5,617 research outputs found

    Universal scaling in BCS superconductivity in two dimensions in non-s waves

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    The solutions of a renormalized BCS model are studied in two space dimensions in ss, pp and dd waves for finite-range separable potentials. The gap parameter, the critical temperature TcT_c, the coherence length ξ\xi and the jump in specific heat at TcT_c as a function of zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small ξ\xi and large TcT_c appropriate to those for high-TcT_c cuprates. The specific heat, penetration depth and thermal conductivity as a function of temperature show universal scaling in pp and dd waves.Comment: 11 pages, LATEX, 4 postscript figures embedded using eps

    Using data network metrics, graphics, and topology to explore network characteristics

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    Yehuda Vardi introduced the term network tomography and was the first to propose and study how statistical inverse methods could be adapted to attack important network problems (Vardi, 1996). More recently, in one of his final papers, Vardi proposed notions of metrics on networks to define and measure distances between a network's links, its paths, and also between different networks (Vardi, 2004). In this paper, we apply Vardi's general approach for network metrics to a real data network by using data obtained from special data network tools and testing procedures presented here. We illustrate how the metrics help explicate interesting features of the traffic characteristics on the network. We also adapt the metrics in order to condition on traffic passing through a portion of the network, such as a router or pair of routers, and show further how this approach helps to discover and explain interesting network characteristics.Comment: Published at http://dx.doi.org/10.1214/074921707000000058 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

    Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

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    We establish universal behavior in temperature dependencies of some observables in (s+id)(s+id)-wave BCS superconductivity in the presence of a weak ss wave. There also could appear a second second-order phase transition. As temperature is lowered past the usual critical temperature TcT_c, a less ordered superconducting phase is created in dd wave, which changes to a more ordered phase in (s+id)(s+id) wave at Tc1T_{c1} (<Tc< T_c). The presence of two phase transitions manifest in two jumps in specific heat at TcT_c and Tc1T_{c1}. The temperature dependencies of susceptibility, penetration depth, and thermal conductivity also confirm the new phase transition.Comment: 6 pages, 5 post-script figures

    Free expansion of fermionic dark solitons in a boson-fermion mixture

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    We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a "notch" in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.Comment: 14 pages, 6 figure

    Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture

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    Employing a time-dependent mean-field-hydrodynamic model we study the generation of black solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical solutions. The black soliton is found to be the first stationary vibrational excitation of the system and is considered to be a nonlinear continuation of the vibrational excitation of the harmonic oscillator state. We illustrate the stationary nature of the black soliton, by studying different perturbations on it after its formation.Comment: 7 pages, 10 figure

    On weighted zero-sum sequences

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    Let G be a finite additive abelian group with exponent exp(G)=n>1 and let A be a nonempty subset of {1,...,n-1}. In this paper, we investigate the smallest positive integer mm, denoted by s_A(G), such that any sequence {c_i}_{i=1}^m with terms from G has a length n=exp(G) subsequence {c_{i_j}}_{j=1}^n for which there are a_1,...,a_n in A such that sum_{j=1}^na_ic_{i_j}=0. When G is a p-group, A contains no multiples of p and any two distinct elements of A are incongruent mod p, we show that s_A(G) is at most D(G)/A+exp(G)1\lceil D(G)/|A|\rceil+exp(G)-1 if |A| is at least (D(G)-1)/(exp(G)-1), where D(G) is the Davenport constant of G and this upper bound for s_A(G)in terms of |A| is essentially best possible. In the case A={1,-1}, we determine the asymptotic behavior of s_{{1,-1}}(G) when exp(G) is even, showing that, for finite abelian groups of even exponent and fixed rank, s_{{1,-1}}(G)=exp(G)+log_2|G|+O(log_2log_2|G|) as exp(G) tends to the infinity. Combined with a lower bound of exp(G)+sumi=1rlog2niexp(G)+sum{i=1}{r}\lfloor\log_2 n_i\rfloor, where G=Zn1...ZnrG=\Z_{n_1}\oplus...\oplus \Z_{n_r} with 1<n_1|... |n_r, this determines s_{{1,-1}}(G), for even exponent groups, up to a small order error term. Our method makes use of the theory of L-intersecting set systems. Some additional more specific values and results related to s_{{1,-1}}(G) are also computed.Comment: 24 pages. Accepted version for publication in Adv. in Appl. Mat

    Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate

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    We discuss a computational mechanism for the generation of a stationary dark soliton, or black soliton, in a trapped Bose-Einstein condensate using the Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction. It is demonstrated that the black soliton with a "notch" in the probability density with a zero at the minimum is a stationary eigenstate of the GP equation and can be efficiently generated numerically as a nonlinear continuation of the first vibrational excitation of the GP equation in both attractive and repulsive cases in one and three dimensions for pure harmonic as well as harmonic plus optical-lattice traps. We also demonstrate the stability of this scheme under different perturbing forces.Comment: 7 pages, 15 ps figures, Final version accepted in J Low Temp Phy
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