相关论文: New approach to Fully Nonlinear Adiabatic TWM Theo…
We analyze a quantized pumping in a nonlinear non-Hermitian photonic system with nonadiabatic driving. The photonic system is made of a waveguide array, where the distances between adjacent waveguides are modulated. It is described by the…
The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood…
Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very…
The paper aims at constructing two different solutions to an elliptic system $$ u \cdot \nabla u + (-\Delta)^m u = \lambda F $$ defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers…
Dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, is considered by applying an accurate method for solving nonlinear systems of differential equations. This method is more general than the…
We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the…
In this paper,we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a non degenerate continuous spectrum. A new strategy is initiated by defining a kind of gap, "a virtual gap", for the…
Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on…
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
We clarify that the nonadiabatic scheme based on a parallel extension of the adiabatic scenario cannot realize the desired goal of quantum computation.
Nonlinear $sl(2)$ algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a general context. The linear $sl(2)$-case…
This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first…
Nonlinear diffusion equations of spectral transfer are systematically derived for anisotropic magnetohydrodynamics in the regime of wave turbulence. The background of the analysis is the asymptotic Alfv\'en wave turbulence equations from…
In this work we derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways, it is applicable both in the adiabatic and in the non-adiabatic regimes and it…
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…
The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wavefunction and a recently proposed quantum hydrodynamical description of its dynamics. An…
Adiabatic topological pumping enables robust transport of energy and information, yet its operational speed is fundamentally constrained by the instantaneous adiabatic condition, which necessitates prohibitively slow parameter variations.…
We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.
There is a close theoretical connection between topological Floquet physics and cavity QED, yet this connection has not been realized experimentally due to complicated cavity QED models that often arise. We propose a simple, experimentally…
The analysis of gravitational wave data may require greater accuracy than is afforded by the adiabatic approximation to the trajectory of and field produced by a particle moving in curved spacetime. Higher accuracy is available with a…