We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and show by explicit calculation that the minimum travel time and the optimal-speed Hamiltonians are determined by the metric operator (inner product...

We investigate a chiral property of the domain-wall fermion (DWF) system using the four-dimensional hermitian Wilson-Dirac operator HW . A formula expressing the Ward-Takahashi identity quark mass m5q with eigenvalues of this operator is derived, which well explains the N5 dependence of m5q observed in previous numerical simulations. We further discuss the chiral property of DWF in the large vo...

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schrödinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of sc...

We study SUSY −intertwining for non-Hermitian Hamiltonians with complex supercharges. Special emphasis is given to the two-dimensional generalized (singular) Morse potential. This model does not allow for separation of variables nevertheless a part of its spectrum and eigenfunctions can be constructed. The spectrum includes both complex conjugated energy pairs and non-paired complex energies fo...

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ5-Hermitian symmetry of the Dirac oper...

We further develop the general theory of quantum time distributions introduced in [D. Jurman and H. Nikolić, Phys. Lett. A 396, 127247 (2021)] apply it to find distribution arrival times at detector. Even though Hamiltonian absence detector is hermitian, evolution system before detection involves dealing with a non-hermitian operator obtained from projection hermitian onto region front Such for...

We investigate the ground state and quantum dynamics of an interacting bosonic chain with nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, can support Mott insulators in systems noninteger filling due competition between hopping on-site interaction. For dynamics, conservation laws for non-Hermitian manifest a stark difference from their counterpart. particular, any operato...

In this note, generalized connections σT,f are investigated, where AσT,fB = TAfT − A (B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol T A denotes a reflexive generalized inverse of a positive bounded linear operator TA. The problem of estimating a given generalized connection by other ones is studied. T...