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Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
No full textWe introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudosupersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum
Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians
No full textWe give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such an operator H the following statements are equivalent: (1) H is pseudo-Hermitian; (2) the spectrum of H consists of real and/or complex-conjugate pairs of eigenvalues and the geometric multiplicity and the dimension of the diagonal blocks for the complex-conjugate eigenvalues are identical; (3) H is Hermitian with respect to a positive-semidefinite inner product. We further discuss the relevance of our findings for the merging of a complex-conjugate pair of eigenvalues of diagonalizable pseudo-Hermitian Hamiltonians in general, and the PT-symmetric Hamiltonians and the effective Hamiltonian for a certain closed FRW minisuperspace quantum cosmological model in particular
A survey of ELF and VLF research on lightning-ionosphere interactions and causative discharges
No full textExtremely low frequency (ELF) and very low frequency (VLF) observations have formed the cornerstone of measurement and interpretation of effects of lightning discharges on the overlying upper atmospheric regions, as well as near-Earth space. ELF (0.3-3 kHz) and VLF (3-30 kHz) wave energy released by lightning discharges is often the agent of modification of the lower ionospheric medium that results in the conductivity changes and the excitation of optical emissions that constitute transient luminous events (TLEs). In addition, the resultant ionospheric changes are best (and often uniquely) observable as perturbations of subionospherically propagating VLF signals. In fact, some of the earliest evidence for direct disturbances of the lower ionosphere in association with lightning discharges was obtained in the course of the study of such VLF perturbations. Measurements of the detailed ELF and VLF waveforms of parent lightning discharges that produce TLEs and terrestrial gamma ray flashes (TGFs) have also been very fruitful, often revealing properties of such discharges that maximize ionospheric effects, such as generation of intense electromagnetic pulses (EMPs) or removal of large quantities of charge. In this paper, we provide a review of the development of ELF and VLF measurements, both from a historical point of view and from the point of view of their relationship to optical and other observations of ionospheric effects of lightning discharges
Silicon microcavity based on 1-D photonic bandgap structure
No full textIn this paper, we report on the design, modeling, fabrication, and characterization of an amorphous silicon microcavity. The microcavity is fabricated using a one-dimensional photonic bandgap structure. The structure was grown by plasma deposition method. Quarter wavelength thick stacks of hydrogenated amorphous silicon nitride and hydrogenated amorphous silicon oxide were consecutively deposited using low temperature plasma enhanced chemical vapor deposition. For the characterization of the dielectric microcavities the intrinsic photoluminescence of the amorphous silicon is used. Bulk amorphous silicon has a luminescence bandwidth of 250 nm. Due to the presence of the microcavity, the luminescence is enhanced by at least an order of magnitude at the resonance wavelength of 700 nm. Additionally, the luminescence is inhibited in the photonic bandgap occupying a spectral band of 150 nm. The microcavity resonance has a quality factor of 120 corresponding to a luminescence linewidth of 6 nm. The enhancement of the photoluminescence is understood by the modified photon density of states of the dielectric microcavity
Hamiltonians generating optimal-speed evolutions
No full textWe 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 provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric (inner product) dependence of the lower bound on the travel time and the universality (metric independence) of the upper bound on the speed of unitary evolutions
Photonic band gap in the triangular lattice of Bose-Einstein-condensate vortices
No full textWe investigate the photonic bands of an atomic Bose-Einstein condensate with a triangular vortex lattice. Index contrast between the vortex cores and the bulk of the condensate is achieved through the enhancement of the index via atomic coherence. The frequency-dependent dielectric function is used in the calculations of the bands, resulting in photonic band gap widths of a few megahertz
Dynamics of quantum phases in a spinor condensate
No full textWe discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground-state distribution of the phases associated with the total atom number (N), the total magnetization (M), and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recovering the two broken continuous symmetries [U(1) and SO(2)] when N and M are conserved, as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with antiferromagnetic interactions
Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using a d=3 tJ model with quenched disorder
No full textWe study a quenched disordered d=3 tJ Hamiltonian with static vacancies as a model of nonmagnetic impurities in high-T-c materials. Using a renormalization-group approach, we calculate the evolution of the finite-temperature phase diagram with impurity concentration p and find several features with close experimental parallels: Away from half filling, we see the rapid destruction of a spin-singlet phase (analogous to the superconducting phase in cuprates) which is eliminated for p greater than or similar to 0.05; in the same region for these dilute impurity concentrations, we observe an enhancement of anti ferromagnetism. The anti ferromagnetic phase near half filling is robust against impurity addition and disappears only for p greater than or similar to 0.40
Nonminimally coupled gravitational and electromagnetic fields: pp-wave solutions
No full textWe give the Lagrangian formulation of a generic nonminimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first-order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact pp-wave solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton
Equilibrium polyelectrolyte bundles with different multivalent counterion concentrations
No full textWe present the results of molecular-dynamics simulations on the salt concentration dependence of the formation of polyelectrolyte bundles in thermodynamic equilibrium. Extending our results on salt-free systems we investigate here deficiency or excess of trivalent counterions in solution. Our results reveal that the trivalent counterion concentration significantly alters the bundle size and size distribution. The onset of bundle formation takes place at earlier Bjerrum length values with increasing trivalent counterion concentration. For the cases of 80%, 95%, and 100% charge compensation via trivalent counterions, the net charge of the bundles decreases with increasing size. We suggest that competition among two different mechanisms, counterion condensation and merger of bundles, leads to a nonmonotonic change in line-charge density with increasing Bjerrum length. The investigated case of having an abundance of trivalent counterions by 200% prohibits such a behavior. In this case, we find that the difference in effective line-charge density of different size bundles diminishes. In fact, the system displays an isoelectric point, where all bundles become charge neutral