Exact solution to the “auxiliary extra-dimension” model of massive gravity

The “auxiliary extra-dimension” model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.     

Nonperturbative deformation of conformal field theory and spontaneously broken inter mass level symmetries in string thery

We study the deformation of conformal field theory without leaving the fixed points. It is found that an infinite number of higher spin background fields are needed to cancel theq-number anomalies when one goes beyond first order weak field calculation. This phenomenon can be interpreted in string theory as spontaneously broken symmetries between particles with different masses.     

Occupation numbers from functional integral

Occupation numbers for non-relativistic interacting particles are discussed within a functional integral formulation. For bosons at zero temperature the Bogoliubov theory breaks down for strong couplings as well as for low-dimensional models. We find that the leading behavior of the occupation numbers for small momentum is governed by a quadratic time derivative in the inverse propagator that is not contained in the Bogoliubov theory. We propose to use a functional renormalization group equation for the occupation numbers in order to implement systematic non-perturbative extensions beyond the Bogoliubov theory. We also discuss interacting fermions, in particular the issue of pseudogaps.     

variant Planck's over 2pi expansion for the periodic orbit quantization of chaotic systems

We report the results of a periodic orbit quantization of classically chaotic billiards beyond Gutzwiller approximation in terms of asymptotic series in powers of the Planck constant (or in powers of the inverse of the wave number kappa in billiards). We derive explicit formulas for the kappa(-1) approximation of our semiclassical expansion. We illustrate our theory with the classically chaotic scattering of a wave on three disks. The accuracy on the real parts of the scattering resonances is improved by one order of magnitude.     

Quantum fluctuations and collective oscillations of a Bose-Einstein condensate in a 2D optical lattice

We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.     

Doped spin liquid: Luttinger sum rule and low temperature order

We analyze a model of two-leg Hubbard ladders weakly coupled by interladder tunneling. At half filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in the single electron Green's function relevant for the Luttinger sum rule now take place at surfaces with both zeros and infinities with important consequences for the interpretation of angle-resolved photoemission spectroscopy experiments. Residual interactions between electron and holelike quasiparticles cause a transition to long range order at low temperatures. The theory can be extended to small doping leading to superconducting order.     

Advantages and Drawbacks of Quantum Mechanical Static and Dynamic Approaches to Modelling Infrared Spectra

利用超简谐振动近似的有效二阶微扰法(VPT2)和变异微扰法(VCI-P)两种静态方法,以及在300和600K下的密度泛函分子动态轨线振动分析方法进行量子力学的振动计算. 比较了这四种方法对于基频跃迁频率和对应的中红外光谱在相同的B3LYP/6-31+G(d,p)基组描述电子结构前提下所得到的计算结果. 总结了对于半刚性和柔性分子的主要结果,并且对这些计算方法的优缺点进行了比较.     

Implicit regularization beyond one-loop order: gauge field theories

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED. PACS  11.10.Gh; 11.15.Bt; 11.15.-q     

High precision mean-field results for lattice gauge theories: with special attention paid to the gauge dependence of mean-field perturbation theory to finite order

We do mean-field perturbation theory for U(1) lattice gauge theory in the axial gauge, and evaluate corrections from fluctuations up to fourth order for the free energy and plaquette energy. Comparing with similar results previously obtained in the Feynman gauge we find, to those orders studied, a gauge dependence of the size of the first correction term neglected with one exception. This gauge dependence decreases rapidly as the order of the approximation is increased. To any finite order, results in axial gauge are better approximations than results in the Feynman gauge. We speculate why. Assuming it to be generally true, we evaluate the first correction beyond the one-loop mean-field approximation to the free energy of SU(2) gauge theory with Wilson action in the axial gauge. This correction brings the mean-field result very close to Monte Carlo results for β > 1.6. It also makes the mean-field result identical, within a narrow margin, to ressumed strong coupling results in the interval 1.6 < β < 2.4, thus showing the absence of a phase transition.For both groups studied, we find that the asymptotic series of mean-field perturbation theory give much better approximations than do ordinary weak coupling series.     

