Abstract:
We address the problem of the Fermi surface renormalization and the quantum confinement regime (QCR) in the two coupled chains model(TCCM) of spinless fermions. We perform a self-consistent calculation of the renormalization group(RG) flows of the renormalized TCCM couplings and quasiparticle weight. On top of that we take explicitly into account the renormalization of the Fermi surface. The flow of the difference of the renormalized Fermi wave vectors associated with the bonding and antibonding bands has a dramatic effect on the single particle spectrum. Although the quasiparticle amplitude is nullified already at intermediate coupling the QCR is only observed at strong coupling. The state associated with this regime has a charge gap and it is not a Luttinger liquid. In contrast, the Fermi liquid regime is stabilized by the umklapp "$g_2$--like" interactions at very weak coupling regime.

Abstract:
We present the two-loop renormalization group (RG) calculations of all the susceptibilities associated with the two-dimensional flat Fermi surface with rounded corners (FS). Our approach follows our fermionic field theory RG method presented in detail earlier on. In one loop order our calculation reproduce the results obtained previously by other RG schemes. All susceptibilities diverge at some energy scale and the antiferromagnetic SDW correlations produce indeed the dominant instability in the physical system. In contrast, in two-loop order, for a given initial set of values of coupling constant regime only one of the susceptibilities at a time seems to diverge.

Abstract:
We analyze the particle-hole symmetric two-dimensional Hubbard model on a square lattice starting from weak-to-moderate couplings by means of the field-theoretical renormalization group (RG) approach up to two-loop order. This method is essential in order to evaluate the effect of the momentum-resolved anomalous dimension $\eta(\textbf{p})$ which arises in the normal phase of this model on the corresponding low-energy single-particle excitations. As a result, we find important indications pointing to the existence of a non-Fermi liquid (NFL) regime at temperature $T\to 0$ displaying a truncated Fermi surface (FS) for a doping range exactly in between the well-known antiferromagnetic insulating and the $d_{x^2-y^2}$-wave singlet superconducting phases. This NFL evolves as a function of doping into a correlated metal with a large FS before the $d_{x^2-y^2}$-wave pairing susceptibility finally produces the dominant instability in the low-energy limit.

Abstract:
We calculate the charge compressibility and uniform spin susceptibility for the two-dimensional (2D) Hubbard model slightly away from half-filling within a two-loop renormalization group scheme. We find numerically that both those quantities flow to zero as we increase the initial interaction strength from weak to intermediate couplings. This result implies gap openings in both charge and spin excitation spectra for the latter interaction regime. When this occurs, the ground state of the lightly doped 2D Hubbard model may be interpreted as an insulating spin liquid as opposed to a Mott insulating state.

Abstract:
We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behavior of two central quantities of a system: the uniform charge and spin susceptibilities. We point out that a consistent renormalization group treatment of them can only be achieved within a two-loop approach or beyond. In the 1D HM, we show that this scheme reproduces correctly the metallic behavior given by the well-known Luttinger liquid fixed-point result. Then, we use the same approach to deal with the more complicated 2D HM. In this case, we are able to show that both uniform susceptibilities become suppressed for moderate interaction parameters as one take the system towards the Fermi surface. Therefore, this result adds further support to the interpretation that those systems are in fact insulating spin liquids. Later, we perform the same calculations in 2D using the conventional random phase approximation, and establish clearly a comparison between the two schemes.

Abstract:
we employ the newton's second law to describe the variable mass oscillator system. we describe and set up an experimental apparatus in order to measure the oscillations and other parameters with the help of equipments available commercially. by using a preconceived model for such a system we are able to fit the experimental results with a good agreement. to accomplish this task we developed a c++ program which can extract the experimental values of the amplitude of the oscillatory movement as well as to rotate the coordinates system in order to set apart the translational movement from the oscillatory one.

Abstract:
We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.} [Phys. Rev. Lett. \textbf{85}, 4940 (2000)], which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.

Abstract:
Mutations leading to constitutive activation of the Wnt pathway and its target genes are frequently observed in cancer. The Wnt pathway promotes cell proliferation and increasing evidence supports its role also in cancer cell metabolism. This study aims to elucidate the role of the Wnt/β-catenin target gene CCND1 in these processes in colorectal cancer. We analyzed whether knock-down of CCND1 affects cell cycle progression and energy metabolism in a colorectal cancer cell line. Down-regulation of CCND1 led to retardation of the cell cycle. The proportion of cells in the G0 phase increased, while the amount of cells in the S- and G2/M phase decreased. Interestingly, knock-down of CCND1 changed the perinuclear localization of mitochondria into a homogeneous distribution within the cytosol. In addition CCND1 knock-down led to an increase of the intracellular ATP level indicating that cyclin D1 reduced mitochondrial activity. Our findings suggest that in addition to its role in cell cycle regulation, the Wnt target gene CCND1 regulates mitochondrial localization and inhibits mitochondrial activity in colorectal cancer cells.

Abstract:
We motivate and provide proofs of Ba?ar and Olsder’s (1995) theorems on the subject. The context is the increasing appreciation that the neoclassical framework is not the only model of the economy.

We separate the “rentier” portion of the budget constraint of the representative agent from the “income-plus-distributed profits” segment. The former’s wealth consists exclusively of returns on government bonds, the latter’s wealth is wage income from working for firms plus the distributed profits of the latter. The non-neoclassical element is the non-imposition of the market-clearing assumption. The Barro-Ricardo theorem only applies to rentiers. The level of activity is shown to depend on the level of employment along with a set of parameters that capture the imperfect competition of the model.