Gaussian quantum fluctuations in the superfluid-Mott phase transition

Recent advances in cooling techniques make now possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gappless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for next future experiments on quantum phase transitions.Comment: 7 pages, 4 figures, to be published in Physical Review

Quantum Interactions Between Non-Perturbative Vacuum Fields

We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field configurations are explicitly integrated out from the path integral. We show how to compute the effective interaction between the vacuum field degrees of freedom both perturbatively (using stochastic perturbation theory) and fully non-perturbatively (using lattice field theory simulations). The present approach holds to all orders in the couplings and does not rely on the semi-classical approximation.Comment: 15 pages, 4 figure

Spontaneous symmetry breaking and Higgs mode: comparing Gross-Pitaevskii and nonlinear Klein-Gordon equations

We discuss the mechanism of spontaneous symmetry breaking and the elementary excitations for a weakly-interacting Bose gas at finite temperature. We consider both the non-relativistic case, described by the Gross-Pitaevskii equation, and the relativistic one, described by the cubic nonlinear Klein-Gordon equation. We analyze similarities and differences in the two equations and, in particular, in the phase and amplitude modes (i.e. Goldstone and Higgs modes) of the bosonic matter field. We show that the coupling between phase and amplitude modes gives rise to a single gapless Bogoliubov spectrum in the non-relativistic case. Instead, in the relativistic case the spectrum has two branches: one is gapless and the other is gapped. In the non-relativistic limit we find that the relativistic spectrum reduces to the Bogoliubov one. Finally, as an application of the above analysis, we consider the Bose-Hubbard model close to the superfluid-Mott quantum phase transition and we investigate the elementary excitations of its effective action, which contains both non-relativistic and relativistic terms.Comment: 11 pages, 0 figures, to be published in the open-access journal Symmetry, special issue "Broken Symmetry" (guest editor B.A. Molomed

Quantum Charge Transport and Conformational Dynamics of Macromolecules

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally-activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder.Comment: 11 pages, 2 figure

Instantons, Chiral Dynamics and Hadronic Resonances

We use the Interacting Instanton Liquid Model (IILM) as a tool to study the role played by the chiral interactions in the lowest-lying vector and axial vector meson resonances. We find that narrow a1 and rho meson resonances can be generated by instanton-induced chiral forces, even in the absence of confinement. In the IILM, these hadrons are found to have masses only about 30% larger than the experimental value and small width <10-50 MeV. This result suggests that chiral interactions are very important in these systems and provide most of their mass. We explore the decaying patterns of the rho meson, in the absence of confinement. We argue that, in our model where only chiral forces are switched on, this meson decays dissociating into its quark anti-quark constituents

Nonlinear Transmission of Financial Shocks: Some New Evidence

Financial shocks generate a protracted and quantitatively important effect on real economic activity and financial markets only if the shocks are both negative and large. Otherwise, their role is quite modest. Financial shocks have become more important for economic fluctuations after 2000 and have contributed substantially to deepening the recessions of 2001 and 2008. The evidence is obtained using a new econometric procedure based on a Vector Moving Average representation that includes a nonlinear function of the financial shock. This method is a contribution of the present work

Computing the Effective Hamiltonian of Low-Energy Vacuum Gauge Fields

A standard approach to investigate the non-perturbative QCD dynamics is through vacuum models which emphasize the role played by specific gauge field fluctuations, such as instantons, monopoles or vortexes. The effective Hamiltonian describing the dynamics of the low-energy degrees of freedom in such approaches is usually postulated phenomenologically, or obtained through uncontrolled approximations. In a recent paper, we have shown how lattice field theory simulations can be used to rigorously compute the effective Hamiltonian of arbitrary vacuum models by stochastically performing the path integral over all the vacuum field fluctuations which are not explicitly taken into account. In this work, we present the first illustrative application of such an approach to a gauge theory and we use it to compute the instanton size distribution in SU(2) gluon-dynamics in a fully model independent and parameter-free way.Comment: 10 pages, 4 figure

Centrifuge modeling of rocking-isolated inelastic RC bridge piers

Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately underdesigning shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil-footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking-isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self-centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. © 2014 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd