相关论文: A non-linear adiabatic theorem for the one-dimensi…
We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fr\"ohlich Hamiltonian with large coupling…
We review recent results concerning the exponential behaviour of transition probabilities across a gap in the adiabatic limit of the time-dependent Schr\"odinger equation. They range from an exponential estimate in quite general situations…
We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schroedinger equations in which either the nonlinear coupling constant or, equivalently, the…
We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest…
Motivated by a problem of one mode approximation for a non-linear evolution with charge accumulation in potential wells, we consider a general linear adiabatic evolution problem for a semi-classical Schr\"odinger operator with a time…
The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the…
We consider the cubic nonlinear Schrodinger equation with a potential in one space dimension. Under the assumptions that the potential is generic, sufficiently localized, and does not have bound states, we obtain the long time asymptotic…
In this paper the one-dimensional nonparaxial nonlinear Schr\"odinger equation is considered. This was proposed as an alternative to the classical nonlinear Schr\"odinger equation in those situations where the assumption of paraxiality may…
We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the…
We formulate an adiabatic approximation for the imaginary-time Schroedinger equation. The obtained adiabatic condition consists of two inequalities, one of which coincides with the conventional adiabatic condition for the real-time…
We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the…
We derive an adiabatic theory for a stochastic differential equation, $ \varepsilon\, \mathrm{d} X(s) = L_1(s) X(s)\, \mathrm{d} s + \sqrt{\varepsilon} L_2(s) X(s) \, \mathrm{d} B_s, $ under a condition that instantaneous stationary states…
We establish adiabatic theorems with and without spectral gap condition for general -- typically dissipative -- linear operators $A(t): D(A(t)) \subset X \to X$ with time-dependent domains $D(A(t))$ in some Banach space $X$. In these…
We prove an adiabatic theorem that applies at timescales short of the typical adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturbation. We directly characterize cross-subspace effects of…
Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation.…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
Avoided crossings of level pairs with opposite slopes can form potential energy curves for the external degree of freedom of quantum particles. We investigate nonadiabatic decay of metastable states on such avoided crossings (MSACs) using…
In this paper, three plausible axioms together with two definitions are employed to build an axiomatic framework, and then with the help of the Dirac formalism, it is demonstrated that the time-dependent Schr\"odinger wave equation is no…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
In this paper we consider the nonlinear one-dimensional time-dependent Schroedinger equation with a periodic potential and a local perturbation. In the limit of large periodic potential the time behavior of the wavefunction can be…