The anomalous effective action in three-dimensional gauge theories

Summary We analyse the effective action for gauge fields in odd dimensions, obtained by integrating out the fermions in the Feynman path integral. In particular, we discuss the generation of a Chern-Simons term by massless fermions minimally coupled to an Abelian gauge field. We review two methods of revealing the presence of a Chern-Simons term in the effective action: first, as the consequence of a nontrivial holonomy of the fermionic ground state, then as the result of the generation of an anomalous imaginary part of the effective action. We derive the most general form of the anomalous effective action at the lowest nontrivial order of a derivative expansion in time. We discuss the implications of our analysis for the theory of the fractional quantum Hall effect as well as for the quantization of anomalous theories. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Resonant fermi gases with a large effective range

We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for a large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest 0.002 fm(-3) < rho < 0.02 fm(-3), for which the interparticle separation is comparable to the effective range. We compare our simple results with those of conventional many-body calculations.     

Effective coupling between two Brownian particles

We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is nonlinear in the variables of interest, and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method, and, besides recovering all the local dynamical properties for each particle, we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms.     

Exactly solvable model for driven dissipative systems

We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different measures of effective temperatures. As an example we demonstrate that fluctuation-dissipation relations hold, however, with an effective temperature differing from the effective temperature defined from the average energy.     

Effective mass in quantum effects of radiation pressure

We study the quantum effects of radiation pressure in a high-finesse cavity with a mirror coated on a mechanical resonator. We show that the optomechanical coupling can be described by an effective susceptibility which takes into account every acoustic modes of the resonator and their coupling to the light. At low frequency this effective response is similar to a harmonic response with an effective mass smaller than the total mass of the mirror. For a plano-convex resonator the effective mass is related to the light spot size and becomes very small for small optical waists, thus enhancing the quantum effects of optomechanical coupling.     

Nucleon propagation through nuclear matter in chiral effective field theory

We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg’s method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature. PACS 11.30.Rd; 12.38.Lg; 12.39.Fe; 24.85.+p     

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.     

Kaluza-Klein monopoles and gauged sigma-models

We propose an effective action for the eleven-dimensional (bosonic) Kaluza-Klein monopole solution. The construction of the action requires that the background fields admit an Abelian isometry group. The corresponding sigma-model is gauged with respect to this isometry. The gauged sigma-model is the source for the monopole solution. A direct (double) dimensional reduction of the action leads to the effective action of a 10-dimensional D-6-brane (IIA Kaluza-Klein monopole). We also show that the effective action of the 10-dimensional heterotic Kaluza-Klein monopole (which is a truncation of the IIA monopole action) is T-dual to the effective action of the solitonic 5-brane. We briefly discuss the kappa-symmetric extension of our proposal and the possible role of gauged sigma-models in connection with the conjectured M-theory 9-brane.     

Gain-clamped S-band discrete Raman amplifier

We demonstrate the advantages of an optically gain-clamped S-band discrete Raman amplifier: low gain variation over a large input dynamic range, effective suppression of Raman transients, and amplifier instability in the strong-pump-weak-signal configuration. We further investigate experimentally the operating conditions necessary for effective gain clamping and demonstrate gain flattening over 30 nm of bandwidth. Thus a gain-clamped discrete Raman amplifier shows promise for practical deployment.     

Spontaneous compactification in quantum Kaluza-Klein theories

We study the one-loop effective action for pure gravity in higher odd-dimensional spaces with a cosmological constant. We develop a method for computing the effective action for backgrounds which are a product of 4-dimensional space-time and an odd-dimensional sphere S^N. For N = 1 in harmonic gauge the potential has an unstable stationary point at which the one-loop corrected Newton constant has a wrong sign. For N > 1 in harmonic gauge there is an imaginary contribution to the effective potential from the Faddeev-Popov ghost. The results for spheres up to N = 17 are presented.     

Effective action and vacuum instability in the chiral σ-model and the standard electroweak model

We develop a partial expansion of the effective action from fermion integration relevant for spatially small configurations of the meson fields in the chiral σ-model. It is shown that this leads (in this semiclassical approximation) to a vacuum instability. For weak Yukawa coupling, when the semiclassical calculation is valid, this would indicate an instability of the Weinberg-Salam model, implying that the latter is only an effective theory. We give an estimate of the approximate length scale at which this occurs.     

Spectral Properties of Effective Dynamics from Conditional Expectations

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.     

Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity

We present a two-dimensional mathematical model of a composite material with conducting inclusions (fibers) embedded in a matrix. Our main objective is to study how polydispersity (two different sizes of particles) affects the overall conductivity of the composite. If the conductivity of inclusions is higher than the conductivity of the matrix, then previous studies suggest an increase of the effective conductivity due to polydispersity. We show that for high volume fraction when inclusions are not well-separated and percolation effects play a significant role, polydispersity may result in either an increase or decrease of the effective conductivity. Our proof is based on the method of functional equations and it provides sufficient conditions for both the increase and the decrease of the effective conductivity.     

Gap Equations and Effective Potentials at Finite Temperature and Chemical Potential in D-Dimensional Four-Fermion Models

We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interactionmodels. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicitexpressions for the effective potentials at zero temperature in the cases of D = 2,3, and 4 for practical use.     

Josephson junction with a magnetic-field tunable ground state

We consider an asymmetric 0-π Josephson junction consisting of 0 and π regions of different lengths L(0) and L(π). As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase ψ so that the effective current-phase relation of this system includes a negative second harmonic ∝sin(2ψ). If its amplitude is large enough, the ground state of the junction is doubly degenerate ψ=±φ, where φ depends on the amplitudes of the first and second harmonics. We study the behavior of such a junction in an applied magnetic field H and demonstrate that H induces an additional term ∝Hcosψ in the effective current-phase relation. This results in a nontrivial ground state tunable by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally.     

Taylor expansions in Hartree-Fock and isoscalar nuclear shifts

We consider changes in the bulk properties of a nucleus when a particle is added to an even system. The main thing we show is that one can determine these changes by doing a Hartree-Fock calculation on the even system only. We must, however, also examine what happens away from equilibrium, or at least get derivates at equilibrium, in the even system. We get expressions for E0 isoscalar effective charges which involve, but do not determine, the nuclear compressibility, likewise expressions for E2 effective charges which involve but do not determine the quadrupolarizability. Illustrative examples using simple interactions are presented. E0 effective charge corrections in a major shell are larger by roughly a factor of two in orbits with high radial quantum number and E2 effective charge corrections are near unity. Finally, we consider simultaneous changes in the radial and quadrupole shapes.     

A generalization of the algebraic approach for effective interactions in nuclei

We generalize the algebraic approach of Schucan and Weidenmüller for effective interactions in nuclei and show that in general one obtains an effecti to that of Brandow by an arbitrary similarity transformation. We then show how this arbitrariness can be utilized to obtain hermitian effective interac