Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians

The complex geometry underlying the Schr\"odinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the centres of coherent states naturally evolve along complex trajectories, which leads to a class of complexified coherent states; (ii) the investigation of the dynamical equations for the real expectation values of position and momentum, for which an Ehrenfest theorem has been derived in a previous paper, yielding real but non-Hamiltonian classical dynamics on phase space for the real centres of coherent states. Both approaches become exact for quadratic Hamiltonians. The apparent contradiction is resolved building on an observation by Huber, Heller and Littlejohn, that complexified coherent states are equivalent if their centres lie on a specific complex Lagrangian manifold. A rich underlying complex symplectic geometry is unravelled. In particular a natural complex structure is identified that defines a projection from complex to real phase space, mapping complexified coherent states to their real equivalents.Comment: 18 pages, small improvements made, similar to published versio

Propagation of Gaussian beams in the presence of gain and loss

We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide profile is locally well approximated by quadratic functions. For Hermitian systems, without any loss or gain, these dynamics are given by Hamilton's equations for the center of the beam and its conjugate momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian component, causing the width of the Gaussian beam to play an important role in its propagation. Here we show how the width affects the motion of the beam and how this may be used to filter Gaussian beams located at the same initial position based on their width

Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator

The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the $PT$-symmetry is unbroken, i.e., the eigenvalues are purely real.Comment: extended version, accepted for publication in J. Phys.

TERAHERTZ RESONATOR

A tunable terahertz resonator includes a semiconductor Substrate and a metal layer contacting a surface of the semiconductor substrate. A depletion layer is formed in the semiconductor substrate near an interface between the metal layer and the semiconductor Substrate. A chiral nanostructure is coupled to the substrate or the metal layer, the chiral nanostructure including a conducting or semiconducting material and having an inductance. A bias circuit applies a bias Voltage across the metal layer and the semiconductor Substrate to control a capacitance of a tunable capacitor that includes the depletion layer. The chiral nanostructure and the tunable capacitor form a tunable resonant circuit. The tunable terahertz resonator can be used in a terahertz radiation emitter or receiver

Tunable plasmonic resonances in highly porous nano-bamboo Si-Au superlattice-type thin films

We report on fabrication of spatially-coherent columnar plasmonic nanostructure superlattice-type thin films with high porosity and strong optical anisotropy using glancing angle deposition. Subsequent and repeated depositions of silicon and gold lead to nanometer-dimension subcolumns with controlled lengths. The superlattice-type columns resemble bamboo structures where smaller column sections of gold form junctions sandwiched between larger silicon column sections ("nano-bamboo"). We perform generalized spectroscopic ellipsometry measurements and finite element method computations to elucidate the strongly anisotropic optical properties of the highly-porous nano-bamboo structures. The occurrence of a strongly localized plasmonic mode with displacement pattern reminiscent of a dark quadrupole mode is observed in the vicinity of the gold subcolumns. We demonstrate tuning of this quadrupole-like mode frequency within the near-infrared spectral range by varying the geometry of the nano-bamboo structure. In addition, coupled-plasmon-like and inter-band transition-like modes occur in the visible and ultra-violet spectral regions, respectively. We elucidate an example for the potential use of the nano-bamboo structures as a highly porous plasmonic sensor with optical read out sensitivity to few parts-per-million solvent levels in water

Optical anisotropy of porous polymer film with inverse slanted nanocolumnar structure revealed via generalized spectroscopic ellipsometry

We use generalized spectroscopic ellipsometry to characterize the biaxial optical properties of porous polymer and slanted nanocolumnar template thin films. The porous polymer with inverse columnar structure was prepared via infiltrating polymer into the voids of the slanted nanocolumnar film and selectively removing the column material (cobalt). The anisotropic Bruggeman effective medium approximation was employed to analyze the ellipsometry data of the porous polymer film and nanocolumnar template. The classification and structure of optical anisotropy are found to be identical for both samples. The interchangeable optical behaviors between two complementary structures are attributed to the equivalency in their anisotropic polarizabilities

