Thermodynamic and transport signatures of a fractionalized Fermi liquid

Several heavy-fermion metals display a quantum phase transition from an antiferromagnetic metal to a heavy Fermi liquid. In some materials, however, recent experiments seem to find that the heavy Fermi liquid phase can be directly tuned into a non-Fermi liquid phase without apparent magnetic order. We analyze a candidate state for this scenario where the local moment system forms a spin liquid with gapless fermionic excitations. We discuss the thermal conductivity and spin susceptibility of this fractionalized state both in two and, in particular, three spatial dimensions for different temperature regimes. We derive a variational functional for the thermal conductivity and solve it with a variational ansatz dictated by Keldysh formalism. In sufficiently clean samples and for an appropriate temperature window, we find that thermal transport is dominated by the spinon contribution which can be detected by a characteristic maximum in the Wiedemann-Franz ratio. For the spin susceptibility, the conduction electron Pauli paramagnetism is much smaller than the spinon contribution whose temperature dependence in three dimensions is logarithmically enhanced as compared to the Fermi liquid result

Information Efficiency of the Capital Market: a Stochastic Calculus Approach Evidence from the Czech Republic (in English)

This paper deals with an important characteristic of the capital market: information efficiency. With the use of geometric Brownian motion, the authors run several projections of stock prices based on varying amount of historic information and compare these projections with the real behavior of the stock prices, examining for predictability. This enables to verify the condition of the weak-efficiency hypothesis in the form of a Markov process. The authors conduct the empirical part of their analysis in the environment of the Czech capital market, thus providing additional information on the development of transition economies.Monte Carlo, stochastic calculus, weak-form information efficiency

Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate $h_{\mathrm{KS}}$ given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian. The derivation takes into account the case of time-dependent Hamiltonians with Floquet instabilities. We show that the entanglement entropy $S_A$ of a Gaussian state grows linearly for large times in unstable systems, with a rate $\Lambda_A \leq h_{KS}$ determined by the Lyapunov exponents and the choice of the subsystem $A$. We apply our results to the analysis of entanglement production in unstable quadratic potentials and due to periodic quantum quenches in many-body quantum systems. Our results are relevant for quantum field theory, for which we present three applications: a scalar field in a symmetry-breaking potential, parametric resonance during post-inflationary reheating and cosmological perturbations during inflation. Finally, we conjecture that the same rate $\Lambda_A$ appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.Comment: 50+17 Pages, 11 figure

Comment on: Nonmonotonic dx2−y2d_{x^{2}-y^{2}} Superconducting Order Parameter in Nd2−x_{2-x}Cex_xCuO4_4

In a recent letter Blumberg and collaborators claim that a non-monotonic $d_{x^2-y^2}$ form for the superconducting order parameter is required to explain their Raman scattering measurements in Nd$_{2-x}$Ce$_x$CuO$_4$ . In this comment we show with a simple model calculation that the basis for this conclusion is insufficient. The proposed functional dependence of the gap is neither consistent with their measured spectra nor compatible with other experimental results. Therefore the issue of the superconduing gap in electron-doped systems cannot be considered solved by now.Comment: Comment to the paper by Blumberg et al., Phys. Rev. Lett., 88, 107002 (2002