Self-acceleration in non-Hermitian Systems

We study self-acceleration in PT and non-PT symmetric systems. We find some novel wave effects that appear uniquely in non-Hermitian systems. We show that integrable self-accelerating waves exist if the Hamiltonian is non-Hermitian. We find that self-accelerating constant intensity waves are possible even when gain and loss are not balanced in the system.Comment: To appear in Phys. Let.

Rydberg blockade with multivalent atoms: effect of Rydberg series perturbation on van der Waals interactions

We investigate the effect of series perturbation on the second order dipole-dipole interactions between strontium atoms in $5sns({^1}S_0)$ and $5snp({^1}P_1)$ Rydberg states as a means of engineering long-range interactions between atoms in a way that gives an exceptional level of control over the strength and the sign of the interaction by changing $n$. We utilize experimentally available data to estimate the importance of perturber states at low $n$, and find that van der Waals interaction between two strontium atoms in the $5snp({^1}P_1)$ states shows strong peaks outside the usual hydrogenic $n^{11}$ scaling. We identify this to be the result of the perturbation of $5snd({^1}D_2)$ intermediate states by the $4d^2({^1}D_2)$ and $4dn's({^1}D_2)$ states in the $n<20$ range. This demonstrates that divalent atoms in general present a unique advantage for creating substantially stronger or weaker interaction strengths than those can be achieved using alkali metal atoms due to their highly perturbed spectra that can persist up to high-$n$

Vertex decomposable graphs, codismantlability, Cohen-Macaulayness and Castelnuovo-Mumford regularity

We call a (simple) graph G codismantlable if either it has no edges or else it has a codominated vertex x, meaning that the closed neighborhood of x contains that of one of its neighbor, such that G-x codismantlable. We prove that if G is well-covered and it lacks induced cycles of length four, five and seven, than the vertex decomposability, codismantlability and Cohen-Macaulayness for G are all equivalent. The rest deals with the computation of Castelnuovo-Mumford regularity of codismantlable graphs. Note that our approach complements and unifies many of the earlier results on bipartite, chordal and very well-covered graphs

Divalent Rydberg atoms in optical lattices: intensity landscape and magic trapping

We develop a theoretical understanding of trapping divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wavefunctions. Optical potential is proportional to the ac Stark polarizability. We find that in the independent particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free electron polarizability, the Rydberg contribution depends both on laser intensity profile and the rotational symmetry of the total electronic wavefunction. We focus on the $J=0$ Rydberg states of Sr and evaluate the dynamic polarizabilities of the 5s$n$s($^1S_0$) and 5s$n$p($^3P_0$) Rydberg states. We specifically choose Sr atom for its optical lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states (5s$^2$($^1S_0$) and 5s5p($^3P_0$)) and the $J=0$ Rydberg states, 5s$n$s($^1S_0$) and 5s$n$p($^3P_0$), vanishes. We tabulate these wavelengths as a function of the principal quantum number $n$ of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\sim$1000 nm are ``universal" as they do not depend on the principal quantum number $n$

EXPORT PERFORMANCE OF FIRMS IN DEVELOPING COUNTRIES AND FOOD QUALITY AND SAFETY STANDARDS IN DEVELOPED COUNTRIES

Turkey changed her economic policy in 1980s towards more liberal economy and higher exports. During this transition, the structure of the exports also changed from agricultural products towards industrial ones. Export of food products, for which the European Union is the largest market, has an important share in total exports. Recently, EU has started to increase the stringency of her regulations related to food quality, safety and environmental standards. This development necessitates the analysis of how Turkish firms exporting into EU should respond to them, and that is what this paper will try to demonstrate. We believe that such analysis is very valuable not only for Turkey but also for other developing countries.Food Consumption/Nutrition/Food Safety, International Relations/Trade,