1-{2-[(2,4-Dichloro­benzyl­idene)amino]eth­yl}-3-methyl­imidazolium hexa­fluoro­phosphate

In the title Schiff base compound, C13H14Cl2N3 +·PF6 −, the dihedral angle between the aromatic ring and imidazole ring in the cation is 6.10 (2)°. Inter­molecular C—H⋯F hydrogen-bonding inter­actions and π–π stacking inter­actions [centoid–centroid distance = 3.7203 (12) Å] help stabilize the crystal packing

Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors

We numerically investigate the quantum transport in a coupled kicked rotors with the $\mathcal{PT}$-symmetric potential. We find that the spontaneous $\mathcal{PT}$-symmetry breaking of wavefunctions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of the $\mathcal{PT}$-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of the modified ballistic energy diffusion where the width of the wavepacket also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the inter-particle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.Comment: 8 pages, 7 figure

Bis(2,6-dichloro­benz­yl)selane

The title mol­ecule, C14H10Cl4Se, features a selenide bridge between two dichloro­benzyl units. The dihedral angle between the two benzene rings is 107.9 (16)°. In the crystal, weak π–π face-to-face aromatic inter­actions are observed [centroid–centroid distance between two adjacent (but crystallographically different) phenyl rings = 3.885 (5) Å], providing some packing stability. Short Cl⋯Cl contacts of 3.41 (2) Å are observed

Necessary conditions for classifying m-separability of multipartite entanglements

We study the norms of the Bloch vectors for arbitrary $n$-partite quantum states. A tight upper bound of the norms is derived for $n$-partite systems with different individual dimensions. These upper bounds are used to deal with the separability problems. Necessary conditions are presented for $\mathbf m$-separable states in $n$-partite quantum systems. Based on the upper bounds, classification of multipartite entanglement is illustrated with detailed examples.Comment: 14 page