Must a Hamiltonian be Hermitian?

A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new Hamiltonians that one can construct that might explain experimental data. One would think that a quantum theory based on a non-Hermitian Hamiltonian violates unitarity. However, if PT symmetry is not broken, it is possible to use a previously unnoticed physical symmetry of the Hamiltonian to construct an inner product whose associated norm is positive definite. This construction is general and works for any PT-symmetric Hamiltonian. The dynamics is governed by unitary time evolution. This formulation does not conflict with the requirements of conventional quantum mechanics. There are many possible observable and experimental consequences of extending quantum mechanics into the complex domain, both in particle physics and in solid state physics.Comment: Revised version to appear in American Journal of Physic

Evaluation of Effects of Wastewater Treatment Discharge on Estuarine Water Quality

This report marks the completion of a two-year project focused on observed and estimated effects of wastewater treatment facilities (WWTFs) on estuarine water quality within the New Hampshire (NH) Seacoast region. This study was designed and carried out in an effort to help the NH Department of Environmental Services (NHDES) and NH Estuaries Project (NHEP) evaluate the effects of WWTF effluent quality on bacterial and nutrient concentrations in New Hampshire’s estuarine waters, as well as to help NHDES/NHEP identify related WWTF infrastructure problems. An extensive database of bacterial and nutrient concentrations in effluent collected post-disinfection from 9 NH WWTFs and 2 Maine WWTFs that discharge into the Great Bay and Hampton/Seabrook estuaries was developed. The data were used to determine ratios between different bacterial indicators in WWTF effluent, estimates of in-stream bacterial concentrations following effluent discharge to receiving waters and estimates of nutrient loading from selected WWTFs

Faster than Hermitian Quantum Mechanics

Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi_I> to |psi_F> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.Comment: 4 page

Bound states of PT-symmetric separable potentials

All of the PT-symmetric potentials that have been studied so far have been local. In this paper nonlocal PT-symmetric separable potentials of the form $V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]$, where $U(x)$ is real, are examined. Two specific models are examined. In each case it is shown that there is a parametric region of the coupling strength $\epsilon$ for which the PT symmetry of the Hamiltonian is unbroken and the bound-state energies are real. The critical values of $\epsilon$ that bound this region are calculated.Comment: 10 pages, 3 figure