相关论文: The non-adiabatic classical geometric phase and it…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve…
We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A…
For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and…
We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick under certain fixed…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…
The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the…
We present an approach for carrying out non-adiabatic molecular dynamics simulations of systems in which non-adiabatic transitions arise from the coupling between the classical atomic motions and a quasi-continuum of electronic quantum…
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We…
A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman-von Neumann formulation of classical mechanics. This classical representation is characterized by the vanishing of the…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
Motivated for the fault tolerant quantum computation, quantum gate by adiabatic geometric phase shift is extensively investigated. In this paper, we demonstrate the nonadiabatic scheme for the geometric phase shift and conditional geometric…
We consider a periodically driven quantum system described by a Hamiltonian which is the product of a slowly varying Hermitian operator $V\left(\boldsymbol{\lambda}\left(t\right)\right)$ and a dimensionless periodic function with zero…
We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for…
It is shown that geometric phase in non-relativistic quantum mechanics is not Galilean invariant.
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…