The Future of Cosmology and the Role of Non-Linear Perturbations

Cosmological perturbation theory is a key tool to study the universe.The linear or first order theory is well understood,however,developing and applying the theory beyond linear order is at the cutting edge of current research in theoretical cosmology.In this article,I will describe some signatures of non-linear perturbation theory that do not exist at linear order,focusing on vorticity generation at second order.In doing so,we discuss why this,among other features such as induced gravitational waves and non-Gaussianities,shows that cosmological perturbation theory is crucial for testing models of the universe.     

Classical diffusion in strong random media

We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.     

Effective theory of excitations in a Feshbach-resonant superfluid

A strongly interacting Fermi gas, such as that of cold atoms operative near a Feshbach resonance, is difficult to study by perturbative many-body theory to go beyond mean-field approximation. Here I develop an effective field theory for the resonant superfluid based on broken symmetry. The theory retains both fermionic quasiparticles and superfluid phonons, the interaction between them being derived nonperturbatively. The theory converges and can be improved order by order, in a manner governed by a low energy expansion rather than by a coupling constant. I apply the effective theory to calculate the specific heat and discuss the theory with a recent heat capacity experiment.     

QCD vacuum as a disordered medium: a simplified model for the QCD dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the dimensionless Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.     

Influence of Lorentz broadening on the stability of monomode ring lasers

We carry out a linear stability analysis of the stationary solutions describing in the frame of the semiclassical theory a Lorentz broadened single running mode in a ring laser. We seek the conditions of destabilization via a Hopf bifurcation and prove that it can occur only in a bad cavity. The threshold intensity is very high when homogeneous broadening dominates, it is of the order of a few saturation intensities when homogeneous and inhomogenous widths are comparable and it tends to zero as the inhomogeneous width increases well beyond the homogeneous width.     

A Novel Approach to the Partial Information Decomposition

We consider the “partial information decomposition” (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we propose a general framework for constructing a multivariate PID. Our framework is defined in terms of a formal analogy with intersection and union from set theory, along with an ordering relation which specifies when one information source is more informative than another. Our definitions are algebraically and axiomatically motivated, and can be generalized to domains beyond Shannon information theory (such as algorithmic information theory and quantum information theory). In the second part of this paper, we use our general framework to define a PID in terms of the well-known Blackwell order, which has a fundamental operational interpretation. We demonstrate our approach on numerous examples and show that it overcomes many drawbacks associated with previous proposals.     

Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures

We consider the problem of heat transport by vibrational modes between Langevin thermostats connected by a central device. The latter is anharmonic and can be subject to large temperature difference and thus be out of equilibrium. We develop a classical formalism based on the equation of motion method, the fluctuation–dissipation theorem and the Novikov theorem to describe heat flow in a multi-terminal geometry. We show that it is imperative to include a quartic term in the potential energy to insure stability and to properly describe thermal expansion. The latter also contributes to leading order in the thermal resistance, while the usually adopted cubic term appears in the second order. This formalism paves the way for accurate modeling of thermal transport across interfaces in highly non-equilibrium situations beyond perturbation theory.     

Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical version of Callan and Coleman. We have calculated the nucleation rate beyond the thin wall approximation by expanding the bubble solution and the fluctuation determinant in powers of the asymmetry parameter. The result is expressed in terms of physical model parameters. Received: 18 August 1999 / Published online: 14 October 1999     

Scaling of the electrical conductivity of granular media

We derive the scaling properties of the dependence of the macroscopic electrical conductivity of granular media (e.g., sands) with a surface mechanism of electrical conduction on the grain size, when the medium is subjected to a given mechanical stress. In order to eliminate the influence of the inter-grain junction capacity, the direct electrical current is considered. We determine the applicability restrictions on the theory which disregards the ultimate crushing compression strength, adhesion, and the effect of charge carrier tunneling at grain junctions beyond the contact surface area. Solutions for several regular packings of grains are obtained as well.     

Form factor perturbation theory from finite volume

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for non-integrable models described as perturbations of integrable ones. This permits to go beyond first order in form factor perturbation theory and in principle works to any order. The procedure is carried out in detail for double sine-Gordon theory, where the vacuum energy density and breather mass correction is evaluated at second order. The results agree with those obtained from the truncated conformal space approach. The regularization procedure can also be used to compute other spectral sums involving disconnected pieces of form factors such as those that occur e.g. in finite temperature correlators.