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We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in…

We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases…

In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to…

The effect of inter-subsystem coupling on the adiabaticity of composite systems and that of its subsystems is investigated. Similar to the adiabatic evolution defined for pure states, non-transitional evolution for mixed states is…

It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy…

We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this…

The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.

Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…

In the quantum-computation scenario, geometric phase-gates are becoming increasingly attractive for their intrinsic fault tolerance to disturbance. With an adiabatic cyclic evolution, Berry phase appears to realize a geometric…

We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersection as well as for an Aharonov-Bohm…

In a recent preprint (cond-mat/9803170), van~Langen, Knops, Paasschens and Beenakker attempt to re-analyze the proposal of Loss, Schoeller and Goldbart (LSG) [Phys. Rev. B~48, 15218 (1993)] concerning Berry phase effects in the…

The unitary operator corresponding to the classical canonical transformation that connects a general closed system to an open system under adiabatic conditions is found. The quantum invariant operator of the adiabatic open system is derived…

In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further…

Beyond the quantum Markov approximation and the weak coupling limit, we present a general theory to calculate the geometric phase for open systems with and without conserved energy. As an example, the geometric phase for a two-level system…

We investigate the geometric phase or Berry phase of adiabatic quantum evolution in the Bose-Einstein condensate (BEC) systems governed by nonlinear Gross-Pitaevskii(GP) equations. We study how this phase is modified by the nonlinearity and…

We have developed an adiabatic Abelian geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase-qubit systems. The fidelity of the designed quantum gate was…

A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.

An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum…

Strong coupling between matter and quantized electromagnetic fields in a cavity has emerged as a possible route toward controlling the phase of matter in the absence of an external drive. We develop a faithful and efficient theoretical…

The effect of inter-subsystem couplings on the Berry phase of a composite system as well as that of its subsystem is investigated in this paper. We analyze two coupled spin-$\frac 1 2 $ particles with one driven by a quantized field as an…