2,216 research outputs found
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
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
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