Two exact properties of the perturbative expansion for the two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit coupling

We have identified two useful exact properties of the perturbative expansion for the case of a two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit interaction and in the absence of magnetic field. The results allow us to draw interesting conclusions regarding the dependence of the exchange and correlation energy and of the quasiparticle properties on the strength of the spin-orbit coupling which are valid to all orders in the electron-electron interaction.Comment: 6 pages, 1 figur

Universal finite size corrections and the central charge in non solvable Ising models

We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength \lambda. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all 0<\lambda<\lambda_0 and \lambda_0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.Comment: 43 pages, 1 figur

Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions

We discuss a general form of the exchange energy for a homogeneous system of interacting electrons in two spatial dimensions which is particularly suited in the presence of a generic spin-orbit interaction. The theory is best formulated in terms of a generalized fractional electronic polarization. Remarkably we find that a net generalized polarization does not necessarily translate into an increase in the magnitude of the exchange energy, a fact that in turn favors unpolarized states. Our results account qualitatively for the findings of recent experimental investigations

Fluctuation Relation beyond Linear Response Theory

The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the fluctuation--dissipation theorem to far from equilibrium systems in a steady state which reduces to the usual Green-Kubo (GK) relation in the limit of small external non conservative forces. FR is a theorem for smooth uniformly hyperbolic systems, and it is assumed to be true in all dissipative ``chaotic enough'' systems in a steady state. In this paper we develop a theory of finite time corrections to FR, needed to compare the asymptotic prediction of FR with numerical observations, which necessarily involve fluctuations of observables averaged over finite time intervals T. We perform a numerical test of FR in two cases in which non Gaussian fluctuations are observable while GK does not apply and we get a non trivial verification of FR that is independent of and different from linear response theory. Our results are compatible with the theory of finite time corrections to FR, while FR would be observably violated, well within the precision of our experiments, if such corrections were neglected.Comment: Version accepted for publication on the Journal of Statistical Physics; minor changes; two references adde

Fermi liquid behavior in the 2D Hubbard model at low temperatures

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.Comment: 66 pages, 10 figure

The many facets of the (non relativistic) Nuclear Equation of State

A nucleus is a quantum many body system made of strongly interacting Fermions, protons and neutrons (nucleons). This produces a rich Nuclear Equation of State whose knowledge is crucial to our understanding of the composition and evolution of celestial objects. The nuclear equation of state displays many different features; first neutrons and protons might be treated as identical particles or nucleons, but when the differences between protons and neutrons are spelled out, we can have completely different scenarios, just by changing slightly their interactions. At zero temperature and for neutron rich matter, a quantum liquid gas phase transition at low densities or a quark-gluon plasma at high densities might occur. Furthermore, the large binding energy of the $\alpha$ particle, a Boson, might also open the possibility of studying a system made of a mixture of Bosons and Fermions, which adds to the open problems of the nuclear equation of state.Comment: 71 pages, 30 figures, accepted by Prog. Part. Nucl. Phys. and in pres

Are direct search experiments sensitive to all spin-independent WIMP candidates?

The common analysis of direct searches for spin-independent Weakly Interacting Massive Particles (WIMPs) assumes that a spin-independent WIMP couples with the same strength with both nucleons, \textit{i.e.} that the spin-independent interaction is also fully isospin-independent. Though in a fully isospin-dependent interaction scenario the spin-independent WIMP-nucleus cross section is strongly quenched, the leading experiments are still sensitive enough to set limits 1-2 orders of magnitude less stringent than those traditionally presented. In the isospin-dependent scenario the difference between the limits of CDMS-II and ZEPLIN-I is significantly reduced. Here, a model-independent framework is discussed and applied to obtain the current general model-independent limits.Comment: 4 pages, 4 figures, revtex4.0, submitted to Phys. Rev. Let