Related papers: Quantum transfer operators and quantum scattering
Consider in $L^2 (\R^l)$ the operator family $H(\epsilon):=P_0(\hbar,\omega)+\epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $\om$, $Q_0$ a bounded pseudodifferential operator with symbol…
We develop a quasi-classical theory of high harmonic generation in semiconductors based on an interband current that has been transformed from Bloch to Wannier basis. The Wannier quasi-classical approach reveals a complete picture of the…
Using an abstract notion of semiclassical quantization for self-adjoint operators, we prove that the joint spectrum of a collection of commuting semiclassical self-adjoint operators converges to the classical spectrum given by the joint…
A canonical quantization procedure is applied to elastic waves interacting with pinned dislocation segments via the Peach-Koehler force. The interaction Hamiltonian, derived from an action principle that classically generates the…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
Let $M$ be a scattering manifold, i.e., a Riemannian manifold with asymptotically conic structure, and let $H$ be a Schr\"odinger operator on $M$. We can construct a natural time-dependent scattering theory for $H$ with a suitable reference…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104…
We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form $H=\d\G(\omega)+ V$ acting on the bosonic Fock space $\G(\ch)$, where $\omega$ is a massive…
Hamilton-Jacobi theory is a fundamental subject of classical mechanics and has also an important role in the development of quantum mechanics. Its conceptual framework results from the advantages of transformation theory and, for this…
Oscillation theory locates the spectrum of a differential equation by counting the zeros of its solutions. We present a version of this theory for canonical systems $Ju'=-zHu$ and then use it to discuss semibounded operators from this point…
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate…
A consistent semiquantitative theoretical analysis of electronic Raman scattering from many-electron quantum dots under resonance excitation conditions has been performed. The theory is based on random-phase-approximation-like wave…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
This is the third paper in a series analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix, $S_h(E)$, for…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction potential, small-data solutions obey dispersion bounds and…
Designing a good transfer channel for arbitrary quantum states in spin chains implies optimizing a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles…