Related papers: Geometric phases without geometry
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase…
We obtain the geometric phase for states of a particle in a spherical infinite potential well with a moving wall in two different cases; First, when the radius of the well increases (or decreases) monotonically. Second, when the radius…
We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of…
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…
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with…
We investigate how low-frequency gravitational waves (LFGWs), originating from distant astrophysical or cosmological sources, can induce purely quantum geometric phases in mesoscopic optomechanical systems. These phases represent subtle…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…
Quantum reactive scattering calculations for the hydrogen exchange reaction H + H$_2$($v=4$, $j=0$) $\to$ H + H$_2$($v'$, $j'$) and its isotopic analogues are reported for ultracold collision energies. Due to the unique properties…
The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a…
Geometric phases play an enormous role in optics and are generally associated with the evolution of light's polarization state on the Poincar\'{e} sphere, or its spin on the sphere of spin directions. Here we put forward a new kind of…
By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz…
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…
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a…
We study the Hessian geometry of toric Gibbons-Hawking metrics and their phase change phenomena via the images of their moment maps.