X. Z. Zhang, L. Jin, Z. Song

Complex potential and non-Hermitian hopping amplitude are building blocks of a non-Hermitian quantum network. Appropriate configuration, such as PT-symmetric distribution, can lead to the full real spectrum. To investigate the underlying mechanism of this phenomenon, we study the phase diagram of a semi-infinite non-Hermitian system. It consists of a finite non-Hermitian cluster and a semi-infinite lead. Based on the analysis of the solution of the concrete systems, it is shown that it can have the full real spectrum without any requirements on the symmetry and the wave function within the lead becomes a unidirectional plane wave at the exceptional point. This universal dynamical behavior is demonstrated as the persistent emission and reflectionless absorption of wave packets in the typical non-Hermitian systems containing the complex on-site potential and non-Hermitian hopping amplitude.

http://arxiv.org/abs/1212.0086

Quantum Physics (quant-ph)

Belal E. Baaquie

The Euclidean action with acceleration has been analyzed in [1], hereafter cited as reference I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation/destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian acting on a Hilbert space. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

http://arxiv.org/abs/1211.7166

Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Belal E. Baaquie

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity, and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of this unbounded transformation is explicitly evaluated. The mapping fails for a critical value of the coupling constants.

http://arxiv.org/abs/1211.7168

Quantum Physics (quant-ph); Mathematical Physics (math-ph)