Berry phase effect

In the previous section, a new current generation mechanism is presented. It is based on the theoretical observation that loop currents should be generated around spin-vortices as a Berry phase effect. In this section, we present experimental evidence... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

The phase-change rule, also known as the Berry phase [101], the geometric phase effect [102,103] or the molecular Aharonov-Bohm effect [104—106], was used by several authors to verify that two near-by surfaces actually cross, and are not repelled apart. This point is of particular relevance for states of the same symmetry. The total electronic wave function and the total nuclear wave function of both the upper and the lower states change their phases upon being transported in a closed loop around a point of conical intersection. Any one of them may be used in the search for degeneracies. 

Summary. We discuss the concept of the Berry phase in a dissipative system. We show that one can identify a Berry phase in a weakly-dissipative system and find the respective correction to this quantity, induced by the environment. This correction is expressed in terms of the symmetrized noise power and is therefore insensitive to the nature of the noise representing the environment, namely whether it is classical or quantum mechanical. It is only the spectrum of the noise which counts. We analyze a model of a spin-half (qubit) anisotropically coupled to its environment and explicitly show the coincidence between the effect of a quantum environment and a classical one. 

Let us mention that there is a more subtle effect introduced by a dynamical JT effect in the form of a new degree of freedom, the berry phase . This can lead to interference effects, which would constrain the tunneling of charge carriers in a lattice of molecules. This can renormalize the electron-electron interaction and it has been proposed that it could favor electronic pairing and possibly superconductivity [17]. 

Further quantum effect can be observed if the links of the polymer contain a spin S = 1/2, 1, 3/2, 2,. .. along the link direction. This can be taken into account by adding the kinetic action (2.30) a Berry phase. For each link [u (t), it corresponds to the interaction of the particle on the surface of a unit sphere in u space with a... 

Key words Geometric phase effect - Conical intersection - Molecular Aharonov-Bohm effect -Berry s phase... 

Berry s 1984 work led to manifestations of the geometric phase effect being detected outside the area of optical spectroscopy discussed by Longuet-Higgins. Observation of the geometric phase effect in molecular spectroscopy has proved surprisingly difficult. One reason for this difficulty is suggested in Sect. 3. 

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