Flow Representation of the Bose-Hubbard Hamiltonian : General Case

In this paper the explicit flow representation to the Bose-Hubbard Hamiltonian is given in the general case. This representation may be useful in creating cat states for the system of atoms trapped in the optical ring.Comment: Latex ; 8 pages ; 1 figure ; minor change

Time resolution below 100 ps for the SciTil detector of PANDA employing SiPM

The barrel time-of-flight (TOF) detector for the PANDA experiment at FAIR in Darmstadt is planned as a scintillator tile hodoscope (SciTil) using 8000 small scintillator tiles. It will provide fast event timing for a software trigger in the otherwise trigger-less data acquisition scheme of PANDA, relative timing in a multiple track event topology as well as additional particle identification in the low momentum region. The goal is to achieve a time resolution of sigma ~ 100 ps. We have conducted measurements using organic scintillators coupled to Silicon Photomultipliers (SiPM). The results are encouraging such that we are confident to reach the required time resolution.Comment: 10 pages, 7 figure

Exact results for quench dynamics and defect production in a two-dimensional model

We show that for a d-dimensional model in which a quench with a rate \tau^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/\tau^{m\nu/(z\nu +1)}, where \nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m=\nu=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.Comment: 4 pages including 4 figures; generalized the discussion of the defect density scaling to the case of arbitrary critical exponents, and added some references; this version will appear in Physical Review Letter

Shell-model calculations for the three-nucleon system

We use Faddeev's decomposition to solve the shell-model problem for three nucleons. The dependence on harmonic-oscillator excitations allowed in the model space, up to $32 \hbar\Omega$ in the present calculations, and on the harmonic-oscillator frequency is studied. Effective interactions derived from Nijmegen II and Reid93 potentials are used in the calculations. The binding energies obtained are close to those calculated by other methods. The structure of the Faddeev equations is discussed and a simple formula for matrix elements of the permutation operators in a harmonic-oscillator basis is given. The Pauli principle is properly treated in the calculations.Comment: 11 pages. REVTEX. 6 PostScript figure

Analyzing powers in inclusive pion production at high energy and the nucleon spin structure

Analyzing powers in inclusive pion production in high energy transversely polarized proton-proton collisions are studied theoretically in the framework of the quark recombination model. Calculations by assuming the SU(6) spin-flavor symmetry for the nucleon structure disagree with the experiments. We solve this difficulty by taking into account the %We overcome this difficulty by taking into account the realistic spin distribution functions of the nucleon, which differs from the SU(6) expectation at large $x$, %but coincides with a perturbative QCD constraint on the ratio of the unpolarized valence distributions, $u/d \to 5$ as $x \to 1$. We also discuss the kaon spin asymmetry and find $A_N(K^+) = -A_N(K^0)$ in the polarized proton-proton collisions at large $x_F$.Comment: 13 pages, 4 figures, late

Aging dynamics in reentrant ferromagnet: Cu0.2_{0.2}Co0.8_{0.8}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Aging dynamics of a reentrant ferromagnet Cu$_{0.2}$Co$_{0.8}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound has been studied using AC and DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($= 9.7$ K) and $T_{RSG}$ ($= 3.5$ K). The relaxation rate $S(t)$ exhibits a characteristic peak at $t_{cr}$ close to a wait time $t_{w}$ below $T_{c}$, indicating that the aging phenomena occur in both the reentrant spin glass (RSG) phase below $T_{RSG}$ and the ferromagnetic (FM) phase between $T_{RSG}$ and $T_{c}$. The relaxation rate $S(t)$ ($=\text{d}\chi_{ZFC}(t)/\text{d}\ln t$) in the FM phase exhibits two peaks around $t_{w}$ and a time much shorter than $t_{w}$ under the positive $T$-shift aging, indicating a partial rejuvenation of domains. The aging state in the FM phase is fragile against a weak magnetic-field perturbation. The time ($t$) dependence of $\chi_{ZFC}(t)$ around $t \approx t_{cr}$ is well approximated by a stretched exponential relaxation: $\chi_{ZFC}(t) \approx \exp[-(t/\tau)^{1-n}]$. The exponent $n$ depends on $t_{w}$, $T$, and $H$. The relaxation time $\tau$ ($\approx t_{cr}$) exhibits a local maximum around 5 K, reflecting a chaotic nature of the FM phase. It drastically increases with decreasing temperature below $T_{RSG}$.Comment: 16 pages,16 figures, submitted to Physical Review

Non-Universal Critical Behaviour of Two-Dimensional Ising Systems

Two conditions are derived for Ising models to show non-universal critical behaviour, namely conditions concerning 1) logarithmic singularity of the specific heat and 2) degeneracy of the ground state. These conditions are satisfied with the eight-vertex model, the Ashkin-Teller model, some Ising models with short- or long-range interactions and even Ising systems without the translational or the rotational invariance.Comment: 17 page

Spikes and diffusion waves in one-dimensional model of chemotaxis

We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity $u_t = u_{xx} - \left(u (K^\prime \ast u)\right)_{x}$ with a given kernel $K'\in L^1(\R)$. We show the existence of global-in-time nonnegative solutions and we study their large time asymptotics. Depending on $K'$, we obtain either linear diffusion waves ({\it i.e.}~the fundamental solution of the heat equation) or nonlinear diffusion waves (the fundamental solution of the viscous Burgers equation) in asymptotic expansions of solutions as $t\to\infty$. Moreover, for certain aggregation kernels, we show a concentration of solution on an initial time interval, which resemble a phenomenon of the spike creation, typical in chemotaxis models