# Haut PDF Semiclassical resolvent estimates in chaotic scattering

### Semiclassical resolvent estimates in chaotic scattering

**resolvent**

**in**the pole free strip below the real axis ...bound

**in**the non-trapping case (that is, the case where all classical trajectories escape to ...Strichartz

**estimates**for the ...

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### Sharp low frequency resolvent estimates on asymptotically conical manifolds

**scattering**theory of the Laplace-Beltrami operator on asymptotically Euclidean or conical manifolds has been widely ...spectrum,

**in**particular the behaviour of the

**resolvent**at low, medium and ...

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### SEMI-CLASSICAL RESOLVENT ESTIMATES FOR L ∞ POTENTIALS ON RIEMANNIAN MANIFOLDS

**semiclassical**

**resolvent**

**estimates**obtained recently

**in**[8], [12], [13] and [14] for the Schr¨ odinger operator

**in**the Euclidean space R n to a large class of non-compact, connected ...

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### Semiclassical asymptotics for nonselfadjoint harmonic oscillators

**in**[31] the spectral study of this partial differential equa- tion on compact Riemannian ...asymptotics

**in**the high frequency limit [31, ...lie

**in**a strip of the complex plane which can be ...

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### Quantum transfer operators and chaotic scattering

**semiclassical**density of eigenvalues: any point situated at distance ≫ h 1/2 from Γ will be pushed out of B(0, R 1 ) through the classical dynamics (either

**in**the past or

**in**the future), within a ...

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### Uniform resolvent estimates for a non-dissipative Helmholtz equation

**in**particular satisfied when V 2 > 0 and ( ...given

**in**the dissipative setting.

**In**this setting we cannot use the dissipative version of Mourre’s commutators ...as

**in**[AK07] ...a ...

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### Resonant eigenstates in quantum chaotic scattering

**scattering**systems. We are particularly interested

**in**open maps admitting a fractal ...appearing

**in**the Fractal Weyl law for the density of resonances; we show that this exponent is not ...

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### Fractal Weyl laws in discrete models of chaotic scattering

**SCATTERING**ST´ EPHANE NONNENMACHER AND MACIEJ ZWORSKI ...quantum

**chaotic**

**scattering**, namely quantized open baker’s ...resonances

**in**the

**semiclassical**...expected

**in**the ...

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### An inverse scattering problem for the Schrödinger equation in a semiclassical process.

**in**{x ∈ IR n : V (x) ≤ ...the

**scattering**amplitude remains unchanged up to O(h ∞ ...the

**resolvent**R(λ + i0, h) due to resonances converging exponentially to the real ...λ.

**In**[16], Yajima ...

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### SEMI-CLASSICAL RESOLVENT ESTIMATES FOR SHORT-RANGE L ∞ POTENTIALS

**resolvent**

**estimates**and resonance free regions for

**semiclassical**Schr¨ odinger operators with bounded potentials, Pure and Applied Analysis, to ...Shapiro,

**Semiclassical**

**resolvent**...

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### Semiclassical scattering amplitude at the maximum point of the potential

**scattering**amplitude for Schr¨ odinger operators at a critical energy level, which is a unique non-degenerate maximum of the ...a

**semiclassical**expansion of the

**scattering**amplitude and compute ...

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### Analytic Continuation and Semiclassical Resolvent Estimates on Asymptotically Hyperbolic Spaces

**semiclassical**-conormal to the diagonal at h = ...elliptic

**in**the usual sense, so it behaves as a

**semiclassical**pseudodifferential operator of order −∞ for our purposes),

**in**order to ...

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### Semiclassical resolvent estimates for Holder potentials

**resolvent**of ...as

**in**the case when n ≡ 1, which

**in**turn is well-known ...Therefore,

**in**this case the low-frequency analysis can be carried out

**in**precisely the same way as ...

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### Tunnel effect for semiclassical random walks

**in**the present setting, proving pointwise convergence (h being fixed) of t n h (x, dy) towards the invariant measure is an easy consequence of some general theorem (see [8], Theorem 2, ...convergence ...

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### Semiclassical dynamics of strongly driven systems

**in**the region of interfer- ence stabilization, gives way to a decreasing g as the ampli- tude of electron oscillations

**in**the external field approaches the characteristic size n 2 of the Kepler ...

5

### Optical Scar in a chaotic fibre

**in**the

**chaotic**billiard are deduced from the NF and FF ...observed

**in**an optical ...modes

**in**our multimode structure, we have investi- gated the influence of a localized gain area ...

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### Semiclassical approach to quantum spin ice

**semiclassical**description that accu- rately captures the properties of quantum spin ice at large length scales and allows for a systematic, perturbative expan- sion, which

**in**principle can be truncated at ...

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### Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials

**in**[16, 27, 8, 9, 18, 34, 35, 38] where the case of slowly varying potentials V (x) is ...view.

**In**fact, our approach is similar to the one given

**in**[18], which derives an analogous result for ...

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### Nonlinear dynamics of semiclassical coherent states in periodic potentials

**in**the derivation of ...stated

**in**dimension d = 1.

**In**all of these situations, the joint effects of nonlinearity, periodicity and dispersion (or, quantum pressure), can lead to the ...

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### Semiclassical analysis of high harmonic generation in bulk crystals

**in**the perturbative realm, and the major outcome of such interactions is the parametric conversion of a few pump laser photons to a single photon of higher energy, ...operates

**in**a highly ...

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