相关论文: Tunnel effect for Kramers-Fokker-Planck type opera…

We study operators of Kramers-Fokker-Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number $n_0$ of local minima. Under suitable additional assumptions, we…

In the first part of this work, we consider second order supersymmetric differential operators in the semiclassical limit, including the Kramers-Fokker-Planck operator, such that the exponent of the associated Maxwellian $\phi$ is a Morse…

In the semiclassical limit h to 0, we analyze a class of self-adjoint Schr\"odinger operators H_h = h^2 L + h W + V id_E acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is…

We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon\mathbf{Z}^d)$, where $V_\varepsilon$ is a multi-well potential and $\varepsilon$ is a small parameter. We derive full…

We establish a tunneling formula for a Schr\"odinger operator with symmetric double-well potential and homogeneous magnetic field, in dimension two. Each well is assumed to be radially symmetric and compactly supported. We obtain an…

In this paper, we consider the semiclassical 2D magnetic Schr{\"o}dinger operator in the case where the magnetic field vanishes along a smooth closed curve. Assuming that this curve has an axis of symmetry, we prove that semi-classical…

For quickly decreasing potentials with one position variable, the first threshold zero is always a resonance of the Kramers-Fokker-Planck operator. In this article we study low-energy spectral properties of the operator and calculate large…

We consider tunneling between 2 symmetric potential wells for a 2-d Schrodinger operator, in the case of eigenvalues associated with quasi-modes supported on KAM or Birkhoff tori.

We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schr\"odinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the…

We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on a closed curve. We derive a classical and quantum normal form which allows us, in…

In this article we study some Kramers-Fokker-Planck operators with a polynomial potential $V(q)$ of degree greater than two having quadratic limiting behavior. This work provides an accurate global subelliptic estimate for KFP operators…

We investigate the spectral analysis of a class of pseudo-differential operators in one dimension. Under symmetry assumptions, we prove an asymptotic formula for the splitting of the first two eigenvalues. This article is a first example of…

The study of tunneling splitting is fundamental to get insight into the dynamics of a multitude of molecular systems. In this paper, a novel approach to the analysis of the ground-state tunneling splitting is presented and explicitly…

We study the quadratic Kramers-Fokker-Planck operator with a constant magnetic field and with a quadratic potential. We describe the exact expression of the norm of the semi-group associated to the operator near the equilibrium. At this…

The present article is concerned with global subelliptic estimates for Kramers-Fokker-Planck operators with polynomials of degree less than or equal to two. The constants appearing in those estimates are accurately formulated in terms of…

We consider tunneling between symmetric wells for a 2-D semi-classical Schr\"odinger operator for energies close to the quadratic minimum of the potential V in two cases: (1) excitations of the lowest frequency in the harmonic oscillator…

We consider the non-selfadjoint, semiclassical Schr\"odinger operator $\mathscr{L}(h) := -h^2\partial_x^2+e^{i\alpha}V$, where $\alpha \in (-\pi,\pi)$ and $V: \mathbb{R}\to \mathbb{R}_+$ is even and vanishes at exactly two (symmetric)…

We consider a magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a two-dimensional Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the…

This paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electric wells are connected by two geodesics for the Agmon…

In this paper, we study an L2 version of the semiclassical approximation of magnetic Schroedinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence…