Spectral analysis of dissipative quantum systems

(Old research topics)

Adiabatic control of photodissociative systems

Study of the photodissociative regimes of diatomic molecules; vibrational control and cooling of diatomic molecules with laser fields; Schrödinger-Floquet approach of light-matter interaction.

Wave operators, effective Hamiltonians and optical potentials

Solving stationary and time-dependent Schrödinger equations by using the wave operator method; effective Hamiltonians and active spaces to L2-finite representations of large dimensional systems; optical potential (absorbing boundaries) to force initial conditions to Floquet quasienergy states; nonlinear eigenvalue equations.

Adiabatic approximations for non-selfadjoint Hamiltonians

Adiabatic tracking of state populations, resonances and continua in adiabatic transport, almost adiabatic regimes, adiabatic limit of wave operators.
  1. G. Jolicard, D. Viennot, J.P. Killingbeck & J.M. Zucconi, A new iterative eigenvalues method using the Bloch wave operator formalism with Padé approximants and absorbing boundaries , Phys. Rev. E 70, 046703 (2004).
  2. G. Jolicard, D. Viennot & J.P. Killingbeck, Constrained adiabatic trajectory method, J. Phys. Chem. A 109, 8580 (2004).
  3. D. Viennot, G. Jolicard, J.P. Killingbeck & M.Y. Perrin, Adiabatic theorem for the time-dependent wave operator, Phys. Rev. A 71, 052706 (2005).
  4. D. Viennot, G. Jolicard & J.P. Killingbeck, Berry phase and time-dependent wave operators, J. Phys. A : Math. Gen. 39, 7065 (2006).
  5. D. Viennot, Geometry of quantum active subspaces and of effective Hamiltonians, J. Math. Phys. 48, 052102 (2007).
  6. G. Jolicard, J.P. Killingbeck, D. Viennot, J. Buldyreva & P. Joubert, Transitional and permanent regimes in the adiabatic Floquet approach to photodissociation processes, J. Phys. A : Math. Theor. 41, 095303 (2008).
  7. D. Viennot, G. Jolicard & J.P. Killingbeck, The topology of the adiabatic passage process for molecular photodissociative dynamics, J. Phys. A : Math. Theor. 41, 145303 (2008).
  8. G. Dridi, S. Guérin, H.R. Jauslin, D. Viennot & G. Jolicard, Adiabatic approximation for quantum dissipative systems : formulation, topology and superadiabatic tracking, Phys. Rev. A 82, 022109 (2010).
  9. A. Leclerc, G. Jolicard, D. Viennot & J.P. Killingbeck, Constrained adiabatic trajectory method: a global integrator for explicitly time-dependent Hamiltonians, J. Chem. Phys. 136, 014106 (2012).
  10. A. Leclerc, D. Viennot & G. Jolicard, The role of the geometric phases in adiabatic populations tracking for non-hermitian Hamiltonians, J. Phys. A : Math. Theor. 45, 415201 (2012).
  11. D. Viennot, A. Leclerc, G. Jolicard & J.P. Killingbeck, Consistency between adiabatic and nonadiabatic geometric phases for nonselfadjoint hamiltonians, J. Phys. A : Math. Theor. 45, 335301 (2012).
  12. D. Viennot, Almost quantum adiabatic dynamics and generalized time dependent wave operators, J. Phys. A: Math. Theor. 47, 065302 (2014).
  13. G. Jolicard, A. Leclerc, D. Viennot & J.P. Killingbeck, Global integration of the Schrödinger equation within the wave operator formalism: the role of the effective Hamiltonian un multidimensional active spaces, J. Phys. A: Math. Theor. 49, 195305 (2016).
  14. A. Leclerc, D. Viennot, G. Jolicard, R. Lefebvre & O. Atabek, Controlling vibrational cooling with zero-width resonances: an adiabatic Floquet approach, Phys. Rev. A 94, 043409 (2016).
  15. A. Leclerc, D. Viennot, G. Jolicard, R. Lefebvre & O. Atabek, Exotic states in the strong field control of H2+ dissociation dynamics: from exceptional points to zero-width resonances, J. Phys. B: At. Mol. Opt. Phys. 50, 234002 (2017).
  16. D. Finkelstein-Shapiro, D. Viennot, I. Saideh, T. Hansen, T. Pullerits & A. Keller, Adiabatic elimination and sub-space evolution of open quantum systems, Phys. Rev. A 101, 042102 (2020).