Four types of special functions of G_2 and their discretization

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the other two (S^L- and S^S-functions) are not found elsewhere in the literature. It is shown explicitly that all four families have similar properties. In particular, they are orthogonal when integrated over a finite region F of the Euclidean space, and they are discretely orthogonal when their values, sampled at the lattice points F_M \subset F, are added up with a weight function appropriate for each family. Products of ten types among the four families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S, S^LS^S and S^LS^L, are completely decomposable into the finite sum of the functions. Uncommon arithmetic properties of the functions are pointed out and questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table

Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Surface-acoustic-wave-driven luminescence from a lateral p-n junction

The authors report surface-acoustic-wave-driven luminescence from a lateral p-n junction formed by molecular beam epitaxy regrowth of a modulation doped GaAs/AlGaAs quantum well on a patterned GaAs substrate. Surface-acoustic-wave-driven transport is demonstrated by peaks in the electrical current and light emission from the GaAs quantum well at the resonant frequency of the transducer. This type of junction offers high carrier mobility and scalability. The demonstration of surface-acoustic-wave luminescence is a significant step towards single-photon applications in quantum computation and quantum cryptography.Comment: 4 pages, 3 figure

Unitary Gate Synthesis for Continuous Variable Systems

We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed by Hamiltonian H interspaced by local phase shifts applied to A and B. We concentrate on protocols that require the minimum necessary number of steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to the Hamiltonian x_A p_B that describes the effective off-resonant interaction of light with the collective atomic spin.Comment: 7 pages, minor text modifications, references adde

Canonical Decompositions of n-qubit Quantum Computations and Concurrence

The two-qubit canonical decomposition SU(4) = [SU(2) \otimes SU(2)] Delta [SU(2) \otimes SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (C.C.D.) SU(2^n)=KAK. The group K fixes a bilinear form related to the concurrence, and in particular any computation in K preserves the tangle ||^2 for n even. Thus, the C.C.D. shows that any n-qubit quantum computation is a composition of a computation preserving this n-tangle, a computation in A which applies relative phases to a set of GHZ states, and a second computation which preserves it. As an application, we study the extent to which a large, random unitary may change concurrence. The result states that for a randomly chosen a in A within SU(2^{2p}), the probability that a carries a state of tangle 0 to a state of maximum tangle approaches 1 as the even number of qubits approaches infinity. Any v=k_1 a k_2 for such an a \in A has the same property. Finally, although ||^2 vanishes identically when the number of qubits is odd, we show that a more complicated C.C.D. still exists in which K is a symplectic group.Comment: v2 corrects odd qubit CCD misstatements, reference chapter for KAK v3 notation change to coincide with sequel, typos. 20 pages, 0 figure

Invariants of Lie Algebras with Fixed Structure of Nilradicals

An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n<\infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.Comment: LaTeX2e, 19 page

Attaching NorA efflux pump inhibitors to methylene blue enhances antimicrobial photodynamic inactivation of Escherichia coli and Acinetobacter baumannii in vitro and in vivo

Resistance of bacteria to antibiotics is a public health concern worldwide due to the increasing failure of standard antibiotic therapies. Antimicrobial photodynamic inactivation (aPDI) is a promising non-antibiotic alternative for treating localized bacterial infections that uses non-toxic photosensitizers and harmless visible light to produce reactive oxygen species and kill microbes. Phenothiazinium photosensitizers like methylene blue (MB) and toluidine blue O are hydrophobic cations that are naturally expelled from bacterial cells by multidrug efflux pumps, which reduces their effectiveness. We recently reported the discovery of a NorA efflux pump inhibitor-methylene blue (EPI-MB) hybrid compound INF55-(Ac)en-MB that shows enhanced photodynamic inactivation of the Gram-positive bacterium methicillin-resistant Staphylococcus aureus (MRSA) relative to MB, both in vitro and in vivo. Here, we report the surprising observation that INF55-(Ac)en-MB and two related hybrids bearing the NorA efflux pump inhibitors INF55 and INF271 also show enhanced aPDI activity in vitro (relative to MB) against the Gram-negative bacteria Escherichia coli and Acinetobacter baumannii, despite neither species expressing the NorA pump. Two of the hybrids showed superior effects to MB in murine aPDI infection models. The findings motivate wider exploration of aPDI with EPI-MB hybrids against Gram-negative pathogens and more detailed studies into the molecular mechanisms underpinning their activity

Dorsal Raphe Dopamine Neurons Modulate Arousal and Promote Wakefulness by Salient Stimuli

Ventral midbrain dopamine (DA) is unambiguously involved in motivation and behavioral arousal, yet the contributions of other DA populations to these processes are poorly understood. Here, we demonstrate that the dorsal raphe nucleus DA neurons are critical modulators of behavioral arousal and sleep-wake patterning. Using simultaneous fiber photometry and polysomnography, we observed time-delineated dorsal raphe nucleus dopaminergic (DRNDA) activity upon exposure to arousal-evoking salient cues, irrespective of their hedonic valence. We also observed broader fluctuations of DRNDA activity across sleep-wake cycles with highest activity during wakefulness. Both endogenous DRNDA activity and optogenetically driven DRNDA activity were associated with waking from sleep, with DA signal strength predictive of wake duration. Conversely, chemogenetic inhibition opposed wakefulness and promoted NREM sleep, even in the face of salient stimuli. Therefore, the DRNDA population is a critical contributor to wake-promoting pathways and is capable of modulating sleep-wake states according to the outside environment, wherein the perception of salient stimuli prompts vigilance and arousal

On the practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer and Cirac [Phys. Rev. Lett. 88 (2002) 237902] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.Comment: 9 pages, 2 figure