摘要
The dilation method is a practical way to experimentally simulate non-Hermitian, especially PT-symmetric, quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet nontrivial exactly solvable dilation problem for two-dimensional time-dependent PT-symmetric Hamiltonians. Our system is initially set in the unbroken PT-symmetric phase, then goes across the so-called exceptional point, and ends in the broken PT-symmetric phase. For this system, the dilated Hamiltonian and the evolution of PT-symmetric system are analytically worked out. By investigating the large-time behaviors, we give an effective method to choose and adjust the dilation parameters. Our result also shows that the exceptional points do not have much physical relevance in a time-dependent system.