of products formed in a branching chemical reaction. These control methods are based on exploitation of quantum interference effects. One scheme achieves control over the ratio of products by manipulating the phase difference between two excitation pathways between the same initial and final states. Another scheme achieves control over the ratio of products by manipulating the time interval between two pulses that connect various states of the molecule. These schemes are special cases of a general methodology that determines the pulse duration and spectral content that maximizes the yield of a desired product. Experimental verifications of the first two schemes mentioned have been reported. Consequently, it is appropriate to state that control of quantum many-body dynamics is both in principle possible and is... 

Ze /I fj — U represents potential energy of interaction of all electrons with all nuclei. The last term describes the Coulomb electron-electron interactions. Calculation of this term presents great difficulties. We must consider the Coulomb interactions between each electron and aU other electrons in the atom. The determination of the ground-state eigenfunction and the ground-state energy of a quantum many-body system appears to be a formidable problem. 

C. Negrevergne, R. Somma, G. Ortiz, E. Knfll, R. Laflamme, Liquid-state NMR simulations of quantum many-body problems, Phys. Rev. A 71 (2005) 032344. 

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