Symmetries and collective excitations in large superconducting circuits

The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics. If realizable, quantum coherence in larger circuit networks has great potential for advances in quantum information processing including topological protection from decoherence. Here, we present theory suitable for quantitative modeling of such large circuits and discuss its application to the fluxonium device. Our approach makes use of approximate symmetries exhibited by the circuit, and enables us to obtain new predictions for the energy spectrum of the fluxonium device which can be tested with current experimental technology

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Mahonian Pairs

We introduce the notion of a Mahonian pair. Consider the set, P^*, of all words having the positive integers as alphabet. Given finite subsets S,T of P^*, we say that (S,T) is a Mahonian pair if the distribution of the major index, maj, over S is the same as the distribution of the inversion number, inv, over T. So the well-known fact that maj and inv are equidistributed over the symmetric group, S_n, can be expressed by saying that (S_n,S_n) is a Mahonian pair. We investigate various Mahonian pairs (S,T) with S different from T. Our principal tool is Foata's fundamental bijection f: P^* -> P^* since it has the property that maj w = inv f(w) for any word w. We consider various families of words associated with Catalan and Fibonacci numbers. We show that, when restricted to words in {1,2}^*, f transforms familiar statistics on words into natural statistics on integer partitions such as the size of the Durfee square. The Rogers-Ramanujan identities, the Catalan triangle, and various q-analogues also make an appearance. We generalize the definition of Mahonian pairs to infinite sets and use this as a tool to connect a partition bijection of Corteel-Savage-Venkatraman with the Greene-Kleitman decomposition of a Boolean algebra into symmetric chains. We close with comments about future work and open problems.Comment: Minor changes suggested by the referees and updated status of the problem of finding new Mahonian pairs; [email protected] and [email protected]

Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin $1/2$ Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number $k$ fixing the polarization in the subsystem conservation of $S_{z}$ and with respect to the irreducible representations of the $\mathbf{S_{n}}$ group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the R\'{e}nyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.Comment: Festschrift in honor of the 60th birthday of Professor Vladimir Korepin (11 pages, 5 figures

Optical constants of solid methane

Methane is the most abundant simple organic molecule in the outer solar system bodies. In addition to being a gaseous constituent of the atmospheres of the Jovian planets and Titan, it is present in the solid form as a constituent of icy surfaces such as those of Triton and Pluto, and as cloud condensate in the atmospheres of Titan, Uranus, and Neptune. It is expected in the liquid form as a constituent of the ocean of Titan. Cometary ices also contain solid methane. The optical constants for both solid and liquid phases of CH4 for a wide temperature range are needed for radiative transfer calculations, for studies of reflection from surfaces, and for modeling of emission in the far infrared and microwave regions. The astronomically important visual to near infrared measurements of solid methane optical constants are conspicuously absent from the literature. Preliminary results are presented on the optical constants of solid methane for the 0.4 to 2.6 micrometer region. Deposition onto a substrate at 10 K produces glassy (semi-amorphous) material. Annealing this material at approximately 33 K for approximately 1 hour results in a crystalline material as seen by sharper, more structured bands and negligible background extinction due to scattering. The constant k is reported for both the amorphous and the crystalline (annealed) states. Typical values (at absorption maxima) are in the .001 to .0001 range. Below lambda = 1.1 micrometers the bands are too weak to be detected by transmission through the films less than or equal to 215 micrometers in thickness, employed in the studies to date. Using previously measured values of the real part of the refractive index, n, of liquid methane at 110 K, n is computed for solid methane using the Lorentz-Lorenz relationship. Work is in progress to extend the measurements of optical constants n and k for liquid and solid to both shorter and longer wavelengths, eventually providing a complete optical constants database for condensed CH4

Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals

We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension. Exploiting this result, we introduce a new model for a crossover transition between Poisson and Wigner statistics: random points on a continuous family of self-similar curves with fractal dimension between 1 and 2. The implications to quantum chaos are discussed, and a connection to conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image available (upon request) from the author

The Effect of stem cell mobilisation with granulocyte colony-stimulating factor on the morphology of the haematopoietic organs in mice

The cellular mobilisation of mice with granulocyte colony-stimulating factor (G-CSF) results in an egress of haematopoietic stem/progenitor cells from the bone marrow and an increase in their level in the peripheral blood. While the mobilisation process with different agents is widely studied, little is known about the morphology of the murine haematopoietic organs during the mobilisation. The purpose of this study was to examine the morphology of the bone marrow, spleen and liver in mice mobilised with G-CSF. To address this issue mice were injected subcutaneously with G-CSF for 6 consecutive days. Morphological analysis revealed an increase in the number of mature neutrophils close to the wall of sinusoids in the bone marrow as well as hypertrophy of the red pulp in the spleen. At the same time no morphological changes were noticed in the livers of G-CSF-mobilised mice. In conclusion, G-CSF induces discrete ultrastructural changes in the bone marrow, which intensify the transendothelial traverse of haematopoietic stem and progenitor cells from it. The changes in the spleen are related to repopulation of this organ by mobilised early haematopoietic cells circulating in the peripheral blood. We also noticed that the process of migration of haematopoietic cells from the bone marrow into the peripheral blood began on day 2 and was most pronounced on day 4 after stimulation with G-CSF

