Time dependent local potential in a Tomonaga-Luttinger liquid

We study the energy deposition in a one dimensional interacting quantum system with a point like potential modulated in amplitude. The point like potential at position $x=0$ has a constant part and a small oscillation in time with a frequency $\omega$. We use bosonization, renormalization group and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter $K$ of the system, a crossover between week and strong coupling for the backscattering due to the potential is possible. We compute the frequency scale $\omega_\ast$, at which such crossover exists. We find that the energy deposition due to the backscattering shows different exponent for $K>1$ and $K<1$. We discuss possible experimental consequences, in the context of cold atomic gases, of our theoretical results.Comment: 13 pages, 3 figure

Dynamics of a Mobile Impurity in a Two Leg Bosonic Ladder

We have analyzed the behavior of a mobile quantum impurity in a bath formed by a two-leg bosonic ladder by a combination of field theory (Tomonaga-Luttinger liquid) and numerical (Density Matrix Renormalization Group) techniques. Computing the Green's function of the impurity as a function of time at different momenta, we find a power law decay at zero momentum, which signals the breakdown of any quasi-particle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, we find that the impurity experiences the ladder as a single channel one-dimensional bath, but effective coupling is reduced by a factor of $\sqrt 2$, thus the impurity is less mobile in the ladder compared to a one dimensional bath. We compared the numerical results for the exponent at zero momentum with a semi-analytical expression that was initially established for the chain and find excellent agreement without adjustable parameters. We analyze the dependence of the exponent in the transverse hopping in the bath and find surprisingly an increase of the exponent at variance with the naive extrapolation of the single channel regime. We study the momentum dependence of the impurity Green's function and find that, as for the single chain, two different regime of motion exist, one dominated by infrared metatrophy and a more conventional polaronic behavior. We compute the critical momentum between these two regimes and compare with prediction based on the structure factor of the bath. In the polaronic regime we also compute numerically the lifetime of the polaron. Finally we discuss how our results could be measured in cold atomic experiments.Comment: 14 Pages, 13 figure

Mobile Impurity in a Two-Leg Bosonic Ladder

We study the dynamics of a mobile impurity in a two-leg bosonic ladder. The impurity moves both along and across the legs and interacts with a bath of interacting bosonic particles present in the ladder. We use both analytical (Tomonaga-Luttinger liquid - TLL) and numerical (Density Matrix Renormalization Group - DMRG) methods to compute the Green's function of the impurity. We find that for a small impurity-bath interaction, the bonding mode of the impurity effectively couples only to the gapless mode of the bath while the anti-bonding mode of the impurity couples to both gapped and gapless mode of the bath. We compute the time dependence of the Green's function of the impurity, for impurity created either in the anti-bonding or bonding mode with a given momentum. The later case leads to a decay as a power-law below a critical momentum and exponential above, while the former case always decays exponentially. We compare the DMRG results with analytical results using the linked cluster expansion and find a good agreement. In addition we use DMRG to extract the lifetime of the quasi-particle, when the Green's function decays exponentially. We also treat the case of an infinite bath-impurity coupling for which both the bonding and antibonding modes are systematically affected. For this case the impurity Green's function in the bonding mode decays as a power-law at zero momentum.The corresponding exponent increases with increasing transverse-tunneling of the impurity. We compare our results with the other impurity problems for which the motion of either the impurity or the bath is limited to a single chain. Finally we comments on the consequences of our findings for experiments with the ultracold gasses.Comment: 11 pages, 15 figure

Thermal decomposition kinetics of sodium carboxymethyl cellulose: Model-free methods

Thermal analysis techniques such as thermogravimetric analysis (TGA) have been widely used because they provide rapid quantitative determination of various processes under isothermal or non-isothermal conditions. It allows the estimation of effective kinetic and thermodynamic parameters for various decomposition and thermal reactions. In this article, thermal degradation of sodium carboxymethyl cellulose (SMC) is investigated by means of dynamic thermogravimetric/derivative thermogravimetry (TG/DTG) in helium atmosphere with the flow rate 100 mL/min at the heating rate of 10-30 °C/min until the furnace wall temperature reached 700 °C. The non-isothermal degradation of SMC found to be taking place occurred major one step and minor two steps. Using a non-isothermal kinetic method based on a TGA data, kinetic parameters (Eand ln A) are calculated by Kissinger-Akahira-Sunose (KAS), Flynn-Wall-Ozawa (FWO) and Friedman methods. The results of studied polymer demonstrated that E and ln A is varied with function of conversion (α), which is in good agreement with literature data

Synthesis, characterization and thermal decomposition kinetics of poly(2-imidazolidinthione-formaldehyde)

A polymeric ligand, 2-imidazolidinthione-formaldehyde (poly-IF), bearing nitrogen and sulfur donor group was synthesized by the polycondensation of 2-imidazolidinthione and formaldehyde in alkaline medium. The synthetic ligand was characterized with micro-analytical and spectral studies. The thermal degradation is investigated by means of dynamic thermogravimetry (TG/DTG) in helium and air atmosphere at various heating rate. The non-isothermal degradation of poly-IF compound was occurred in an inert and air atmosphere. Degradation activation energies were calculated using model free multiple heating rate methods i.e. Flynn-Wall-Ozawa (FWO), Friedman and Kissinger. The compound poly-IF was also tested against strain (Escherichia coli) and it inhibits the proliferation of bacterial growth

Three Dimensional Analysis of Drag-flick in The Field Hockey of University Players

The penalty corner one of the most important technique to score the goal in field hockey. The penalty corner depends upon three different technical applications like push, stop and drag. Technical application of drag flick in penalty corner covered maximum number of successful goal. The main aim of this study was to analyze spatial and temporal kinematics in the drag flick of elite field hockey players. Two main drag flickers from Aligarh Muslim University, Aligarh hockey team were selected as a subject for this study. The body weight, Height and Age of each subject ware recorded subsequently Sub1=65 kg body weight, 180.50cm of height and 19 years of age and Sub2= 60 kg body weight, 167.00 cm of height and 19 years of age. A static calibration method was used to capture drag flick by Two Cameras, sampling at 50 Hz. Six successful trials at target were selected from each subject for the study.  Videos of selected trials were digitized by the Max Track 3D motion analysis software. The three dimensional (3D) motion was determined from digitized video analysis using 18-point body model together. Results of this study shows that spatial / temporal variable between the players, there exist little difference in stance width in ball contact phase, recommended that little or no difference exist in techniques between both players. Key points: spatial / temporal, kinematics, drag, digitized.

Critical behavior in Ni2MnGa and Ni2Mn0.85Cu0.15Ga

The critical behaviors of polycrystalline Ni2MnGa and Ni2Mn0.85Cu0.15Ga have been examined through high-resolution bulk magnetization measurements. The critical exponents, β and γ, were derived from modified Arrott plots using the Kouvel-Fisher method. The values of the extracted critical exponents satisfied the scaling equation of state and associated exponent relations, indicating self-consistency of the extracted values. In Ni2MnGa, the critical exponents (β = 0.401 ± 0.003, γ = 1.27 ± 0.02) indicate a deviation from the 3D-Heisenberg values toward the mean-field values, likely due to the presence of long-range Ruderman-Kittel-Kasuya-Yosida interactions. However, the critical exponents of Ni2Mn0.85Cu0.15Ga (β = 0.389 ± 0.004, γ = 1.39 ± 0.02) are closer to the 3D-Heisenberg values. This indicates a weakening of the long-range exchange interactions due to the substitution of Cu in the Mn site