2. Freiberger Ledertage - Abstractband: 25. und 26. April 2013, Sinsheim: Leder up to date

Der Verein für Gerberei-Chemie und -Technik (VGCT) wurde 1949 zur Förderung wissenschaftlicher und technischer Forschung, zum Zwecke des fachlichen Erfahrungsaustausches sowie zur Förderung des beruflichen Nachwuchses gegründet. Gegenwärtig hat er ca. 300 Mitglieder, welche sowohl einzelne Personen als auch Firmen sind. Im VGCT treffen sich Ledertechniker, Maschinenbauer, Chemiker und andere am „Ledermachen“ interessierte Menschen zum Austausch und zu gemeinsamer Arbeit. Der Verein bietet eine Plattform für den fachlichen Austausch indem er jährliche Fachtagungen und fachliche Kooperationen in firmenübergreifenden Arbeitsgruppen (Kommissionen) organisiert, technische Veröffentlichungen in der Fachpresse mit eigenen Seiten fördert und sich aktiv an Umweltschutz, Arbeitssicherheit sowie Gesundheitsschutz beteiligt.The Association for Chemistry and Technology in Tanning (VGCT) was founded in 1949 in order to facilitate scientifi c and technical research and exchange of professional experience as well as to promote young talents. Currently it has some 300 members – single persons as well as enterprises. In the VGCT, leather technologists, mechanical engineers, chemists and other people interested in “making leather” meet in order to exchange ideas and work together. The association offers a platform for sharing professional experience by organizing annual meetings and professional co-operations in groups from across various companies (commissions), by facilitating technical publications in specialist press with own pages and actively participating in environmental protection, occupational safety and health protection

Wave packet evolution in non-Hermitian quantum systems

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase space metric---a phenomenon having no analog in Hermitian theories.Comment: Example added, references updated, 4 pages, 2 figure

Optical, structural, and magnetic properties of cobalt nanostructure thin films

We report on optical, structural, and magnetic properties of two substantially different cobalt nanostructure thin films deposited at an oblique angle of incidence of 85° away from the substrate normal. Comparison is made between an achiral columnar thin film grown without substrate rotation and a chiral nanocoil sculptured thin film by glancing angle deposition with substrate rotation. Generalized spectroscopic ellipsometry is employed to determine geometrical structure properties and the anisotropic optical constants of the films in the spectral range from 400 to 1000 nm. The magnetic properties are analyzed with a superconducting quantum interference device magnetometer. Both nanostructure thin films show highly anisotropic optical properties such as strong form birefringence and large dichroism. In particular, Co slanted columnar thin films are found to possess monoclinic optical properties. Magnetic measurements at room temperature show hysteresis anisotropy with respect to a magnetic field either parallel or perpendicular to the nanostructures’ long axis. We find extremely large coercive fields of approximately 3 kOe for our achiral columnar nanostructures

Free polyethylenimine enhances substrate-mediated gene delivery on titanium substrates modified with RGD-functionalized poly(acrylic acid) brushes

Substrate mediated gene delivery (SMD) is a method of immobilizing DNA complexes to a substrate via covalent attachment or nonspecific adsorption, which allows for increased transgene expression with less DNA compared to traditional bolus delivery. It may also increase cells receptivity to transfection via cell-material interactions. Substrate modifications with poly(acrylic) acid (PAA) brushes may improve SMD by enhancing substrate interactions with DNA complexes via tailored surface chemistry and increasing cellular adhesion via moieties covalently bound to the brushes. Previously, we described a simple method to graft PAA brushes to Ti and further demonstrated conjugation of cell adhesion peptides (i.e., RGD) to the PAA brushes to improve biocompatibility. The objective of this work was to investigate the ability of Ti substrates modified with PAA-RGD brushes (PAA-RGD) to immobilize complexes composed of branched polyethyleneimine and DNA plasmids (bPEI-DNA) and support SMD in NIH/3T3 fibroblasts. Transfection in NIH/3T3 cells cultured on bPEI-DNA complexes immobilized onto PAA-RGD substrates was measured and compared to transfection in cells cultured on control surfaces with immobilized complexes including Flat Ti, PAA brushes modified with a control peptide (RGE), and unmodified PAA. Transfection was two-fold higher in cells cultured on PAA-RGD compared to those cultured on all control substrates. While DNA immobilization measured with radiolabeled DNA indicated that all substrates (PAA-RGD, unmodified PAA, Flat Ti) contained nearly equivalent amounts of loaded DNA, ellipsometric measurements showed that more total mass (i.e., DNA and bPEI, both complexed and free) was immobilized to PAA and PAA-RGD compared to Flat Ti. The increase in adsorbed mass may be attributed to free bPEI, which has been shown to improve transfection. Further transfection investigations showed that removing free bPEI from the immobilized complexes decreased SMD transfection and negated any differences in transfection success between cells cultured on PAA-RGD and on control substrates, suggesting that free bPEI may be beneficial for SMD in cells cultured on bPEI-DNA complexes immobilized on PAA-RGD grafted to Ti. This work demonstrates that substrate modification with PAA-RGD is a feasible method to enhance SMD outcomes on Ti and may be used for future applications such as tissue engineering, gene therapy, and diagnostics. © 2019 Mantz, Rosenthal, Farris, Kozisek, Bittrich, Nazari, Schubert, Schubert, Stamm, Uhlmann and Pannier