Single particle models in the shell correction approach

We investigate the dependence of the shell correction energy on the parameters as they occur in the Nilsson model and the single particle model with a Woods-Saxon potential. We give criteria, how these parameters should be chosen in order that the shell correction energies become fairly model-independent. The different models yield now a value of about ?20 MeV for²⁰⁸Pb, substantially larger than in previous work. Its relation to the remainder of the mass formula fit is discussed. We find that shell energies have an extremum. The minimum occurs close to the conventional parameter values (except the potential diffuseness of the protons) and close to the minimum of the total binding energy. The minimum in shell energy corresponds to a maximum bunching of single particle states. The gross properties of these extremal shells agree considerably better with the experimental spectra (for both the neutrons and the protons) than those of conventional model parameters.     

Three-body effective interactions in the f72 region

The three-body effective forces in a pure $\text{(0}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{<mtext>n</mtext>}}$ model space are calculated to second order in perturbation theory. The full effect of the $\text{(0f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}{}^3$ configuration on the effective interaction in the $\text{(0}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^3$ model space leading to three-body forces is calculated to all orders in G. The resulting three-body force matrix elements come out much weaker than demanded by phenomenological fits. Their main effect is to push the spectra as a whole up in energy, improving the fit of the calculated ground state binding energies with experiment. The biggest three-body-force contribution appears toward the end of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ shell where its main object is to compensate for Pauli violations arising from the two-body diagrams.     

Optically pumped GaAs waveguide lasers with a fundamental 0.11 μ corrugation feedback

Surface corrugations with a period of 0.115 μ were ion-milled on GaAs dielectric waveguides. Laser action was observed under optical pumping. Single mode as well as multimode oscillation was obtained under different pumping conditions.     

Narrowing and rebroadening of amplified spontaneous emission in high gain laser media

A series of recent papers by Allen and Peters on line narrowing in high gain laser media is criticized. New data demonstrating spectral narrowing followed by rebroadening are presented.     

Bessel identities in the waldspurger correspondence over the real numbers

We prove certain identities between Bessel functions attached to irreducible unitary representations ofPGL ₂(R) and Bessel functions attached to irreducible unitary representations of the double cover ofSL ₂(R). These identities give a correspondence between such representations which turns out to be the Waldspurger correspondence. In the process we prove several regularity theorems for Bessel distributions which appear in the relative trace formula. In the heart of the proof lies a classical result of Weber and Hardy on a Fourier transform of classical Bessel functions. This paper constitutes the local (real) spectral theory of the relative trace formula for the Waldspurger correspondence for which the global part was developed by Jacquet. Research of first author was partially supported by NSF grant DMS-0070762. Research of second author was partially supported by NSF grant DMS-9729992 and DMS 9971003.     

GaAs distributed Bragg reflector lasers

An equivalent cavity approach is used to derive the oscillation condition of a distributed Bragg reflector laser. The oscillation frequencies and thresholds are determined graphically. The effect of lossy reflectors is discussed. Several advantages and potential applications of distributed Bragg reflector structures are pointed out. Experimental results on optically pumped GaAs lasers are presented.     

DNA unzipping and the unbinding of directed polymers in a random media

We consider the unbinding of a directed polymer in a random media from a wall in d=1+1 dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are identical up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems, a method which allows us to reduce the dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance z from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process.     

Giant fiber lasers: a new paradigm for secure key distribution

We propose and analyze a new concept for secure key distribution based on establishing laser oscillations between the sender and receiver. Compared to quantum mechanics based systems, our scheme allows for significantly higher key-establishing rates and longer ranges. By properly designing the laser structure, it is possible to increase the difficulty of eavesdropping almost arbitrarily, thus making our scheme an intriguing alternative and a complementary technology to quantum key-distribution systems.     

Cusp Singularities in Boundary-Driven Diffusive Systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities. The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.     

Flat corannulene: when a transition state becomes a stable molecule

Flat corannulene has been considered so far only as a transition state of the bowl-to-bowl inversion process. This study was driven by the prediction that substituents with strong steric repulsion could destabilize the bowl-shaped conformation of this molecule to such an extent that the highly unstable planar geometry would become an isolable molecule. To examine the substituents'' effect on the corannulene bowl depth, optimized structures for the highly-congested decakis(t-butylsulfido)corannulene were calculated. The computations, performed with both the M06-2X/def2-TZVP and the B3LYP/def2-TZVP methods (the latter with and without Grimme''s D3 dispersion correction), predict that this molecule can achieve two minimum structures: a flat carbon framework and a bowl-shaped structure, which are very close in energy. This rather unusual compound was easily synthesized from decachlorocorannulene under mild reaction conditions, and X-ray crystallographic studies gave similar results to the theoretical predictions. This compound crystallized in two different polymorphs, one exhibiting a completely flat corannulene core and the other having a bowl-shaped conformation.

The first flat metal-free corannulene derivative was predicted by computations and achieved by synthesis.