Dinuclear platinum(II) sulfide–thiolate complexes [Pt₂(μ-S)(μ-SR)(PPh₃)₄]⁺ containing fluorinated substituents and the identification of a SC₆F₅ π interaction in the crystal structure of [Pt₂(μ-S)(μ-SCH₂C₆F₅)(PPh₃)₄]BPh₄•2C₆H₆

Reactions of the platinum(II) sulfido complex [Pt₂(μ-S)₂(PPh₃)₄] with the alkyl iodides ICH₂CH₂(CF₂)nCF₃ (n = 3, 7) gives good yields of the monoalkylated products [Pt₂(μ-S){μ-SCH₂CH₂(CF₂)nCF₃}(PPh₃)₄]⁺, which were isolated as PF₆⁺or BPH₄⁻ salts, and characterised by ESI mass spectrometry, NMR spectroscopy and elemental analysis. The complex [Pt₂(μ-S){μ-SCH₂CH₂(CF₂)nCF₃}(PPh₃)₄]⁺ appears to have normal reactivity for this type of complex, namely reaction with Ph₃PAuCl to give [Pt₂(μ-SAuPPh₃){μ-SCH₂CH₂(CF₂)nCF₃}(PPh₃)₄]₂⁺, and reaction with Me₂SO₄ to give [Pt₂(μ-SMe){μ-SCH₂CH₂(CF₂)nCF₃}(PPh₃)₄]₂⁺. Reaction of [Pt₂(μ-S)₂(PPh₃)₄] with C₆F₅CH₂Br gave [Pt₂(μ-S)(μ-SCH₂C₆F₅)(PPh₃)₄]⁺, isolated as BPh₄⁻ its salt, and characterised by NMR spectroscopy and a single-crystal X-ray structure determination. The C₆F₅ group lies above the {Pt₂S₂} core of the complex as a result of a SC₆F₅ π interaction, in contrast to the published structure of [Pt₂(μ-S)(μ-SCH₂C₆H₅)(PPh₃)₄]PF₆, where the C₆H₅ group projects away from the {Pt₂S₂} core

What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio

On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Noise and decoherence in quantum two-level systems

Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. To evaluate the dephasing time for transverse 1/f noise second-order contributions have to be taken into account. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.Comment: To appear in Proceedings of the Nobel Jubilee Symposium on Condensation and Coherence in Condensed Systems (Physica Scripta

Two Speed TASEP with Step Initial Condition

In this paper, we consider zero range process with an initial condition which is equivalent to step initial condition in total asymmetric simple exclusion process (TASEP) as described in a paper by R\'akos, A. and Sch\"utz by using techniques developed by Borodin, Ferrari, and Sasamoto. The solution for the transition probability of total asymmetric simple exclusion process for particles with different hopping rates was first worked out by Sch\"utz and Rak\"os (2005) for the case when $p=1$ or $q=1$. The formula was later applied to analyze two speed TASEP (Borodin, Ferrari, and Sasamoto, 2009) with alternating initial condition. Here we will investigate the two speed TASEP case with step initial condition