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Long-range interaction in a quantum model of interacting Fermi-particles

Long-range interaction in a quantum model of interacting Fermi-particles. Felix Izrailev Instituto de Física, BUAP Puebla, México. in collaboration with Fausto Borgonovi , Brescia, Italy A. Smerzi – Trento, Italy G. Berman – Los Alamos, USA. in collaboration with:.

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Long-range interaction in a quantum model of interacting Fermi-particles

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  1. Long-range interaction in a quantum model of interacting Fermi-particles Felix Izrailev Instituto de Física, BUAP Puebla, México in collaboration with Fausto Borgonovi, Brescia, Italy A. Smerzi – Trento, Italy G. Berman – Los Alamos, USA in collaboration with: www.felix.izrailev.com

  2. Introduction The model Mean field representation Delocalization border versus chaos border Short versus long-range interaction Conclusions

  3. M.Dyakonov, cond-mat/0110326

  4. Solid state model of a quantum computer 1D spin-chain in - direction, in a rotating magnetic field : with - magnetic pulses specified by In what follows we analyze what is going on during a single pulse

  5. Total (time-dependent) Hamiltonian for - Ising interaction between n-th and k-th qubit - Larmor frequency - Rabi frequency - Pauli matrices ;

  6. for Stationary Hamiltonian ”Selective excitation” : ”Non-selective excitation” : for simplicity : with

  7. Hamiltonian under study Nearest-neighbor interaction : (dynamical model in - representation) where matrix is diagonal for and off-diagonal matrix elements Other cases - !!

  8. Mean field representation in the basis where is diagonal : where

  9. Magnetic field with a constant gradient then, for and and in this case, Therefore, Quasi-integrability !

  10. Integrability if we neglect and the model is : where and !! the model is integrable, independent on Young, Rieger (1996); Young (1997); Lieb, Schultz, Mattis (1961)

  11. Delocalization border let us consider central band : number of states - size of the band - Distance between directly coupled states - should be compares with As a result, !! does not depends on

  12. Chaos border The mechanism of chaos is the band overlap for non-selective regime the estimate is : - delocalization border - chaos border ( for ) do not coincide !!

  13. All-to-all interaction Delocalization border coincide with the chaos border !

  14. Long-range interaction in a random model are random number in the interval short- range interaction long- range interaction under-critical region over-critical region

  15. Conclusion / remarks • For the magnetic field with a constant gradient, one can avoid quantum chaos • The border of delocalization can be very different form the chaos border ! • 3. For short-range interaction the two borders different, however, for long-range interaction they are the same.

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