242. Analiza ekspresji EGFR i angiogenezv w utkaniu niedrobnokomórkowego raka płuc oraz związku z czasem przeżycia pacjentów w stadiach zaawansowania klinicznego I-IIIA

Cel pracyWciąż niezadowalające wskaźniki przeżycia pacjentów z rakiem płuca, mimo radykalnego leczenia operacyjnego, skłaniają do poszukiwań nowych czynników prognostycznych. Wiadomym jest, że receptor naskórkowego czynnika wzrostu (EGFR) wpływa na wzrost komórek guza i jego progresję, jak również tworzenie przerzutów – głównie poprzez oddziaływanie na tworzenie nowych naczyń krwionośnych. Jego prognostyczna rola u pacjentów z niedrobnokomórkowym rakiem płuca (NRP) jest niejasna. Natomiast gęstość naczyń krwionośnych (GNK), będąca miernikiem angiogenezy w guzie, jest podawana jako marker prognostyczny w wielu nowotworach. Celem naszego badania była ocena zależności między ekspresją EGFR i GNK w utkaniu guza nowotworowego a przeżyciem pacjentów z NRP.Materiał i metodyBadaniem objęto 75 pacjentów z NRP w stadiach zaawansowania klinicznego I-IIIA. Wycinki z guza pobierano z materiału operacyjnego, utrwalonego w formalinie. Na uzyskanych skrawkach parafinowych wykonywano odczyny immunohistochemiczne z zastosowaniem monoklonalnego przeciwciała przeciw receptorowi naskórkowego czynnika wzrostu oraz monoklonalnego przeciwciała przeciw CD31.WynikiWśród 75 pacjentów było 5 kobiet (6.7%) i 70 mężczyzn (93.3%) w wieku od 42 lat do 74 lat (średnio 59 lat). W badanej grupie chorych stwierdzono raka płaskonabłonkowego u 53 pacjentów (70.7%), gruczolakoraka u 11 chorych (14.7%) i raka wielkokomórkowego także u 11 pacjentów. Analizując uzyskane dane nie stwierdzono istotności statystycznej między ekspresją EGFR i czasem przeżycia pacjentów. Również GNK nie miała istotnego wpływu na przeżycie pacjentów. Jedynie stan węzłów chłonnych (cecha N; p<0.05), typ histologiczny raka (p<0.001) oraz wiek (p<0.05) w badanej grupie chorych miały istotny statystycznie wpływ na czas przeżycia.WnioskiUzyskane w tym badaniu wyniki nie są zgodne z wynikami innych doniesień mówiących o tym, że ekspresja EGFR i GNK w NRP mogą być traktowane jako czynniki prognostyczne. Należy jednak podkreślić, że analizowana grupa pacjentów była mała, a większość chorych (59 pacjentów, 78.7%) znajdowała się w stadium znacznego zaawansowania nowotworu

Separation of colour degree of freedom from dynamics in a soliton cellular automaton

We present an algorithm to reduce the coloured box-ball system, a one dimensional integrable cellular automaton described by motions of several colour (kind) of balls, into a simpler monochrome system. This algorithm extracts the colour degree of freedom of the automaton as a word which turns out to be a conserved quantity of this dynamical system. It is based on the theory of crystal basis and in particular on the tensor products of sl_n crystals of symmetric and anti-symmetric tensor representations.Comment: 19 page

Characterization of extrasolar terrestrial planets from diurnal photometric variability

The detection of massive planets orbiting nearby stars has become almost routine, but current techniques are as yet unable to detect terrestrial planets with masses comparable to the Earth's. Future space-based observatories to detect Earth-like planets are being planned. Terrestrial planets orbiting in the habitable zones of stars-where planetary surface conditions are compatible with the presence of liquid water-are of enormous interest because they might have global environments similar to Earth's and even harbor life. The light scattered by such a planet will vary in intensity and colour as the planet rotates; the resulting light curve will contain information about the planet's properties. Here we report a model that predicts features that should be discernible in light curves obtained by low-precision photometry. For extrasolar planets similar to Earth we expect daily flux variations up to hundreds of percent, depending sensitively on ice and cloud cover. Qualitative changes in surface or climate generate significant changes in the predicted light curves. This work suggests that the meteorological variability and the rotation period of an Earth-like planet could be derived from photometric observations. Other properties such as the composition of the surface (e.g., ocean versus land fraction), climate indicators (for example ice and cloud cover), and perhaps even signatures of Earth-like plant life could be constrained or possibly, with further study, even uniquely determined.Comment: Published in Nature. 9 pages including 3 figure