2 research outputs found
Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
We consider the evolution of a quantum state of a Hamiltonian which is
parametrically perturbed via a term proportional to the adiabatic parameter
\lambda (t). Starting with the Pechukas-Yukawa mapping of the energy
eigenvalues evolution on a generalised Calogero-Sutherland model of 1D
classical gas, we consider the adiabatic approximation with two different
expansions of the quantum state in powers of d\lambda/dt and compare them with
a direct numerical simulation. We show that one of these expansions (Magnus
series) is especially convenient for the description of non-adiabatic evolution
of the system. Applying the expansion to the exact cover 3-satisfability
problem, we obtain the occupation dynamics which provides insight on the
population of states.Comment: 12 pages, 6 figure
Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise
Quantum systems are prone to decoherence due to both intrinsic interactions as well as random fluctuations from the environment. Using the Pechukas-Yukawa formalism, we investigate the influence of noise on the dynamics of an adiabatically evolving Hamiltonian which can describe a quantum computer. Under this description, the level dynamics of a parametrically perturbed quantum Hamiltonian are mapped to the dynamics of one-dimensional classical gas. We show that our framework coincides with the results of the classical Landau-Zener transitions upon linearization. Furthermore, we determine the effects of external noise on the level dynamics and its impact on Landau-Zener transitions