The calculation of nonadiabatic Berry phases

A countable set of asymptotic space -localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T , where T ≫ 1 is the adiabatic evolution time.A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Hartree type equation. For the solutions constructed, the Berry phases are found in explicit form.

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“…There exists a limit asκ → 0 for every expression obtained, and the limits agree with results of linear quantum theory (see, e.g., [10,12,37]). …”

Section: Resultssupporting

confidence: 81%

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

Litvinets¹,

Шаповалов²,

Trifonov³

2007

J. Phys. A: Math. Theor.

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“…(46) in the Lorenz gauge. The calculations were done on the 12 4 and 4 x 12 3 lattices with periodic boundary conditions using 30 well equilibrated and statistically independent configurations. We used the local over-relaxation algorithm to fix the Lorenz gauge.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We have measured the density ρ in the Lorenz gauge as a function of the bare coupling β = 4/g 2 . The logarithm of ρ versus β on the symmetric 12 4 lattice is shown on the Fig. 1a.…”

Section: Numerical Resultsmentioning

confidence: 99%

The Berry Phase and Monopoles in Non-Abelian Gauge Theories

Gubarev

Захаров

2002

Int. J. Mod. Phys. A

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We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorenz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

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“…За эти годы понятие геометрической фазы (ГФ), или фазы Берри, существенно расширилось и проникло в самые различные разделы физики; см. обзоры [3,4] и популярные статьи [5,6]. С ГФ связаны эффекты Санъяка, Ааронова-Бома, Яна-Теллера, Холла, некоторые особенности спектров молекул и ядер, вихри в сверхтекучем гелии, хиральные аномалии в калибровочных теориях поля.…”

unclassified

Berry geometric phase in oscillatory processes

Klyshko¹

1993

Usp. Fiz. Nauk

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The calculation of nonadiabatic Berry phases

Cited by 69 publications

References 66 publications

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

The Berry Phase and Monopoles in Non-Abelian Gauge Theories

Berry geometric phase in oscillatory processes

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