Related papers: Recent Results on Non--Adiabatic Transitions in Qu…
We propose a new analytical potential function to model proton transfer in the adenine-thymine base pair and develop a non-adiabatic quantum mechanical framework to calculate genetic mutation probabilities. This potential has been used to…
Shortcuts to adiabaticity are alternative fast processes which reproduce the same final state as the adiabatic process in a finite or even shorter time, which have been extended from Hermitian systems to non-Hermitian systems in recent…
The use of the adiabatic approximation in practical applications, as in adiabatic quantum computation, demands an assessment of the errors made in finite-time evolutions. Aiming at such scenarios, we derive bounds relating error and…
A new approach to the path integral over fermionic fields, based on the extension of a reformulation of the adiabatic approximation to some quantum mechanical systems, is presented. A novel non-analytic contribution to the efective…
Quantum systems with chaotic classical counterparts cannot be treated by perturbative techniques or any kind of adiabatic approximations. This is so, in spite of the quantum suppression of classical chaos. We explicitly calculate the…
A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly…
We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to…
An asymptotic approach for a Schroedinger type equation with non selfadjoint Hamiltonian of a special type in the case of two close degeneracy (turning) points is developed. Both real and complex degeneracy points are treated by a method of…
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate…
We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion…
We report the potential energy curve, the diagonal Born-Oppenheimer, non-adiabatic mass, relativistic, and leading-order QED corrections for the ground electronic state of the helium dimer cation; the higher-order QED and finite-nuclear…
In these lecture notes, we review the adiabatic theorem in quantum mechanics, focusing on a recent extension to many-body systems. The role of locality is emphasized and the relation to the quasi-adiabatic flow discussed. An important…
Far-off-resonant pulsed laser fields produce negligible excitation between two atomic states but may induce considerable phase shifts. The acquired phases are usually calculated by using the adiabatic-elimination approximation. We analyze…
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and…
We consider quantum dynamics for which the strict adiabatic approximation fails but which do not escape too far from the adiabatic limit. To treat these systems we introduce a generalisation of the time dependent wave operator theory which…
Quantum adiabatic processes -that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian- are very useful to prepare and manipulate states, but take typically a long time. This is often problematic…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate…
We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated…
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric…