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arXiv:quant-ph/0003049 · Physica A Statistical Mechanics and its Applications

Berry's phase in the presence of a dissipative medium

K.M.Fonseca Romero, A.C.Aguiar Pinto, M. T. Thomaz

Published Apr 1, 2002• 41 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(01)00589-1

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Berry's phase in the presence of a dissipative medium

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We consider the spin 12 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.

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Berry's Phase in the Presence of a Dissipative Medium: Analytical Results

K. M. Fonseca-Romero, A.C. Aguiar Pinto, J. G. Peixoto de Faria +2 more

We consider the well known model of spin 1/2 coupled to a slowly varying magnetic field in the presence of a weak damping represented by a Lindblad-form operator. We show that Berry's geometrical phase remains unaltered by dissipation. A clear and physically appealing interpretation of this dynamics is given in terms of Bloch's vector. Dissipation effects are twofold: a shrinking in the modulus of this vector, which (geometrically) characterizes coherence loss and a time dependent (dissipation related) precession angle. Experimentally accessible effects are calculated.

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We consider the spin 12 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.
We consider the well known model of spin 1/2 coupled to a slowly varying magnetic field in the presence of a weak damping represented by a Lindblad-form operator. We show that Berry's geometrical phase remains unaltered by dissipation. A clear and physically appealing interpretation of this dynamics is given in terms of Bloch's vector. Dissipation effects are twofold: a shrinking in the modulus of this vector, which (geometrically) characterizes coherence loss and a time dependent (dissipation related) precession angle. Experimentally accessible effects are calculated.