相关论文: Contributions of non-extremum critical points to t…
We study the semi-classical trace formula at a critical energy level for an $h$-pseudo-differential operator on $\mathbb{R}^{n}$ whose principal symbol has a totally degenerate critical point for that energy. This problem is studied for a…
We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator whose principal symbol has a unique non-degenerate critical point for that energy. This leads to the study of Hamiltonian systems…
We study the semi-classical trace formula at a critical energy level for a Schr\"odinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local maximum. The main result,…
We study the semi-classical trace formula at a critical energy level for a Schr\"odinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result,…
We establish spectral estimates at a critical energy level for $h$-pseudors . Via a trace formula, we compute the contribution of isolated (non-extremum) critical points under a condition of "real principal type". The main result holds for…
In previous work, we gave a local formula for the index of Heisenberg elliptic operators on contact manifolds. We constructed a cocycle in periodic cyclic cohomology which, when paired with the Connes-Chern character of the principal…
A new pseudodifferential calculus of Shubin type is introduced. The calculus contains operators depending on a non negative real parameter as well as operators independent of the parameter. Resolvents of Shubin type pseudodifferential…
Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace…
Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is…
We show that the noncommutative residue density, resp. the cut-off regularised integral are the only closed linear, resp. continuous closed linear forms on certain classes of symbols. This leads to alternative proofs of the uniqueness of…
We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two…
We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings…
We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…
Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We…
Semiclassical expansions for traces involving Greens functions have two contributions, one from the periodic or recurrent orbits of the classical system and one from the phase space volume, i.e. the paths of infinitesimal length.…
We study the functional calculus for operators of the form $f_h(P(h))$ within the theory of semiclassical pseudodifferential operators, where $\{f_h\}_{h\in (0,1]}\subset C^\infty_c(\mathbb{R})$ denotes a family of $h$-dependent functions…
We have derived an analytical trace formula for the level density of the H\'enon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has…
We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…
We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (\rho,z,p_\rho,p_z) and have p_\phi = m\hbar where m is the azimuthal…
In this paper, we develop a semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we…