Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data

We consider the one-dimensional focusing nonlinear Schr\"odinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a B\"acklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, earlier work on the problem by Holmer and Zworski

Phonon effects in molecular transistors: Quantum and classical treatment

We present a comprehensive theoretical treatment of the effect of electron-phonon interactions in molecular transistors, including both quantal and classical limits and we study both equilibrated and out of equilibrium phonons. We present detailed results for conductance, noise and phonon distribution in two regimes. One involves temperatures large as compared to the rate of electronic transitions on and off the dot; in this limit our approach yields classical rate equations, which are solved numerically for a wide range of parameters. The other regime is that of low temperatures and weak electron-phonon coupling where a perturbative approximation in the Keldysh formulation can be applied. The interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented. We also discuss the nature of the low-T to high-T crossover.Comment: 20 pages, 19 figures. Minor changes, version accepted for publication in Phys. Rev.

Specific Heat Study of the Magnetic Superconductor HoNi2B2C

The complex magnetic transitions and superconductivity of HoNi2B2C were studied via the dependence of the heat capacity on temperature and in-plane field angle. We provide an extended, comprehensive magnetic phase diagram for B // [100] and B // [110] based on the thermodynamic measurements. Three magnetic transitions and the superconducting transition were clearly observed. The 5.2 K transition (T_{N}) shows a hysteresis with temperature, indicating the first order nature of the transition at B=0 T. The 6 K transition (T_{M}), namely the onset of the long-range ordering, displays a dramatic in-plane anisotropy: T_{M} increases with increasing magnetic field for B // [100] while it decreases with increasing field for B // [110]. The anomalous anisotropy in T_{M} indicates that the transition is related to the a-axis spiral structure. The 5.5 K transition (T^{*}) shows similar behavior to the 5.2 K transition, i.e., a small in-plane anisotropy and scaling with Ising model. This last transition is ascribed to the change from a^{*} dominant phase to c^{*} dominant phase.Comment: 9 pages, 11 figure

Further analysis of the quantum critical point of Ce1−x_{1-x}Lax_{x}Ru2_{2}Si2_{2}

New data on the spin dynamics and the magnetic order of Ce$_{1-x}$La$_{x}$Ru$_{2}$Si$_{2}$ are presented. The importance of the Kondo effect at the quantum critical point of this system is emphasized from the behaviour of the relaxation rate at high temperature and from the variation of the ordered moment with respect to the one of the N\'eel temperature for various $x$.Comment: Contribution for the Festschrift on the occasion of Hilbert von Loehneysen 60 th birthday. To be published as a special issue in the Journal of Low Temperature Physic

Transition to meson-dominated matter at RHIC. Consequences for kaon flow

Anisotropic flow of kaons and antikaons is studied in heavy-ion collisions at CERN SPS and BNL RHIC energies within the microscopic quark-gluon string model. In the midrapidity range the directed flow of kaons v_1 differs considerably from that of antikaons at SPS energy (E_{lab} = 160 AGeV), while at RHIC energy (\sqrt{s} = 130 AGeV) the excitation functions of both, kaon and antikaon, flows coincide within the statistical error bars. The change is attributed to formation of dense meson-dominated matter at RHIC, where the differences in interaction cross-sections of kaons and antikaons become unimportant. The time evolution of the kaon anisotropic flow is also investigated. The elliptic flow of these hadrons is found to develop at midrapidity at times 3 < t < 10 fm/c, which is much larger than the nuclear passing time t^{pass} = 0.12 fm/c. As a function of transverse momentum the elliptic flow increases almost linearly with rising p_t. It stops to rise at p_t > 1.5 GeV/c reaching the saturation value $v_2^K (p_t) \approx 10$.Comment: REVTEX, 14 pages, 4 figure

Massive triplet excitations in a magnetized anisotropic Haldane spin chain

Inelastic neutron scattering experiments on the Haldane-gap quantum antiferromagnet \nd are performed at mK temperatures in magnetic fields of almost twice the critical field $H_c$ applied perpendicular to the spin cahins. Above $H_c$ a re-opening of the spin gap is clearly observed. In the high-field N\'eel-ordered state the spectrum is dominated by three distinct long-lived excitation branches. Several field-theoretical models are tested in a quantitative comparison with the experimental data.Comment: 4 pages, 3 figure

Unifying inflation with dark energy in modified F(R) Horava-Lifshitz gravity

We study FRW cosmology for a non-linear modified F(R) Horava-Lifshitz gravity which has a viable convenient counterpart. A unified description of early-time inflation and late-time acceleration is possible in this theory, but the cosmological dynamic details are generically different from the ones of the convenient viable F(R) model. Remarkably, for some specific choice of parameters they do coincide. The emergence of finite-time future singularities is investigated in detail. It is shown that these singularities can be cured by adding an extra, higher-derivative term, which turns out to be qualitatively different when compared with the corresponding one of the convenient F(R) theory.Comment: LaTeX 12 pages, typos are correcte

Stripes and holes in a two-dimensional model of spinless fermions and hardcore bosons

We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of two, three, and four stripes, finding that they repel, and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.Comment: 24 pages, 18 figure

Epidermis recreation in spongy-like hydrogels: New opportunities to explore epidermis-like analogues

[Excerpt] On the road to successfully achieving skin regeneration, 3D matrices/scaffolds that provide the adequate physico-chemical and biological cues to recreate the ideal healing environment are believed to be a key element [1], [2] and [3]. Numerous polymeric matrices derived from both natural [4] and [5] and synthetic [6], [7] and [8] sources have been used as cellular supports; nowadays, fewer matrices are simple carriers, and more and more are ECM analogues that can actively participate in the healing process. Therefore, the attractive characteristics of hydrogels, such as high water content, tunable elasticity and facilitated mass transportation, have made them excellent materials to mimic cells’ native environment [9]. Moreover, their hygroscopic nature [10] and possibility of attaining soft tissues-like mechanical properties mean they have potential for exploitation as wound healing promoters [11], [12], [13] and [14]. Nonetheless, hydrogels lack natural cell adhesion sites [15], which limits the maximization of their potential in the recreation of the cell niche. This issue has been tackled through the use of a range of sophisticated approaches to decorate the hydrogels with adhesion sequences such as arginine-glycine-aspartic acid (RGD) derived from fibronectin [16], [17] and [18], and tyrosine-isoleucine-glycine-serine-arginine (YIGSR) derived from laminin [18] and [19], which not only aim to modulate cell adhesion, but also influencing cell fate and survival [18]. Nonetheless, its widespread use is still limited by significant costs associated with the use of recombinant bioactive molecules

Distribution of exchange energy in a bond-alternating S=1 quantum spin chain

The quasi-one-dimensional bond-alternating S=1 quantum antiferromagnet NTENP is studied by single crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron scattering intensities are also analyzed using the 1st-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principle DMRG calculations are used to study the relation between these two quantities.Comment: 10 pages, 10 figure