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F. David

Publications and source records attributed to F. David.

8 recordsLinked to original sources
arXiv2025

Monolithic 4H-SiC nanomechanical resonators with high intrinsic quality factors

We present an extensive study of 4H-SiC nanomechanical resonators electrochemically etched out of a monocrystalline wafer. Combining piezo-driven interferometric determination of the mechanical spectra with scanning-laser-Doppler vibrometry, an unambiguous assignment of resonance peaks to flexural and torsional modes is achieved. The investigation of multiple harmonic eigenmodes of singly and doubly clamped resonators with varying geometry allows for a comprehensive characterization. Excellent intrinsic mechanical quality factors up to $2\times10^5$ are found at room temperature, approaching the thermoelastic limit at eigenfrquencies exceeding 10 MHz. Mechanical stress is essentially absent. Young's modulus in agreement with literature. These findings are robust under post-processing treatments, in particular atomic layer etching and high-temperature thermal annealing. The resulting on-chip high-quality mechanical resonators represent a valuable technological element for a broad range of applications. In particular, the monolithic architecture meets the requirements of spin-based photonic quantum technologies on the upcoming SiC platform.

cond-mat.mes-hall↗
arXiv1995

Self-avoiding Tethered Membranes at the Tricritical Point

The scaling properties of self-avoiding tethered membranes at the tricritical point (theta-point) are studied by perturbative renormalization group methods. To treat the 3-body repulsive interaction (known to be relevant for polymers), new analytical and numerical tools are developped and applied to 1-loop calculations. These technics are a prerequisite to higher order calculations for self-avoiding membranes. The cross-over between the 3-body interaction and the modified 2-body interaction, attractive at long range, is studied through a new double epsilon-expansion. It is shown that the latter interaction is relevant for 2-dimensional membranes at the theta-point.

cond-mat↗
arXiv1993

Renormalization and Hyperscaling for Self-Avoiding Manifold Models

The renormalizability of the self-avoiding manifold (SAM) Edwards model is established. We use a new short distance multilocal operator product expansion (MOPE), which extends methods of local field theories to a large class of models with non-local singular interactions. This validates the direct renormalization method introduced before, as well as scaling laws. A new general hyperscaling relation for the configuration exponent gamma is derived. Manifolds at the Theta-point, and long range Coulomb interactions are briefly discussed.

cond-mat↗
arXiv1993

Simplicial Quantum Gravity and Random Lattices

Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus - dynamical triangulations 3. Two dimensional quantum gravity, dynamical triangulations and matrix models continuum formulation - dynamical triangulations and continuum limit - one matrix model - various matrix models - numerical studies - c=1 barrier - intrinsic geometry of 2d gravity - Liouville at c>25 4. Euclidean quantum gravity in three and four dimensions what are we looking for? - 3d simplicial gravity - 4d simplicial gravity - 3d and 4d Regge calculus 5. Non-perturbative problems in two dimensional quantum gravity double scaling limit - string equation - non-perturbative properties of the string equation - divergent series and Borel summability - non-perturbative effects in 2d gravity and string theories - stabilization proposals 6. Conclusion

hep-th↗
arXiv1992

Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity

The most general large N eigenvalues distribution for the one matrix model is shown to consist of tree-like structures in the complex plane. For the m=2 critical point, such a split solution describes the strong coupling phase of 2d quantum gravity (c=0 non-critical string). It is obtained by taking combinations of complex contours in the matrix integral, and the relative weight of the contours is identified with the non-perturbative theta-parameter that fixes uniquely the solution of the string equation (Painleve I). This allows to recover by instanton methods results on the non-perturbative effects obtained by the Isomonodromic Deformation Method, and to construct for each theta-vacuum the observables (the loop correlation functions) which satisfy the loop equations. The breakdown of analyticity of the large N solution is related to the existence of poles for the loop operators.

hep-th↗
arXiv1992

Renormalization of Crumpled Manifolds

We consider a model of D-dimensional tethered manifold interacting by excluded volume in R^d with a single point. By use of intrinsic distance geometry, we first provide a rigorous definition of the analytic continuation of its perturbative expansion for arbitrary D, 0 < D < 2. We then construct explicitly a renormalization operation, ensuring renormalizability to all orders. This is the first example of mathematical construction and renormalization for an interacting extended object with continuous internal dimension, encompassing field theory.

hep-th↗
arXiv1992

Renormalization Theory for Interacting Crumpled Manifolds

We consider a continuous model of D-dimensional elastic (polymerized) manifold fluctuating in d-dimensional Euclidean space, interacting with a single impurity via an attractive or repulsive delta-potential (but without self-avoidance interactions). Except for D=1 (the polymer case), this model cannot be mapped onto a local field theory. We show that the use of intrinsic distance geometry allows for a rigorous construction of the high-temperature perturbative expansion and for analytic continuation in the manifold dimension D. We study the renormalization properties of the model for 0 d* in the attractive case is thus established. To our knowledge, this provides the first proof of renormalizability for a model of extended objects, and should be applicable to the study of self-avoidance interactions for random manifolds.

hep-th↗