Berry's Phase in the Presence of a Dissipative Medium

Abstract

We consider the spin 1/2 model coupled to a slowly varying magnetic field in the presence of a weak damping represented by a Lindblad-form operators. We show that Berry's geometrical phase remains unaltered by the two dissipation mechanism considered. Dissipation effects are twofold: a shrinking in the modulus of the Bloch's vector, which characterizes coherence loss and a time dependent (dissipation related) precession angle. We show that the line broadening of the Fourier transformation of the components of magnetization is only due to the presence of dissipation.

19 pages, 2 figures

References in corpus (2)

• Non-Abelian Boltzmann Equation for Mixing and Decoherence
• Berry's Phase in the Presence of a Stochastically Evolving Environment: A Geometric Mechanism for Energy-Level Broadening

Cited by in corpus (23)

• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• Geometric phase in open systems
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Geometric phase distributions for open quantum systems
• Entanglement, Bell Inequalities and Decoherence in Particle Physics
• Adiabatic Approximation for weakly open systems
• Geometric phase for open quantum systems and stochastic unravellings
• Geometric phase in open systems: beyond the Markov approximation and weak coupling limit
• Geometric phases induced in auxiliary qubits by many-body systems near its critical points
• Geometric phase in dephasing systems
• Temperature effects on mixed state geometric phase
• Geometric phase for an adiabatically evolving open quantum system
• Dynamical invariants and nonadiabatic geometric phases in open quantum systems
• Uhlmann's geometric phase in presence of isotropic decoherence
• Decoherence-induced geometric phase in a multilevel atomic system
• Topological phase structure of entangled qudits
• Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach
• Entanglement dynamics via geometric phases in quantum spin chains
• Imaginary Phases in Two-Level Model with Spontaneous Decay
• A general treatment of geometric phases and dynamical invariants
• Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate Systems
• Quantum trajectory approach to the geometric phase: open bipartite systems
• Temperature effects on quantum cloning of states and entanglement