Solitons in a chain of PT-invariant dimers

Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.Comment: 9 pages, 9 figure

Long-range quantum entanglement in noisy cluster states

We describe a phase transition for long-range entanglement in a three-dimensional cluster state affected by noise. The partially decohered state is modeled by the thermal state of a suitable Hamiltonian. We find that the temperature at which the entanglement length changes from infinite to finite is nonzero. We give an upper and lower bound to this transition temperature.Comment: 7 page

Isolation, X-ray Structures, and Electronic Spectra of Reactive Intermediates in Friedel−Crafts Acylations

Reactive intermediates in the Friedel−Crafts acylation of aromatic donors are scrutinized upon their successful isolation and X-ray crystallography at very low temperatures. Detailed analyses of the X-ray parameters for the [1:1] complexes of different aliphatic and aromatic-acid chlorides with the Lewis acids antimony pentafluoride and pentachloride, gallium trichloride, titanium and zirconium tetrachlorides provide unexpected insight into the activation mechanism for the formation of the critical acylium carbocations. Likewise, the X-ray-structure examinations of aliphatic and aromatic acylium electrophiles also isolated as crystalline salts point to the origins of their electrophilic reactivity. Although the Wheland intermediates (as acylium adducts to arene donors) could not be isolated in crystalline form owing to their exceedingly short lifetimes, transient (UV−vis) spectra of benzenium adducts of acylium carbocations with hexamethylbenzene can be measured and directly related to Wheland intermediates with other cationic electrophiles that have been structurally established via X-ray studies

Isolation and X-ray Structures of Labile Benzoic- and Acetic-Acidium Carbocations

New carbocationic salts (via O-protonation of substituted benzoic acids) are prepared for the first time by controlled hydration of the corresponding benzoylium salts and isolated in pure crystalline form. Precise X-ray structural analyses reveal the rather unexpected (electronic) structure of the carboxylic-acidium functionality