相关论文: Geometric Phases
A teleparallel geometrical description of the nematic phases of liquid crystals is proposed.In the case of the twisted geometry of nematics Cartan torsion is given by a spatial helical form which depends on the twist angle. Geodesics of a…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the…
Some aspects of multidimensional soliton geometry are considered.
In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting scheme was proposed to implement a type of conditional quantum phase gates with built-in fault-tolerant feature via adiabatic evolution of dark eigenstates. In…
We discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa).
We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von…
Geometric quantization procedures go usually through an extension of the original theory (pre-quantization) and a subsequent reduction (selection of the physical states). In this context we describe a full geometrical mechanism which…
Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties…
Some examples and basic properties of ultrametric spaces are briefly discussed.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
We discuss invariants in equivariant birational geometry.
The polarization matrix ($2\times2$) obtained from two component eigen-spinors of spherical harmonics help us to evaluate the differential matrix $N$ of the anisotropic optical medium. The geometric phase is realized through {\it helicity}…
Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated…
Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution…
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…
This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.