Related papers: The Aharonov-Anandan phase of a classical dynamica…

In the Copenhagen viewpoint, part of the world is quantized and the complementary part remains classical. From a formal dynamic aspect, standard theory is incomplete since it does never account for the so-called 'back-reaction' of quantized…

The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…

In this work, we propose an experimentally feasible nonlinear optical realization of a type of non-integrable phase found in interacting quantum systems at quantum phase transitions. We show that an exotic term in the dynamical equation…

A connection is estabilished between the non-Abelian phases obtained via adiabatic driving and those acquired via a quantum Zeno dynamics induced by repeated projective measurements. In comparison to the adiabatic case, the Zeno dynamics is…

A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation…

The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase…

We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a…

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…

The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.

We present a method for calculating the Aharonov-Anandan phase for time-independent Hamiltonians that avoids the calculation of evolution operators. We compare the generic method used to calculate the Aharonov-Anandan phase with the method…

We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…

We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how it could be implemented with superconducting charge qubits. While it may circumvent many of the drawbacks related to the…

In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic…

Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…

We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…

Accessing the physical mechanisms behind non-Markovian phenomena in open quantum dynamics requires the study of the statistical properties of the joint system-environment dynamics. This is impossible at the level of the reduced dynamics of…

Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. Here, we show that for nonadiabatic dynamics with two…