Related papers: Applications of the Complex Geometric "Phase" for …
When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state's projective Hilbert space. A correction term to this geometric phase in addition to the local…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…
We show the explicit expression of the geometric phase for $n$-partite Gaussian states. In our analysis, the covariance matrix can be obtained as a boundary term of the geometric phase.
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the…
We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the $(t,t')$ Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables…
We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the…
In quantum information science, the phase of a wavefunction plays an important role in encoding information. While most experiments in this field rely on dynamic effects to manipulate this information, an alternative approach is to use…
A periodic perturbation such as a laser field cannot induce transitions between two decoupled states for which the transition matrix element vanishes. We show, however, that if in addition some system parameters are varied adiabatically,…
It is shown how to exactly simulate many-body interactions and multi-qubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a…
Geometric phases in particle diffusion systems, an intriguing aspect enlightened from thermal systems, offer a different understanding beyond traditional Brownian motion and Fick's laws. This concept introduces a phase factor with…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Mesoscopic systems have provided an opportunity to study quantum effects beyond the atomic realm. In these systems quantum coherence prevails over the entire sample. We discuss several novel effects related to persistent currents in open…
We study the hadron-quark phase transition with the finite size effects at finite temperature. For the hadron phase, we adopt a realistic equation of state in the framework of the Brueckner-Hartree-Fock theory including hyperons. The…
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…
The Aharonov-Bohm effect is measured in a four-terminal open ring geometry based on a Ga[Al]As heterostructure. Two quantum dots are embedded in the structure, one in each of the two interfering paths. The number of electrons in the two…
Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…