Non-Hermitian Degeneracies in unitary quantum dynamics interrupted by repetitive quantum measurements

Kar, Subhrasmita (2018) Non-Hermitian Degeneracies in unitary quantum dynamics interrupted by repetitive quantum measurements. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

The effect of repeated measurements on unitary evolution of a quantum system at regular intervals has been studied picking a specific example of a quantum, particle moving on a lattice of three sites. Dividing the system into two subsystems, we obtain the survival probability of the particle (i.e. particle not being detected) by time evolution followed by projection onto one subsystem. Using this evolution operator we obtain the expression for effective non-Hermitian Hamiltonian whose dynamics could be mapped to a general firs-order perturbation approach. We obtained a good argument between three approaches followed for calculating the survival probability, namely, the first order perturbative approach, the exact non-hermitian evolution and repeated the non-hermitian measurements interrupting the unitary evolution. Further we obtained the non-Hermitian degeneracies called Exceptional Points using the effective Hamiltonian. Finally, the presence of exceptional point is verified by decomposing the initial state into eigenstates of effective Hamiltonian and observing the behavior of the coefficients of decomposition while traversing through each parameter on which the exceptional point depends.

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