209934211
Anomalous dimensions of tensor operators in 4-epsilon dimensions
37622412
Evidence for a new period-doubling sequence in four-dimensional symplectic maps.
We have numerically investigated period-doubling bifurcations in four-dimensional symplectic maps. Our study indicates the existence of a universally self-similar period-doubling sequence. Unlike the two-dimensional case, the fixed-point map has two unstable directions under the period-doubling operator with two relevant eigenvalues 8.721 097 2 and -15.0786. The four orbital scaling factors along and across the dominant symmetry surface are, respectively, 16.1449, -4.018 07, 16.36, and -7.5393.
121095182
Period doubling: Universality and critical-point order
The dependence of the universal bifurcation ratio on the order of the local maximum is studied for a family of maps $f(x)=1\ensuremath{-}a{x}^{z}$($z=2,4,6,8$). Although these maps all exhibit period doubling, the precise bifurcation ratio depends on the order $z$, and seems to be an increasing function of $z$. We have employed a renormalization-group method to calculate $\ensuremath{\delta}(z)$ to second order. They agree very well with the exact values.
122878082
Induced Topological Terms, Hidden Local Symmetry, and Anyon Superconductivity
We show how the topological Chern-Simons term in three dimensions and the θ-term, in four dimensions can be dynamically generated due to quantum fluctuations in Nambu-Jona-Lasinio models. These results give a vivid demonstration of hidden local symmetry at work. The fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity. Possible phenomenological implications of this approach in particle physics are also discussed.
121822978
The classical Ising model: A quantum renormalization group approach☆
Abstract Proceeding from the equivalence between the d -dimentional classical Ising model and the ( d −1)-dimentional quantum mechanical Ising model in a transverse magnetic field, we study the critical properties of the classical model via the quantum mechanical model. Quantum renormalization group transformations based on the truncation method and the ground state projection operator method are used to calculate the critical exponents. They are found to agree well with the “exact” values.
122050852
VECTOR PAIRING AND FLUCTUATION-INDUCED CHERN-SIMONS TERM IN ANYON SUPERCONDUCTIVITY
Assuming some sorts of vector pairing in high-temperature superconductivity, we show how the topological Chern-Simons term can be generated dynamically due to quantum fluctuations in a BCS-type four-fermion model. This fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity.
122760989
Calculation of the trace anomaly of the conformal energy-momentum tensor in Kasner spacetime by adiabatic regularization
The anomalous trace of the energy-momentum tensor of a quantized massless conformal scalar field in a homogeneous anisotropic, spatially flat background is calculated by the method of adiabatic regularization. It yields the same results as derived by other methods, but has the advantage of simplicity in computation and clarity in physical interpretation. Explicit expressions are also obtained for the regularized energy desity and pressure, which are useful in formulating semiclassical theories of gravity and in calculating the back reaction of quantized fields in relativistic cosmology.
117363004
Coarse-graining and backreaction in inflationary and minisuperspace cosmology.
120106186
Separation of tensor equations in a homogeneous space by group theoretical methods
Details of the group‐theoretical method for the separation of tensor equations in a homogeneous space are given. As illustrations, the vector and tensor harmonics in a SO(3)‐homogeneous space are constructed, with applications to the study of electromagnetic and gravitational perturbations in the mixmaster universe.
117060010
Fluctuations in a Thermal Field and Dissipation of a Black Hole Spacetime: Far-Field Limit
We study the backreaction of a thermal field ina weak gravitational background depicting the far-fieldlimit of a black hole enclosed in a box by the closedtime path (CTP) effective action and the influence functional method. We derive the noise anddissipation kernels of this system in terms ofquantities in quasiequilibrium, and formally prove theexistence of a fluctuation-dissipation relation (FDR) at all temperatures between the quantumfluctuations of the thermal radiance and the dissipationof the gravitational field. This dynamical self-consistent interplay between the quantum field and theclassical spacetime is, we believe, the correct way totreat backreaction problems. To emphasize this point wederive an Einstein–Langevin equation whichdescribes the nonequilibrium dynamics of thegravitational perturbations under the influence of thethermal field. We show the connection between our methodand the linear response theory (LRT), and indicate howthe functional method can provide more accurate results than prior derivations of FDRs via LRT in thetest-field, static conditions. This method is inprinciple useful for treating fully nonequilibrium casessuch as backreaction in black hole collapse.
14617729
Stochastic behavior of effective field theories across threshold
We explore how the existence of a field with a heavy mass influences the low energy dynamics of a quantum field with a light mass by expounding the stochastic characters of their interactions which take on the form of fluctuations in the number of (heavy field) particles created at the threshold, and dissipation in the dynamics of the light fields, arising from the backreaction of produced heavy particles. We claim that the stochastic nature of effective field theories is intrinsic, in that dissipation and fluctuations are present both above and below the threshold. Stochasticity builds up exponentially quickly as the heavy threshold is approached from below, becoming dominant once the threshold is crossed. But it also exists below the threshold and is in principle detectable, albeit strongly suppressed at low energies. The results derived here can be used to give a quantitative definition of the ‘effectiveness’ of a theory in terms of the relative weight of the deterministic versus the stochastic behavior at different energy scales.