Determinism beyond time evolution

Th. Östreich, Lu Jeu Sham

We present an analytical and numerical study of the coherent exciton polarization including exciton-exciton correlation. The time evolution after excitation with ultrashort optical pulses can be divided into a slowly varying polarization component and novel ultrafast collective modes. The frequency and damping of the collective modes are determined by the high-frequency properties of the retarded two-exciton correlation function, which includes Coulomb effects beyond the mean-field approximation. The overall time evolution depends on the low-frequency spectral behavior. The collective mode, well separated from the slower coherent density evolution, manifests itself in the coherent emission of a resonantly excited excitonic system, as demonstrated numerically.

Jose J. Valdes

John Earman

Guanlin Jian, Yuan Yang, Ze Liu +2 more

Abstract In the noisy intermediate-scale quantum (NISQ) era, quantum computers have become important tools to simulate the real-time evolution of strong correlated many-body systems. The general scheme of designing quantum circuits to simulate the quantum dynamics is based on the Trotter-Suzuki decomposition technique, which has its limitation because the accuracy of evolution process depends on the size of trotter steps when the evolution operator is decomposed as quantum gates. Going beyond the limitation of the Trotter-Suzuki scheme, we design a parameterized quantum circuit named α -circuit with simple determined size and the only one control parameter θ to simulate the real-time evolution of the specific XXX Heisenberg model with the specific initial state . The α -circuit can accurately generate the time-evolution results by tuning parameter θ , which means the circuit can also be regarded as a good state preparation machine (SPM).

B. M. Garraway, Stig Stenholm

We consider the well-known JaynesCummings model and ask if it can display randomness. As a solvable Hamiltonian system, it does not display chaotic behaviour in the ordinary sense. Here, however, we look at the distribution of values taken up during the total time evolution. This evolution is determined by the eigenvalues distributed as the square roots of integers and leads to a seemingly erratic behaviour. That this may display a random Gaussian value distribution is suggested by an exactly provable result by Kac. In order to reach our conclusion we use the Kac model to develop tests for the emergence of a Gaussian. Even if the consequent double limits are difficult to evaluate numerically, we find definite indications that the JaynesCummings case also produces a randomness in its value distributions. Numerical methods do not establish such a result beyond doubt, but our conclusions are definite enough to suggest strongly an unexpected randomness emerging in a dynamic time evolution.

C. M. Sparrow