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Register a new userDirected momentum current induced by the PT-symmetric driving
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We investigate the directed momentum current in the quantum kicked rotor model with $mathcal{PT}$ symmetric deriving potential. For the quantum non-resonance case, the values of quasi-energy become to be complex when the strength of imaginary part of the kicking potential exceeds textbf{a} threshold value, which demonstrates the appearance of the spontaneous $mathcal{PT}$ symmetry breaking. In the vicinity of the phase-transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasi-energy are significantly large. Above the phase-transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of quantized increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.
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Entanglement plays a central role in the field of quantum information science. It is well known that the degree of entanglement cannot be increased under local operations. Here, we show that the concurrence of a bipartite entangled state can be increased under the local PT -symmetric operation. This violates the property of entanglement monotonicity. We also use the Bell-CHSH and steering inequalities to explore this phenomenon.
Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix with the same dimension. The generalized PT-symmetric matrices are most general among the three. All self-adjoint matrices process a generalized PT symmetry. For a given matrix, it can be both PT-symmetric and P-pseudo-Hermitian with respect to some P operators. The relation between corresponding P and P operators is established. The Jordan block structures of each class are discussed. Explicit examples in 2x2 are shown.
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its PT symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient. Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of direct simulations. In particular, stable localized modes are found in these systems, although the majority of identified solutions is unstable.
The quantum mechanical brachistochrone system with PT-symmetric Hamiltonian is Naimark dilated and reinterpreted as subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultra-fast brachistochrone regime of [C. M. Bender et al, Phys. Rev. Lett. {bf 98}, 040403 (2007)] in an entangled two-spin system.
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