Geometric phase of a bipartite system with Dzyaloshinski-Moriya interaction

The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously, and can also cause sudden change of the Berry phase for some weak magnetic field cases.     

Berry phase and shot noise for spin-polarized and entangled electrons

Shot noise for entangled and spin-polarized states in a four-probe geometric setup has been studied by adding two rotating magnetic fields in an incoming channel. Our results show that the noise power oscillates as the magnetic fields vary. The singlet, entangled triplet and polarized states can be distinguished by adjusting the magnetic fields. The Berry phase can be derived by measuring the shot noise power.     

Berry phase in superconducting charge qubits interacting with a cavity field

We propose a method for analyzing Berry phase for a multi-qubit system of superconducting charge qubits interacting with a microwave field. By suitably choosing the system parameters and precisely controlling the dynamics, novel connection found between the Berry phase and entanglement creations.     

Berry phase in a bipartite system with general subsystem–subsystem couplings

The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem. The results show that as the coupling constants tend to infinity all geometric phases go to zero, this confirms the prediction given by us previously [X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92 (2004) 150406] for bipartite systems with a specific subsystem–subsystem coupling.     

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

On spin evolution in a time-dependent magnetic field: Post-adiabatic corrections and geometric phases

We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the usual adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.     

Berry’s phase for a spin 1/2 particle in the presence of topological defects

The relativistic quantum dynamics of a spinorial quantum particle in the presence of a chiral conical background is investigated. We study the gravitational Berry geometric quantum phase acquired by a spin 1/2 particle in the chiral cosmic string spacetime. We obtain the result that this phase depends on the global features of this spacetime. We also consider the case that a string possesses an internal magnetic flux and obtain the geometric quantum phase in this case. The spacetime of multiple chiral cosmic strings is considered and the relativistic Berry quantum phase is also obtained.     

Singularities of Berry connections inhibit the accuracy of the adiabatic approximation

Adiabatic approximation for quantum evolution is investigated addressing its dependence on the Berry connections that are functions of a slowly-varying parameter R  . When the Berry connections have singularities of type 1/Rσ$1/R^{\sigma }$ with σ<1$\sigma <1$, the adiabatic fidelity converges to unit according to a power-law; When the singularity index σ becomes larger than one, adiabatic approximation breaks down. Two-level models are used to substantiate our theory.     

Berry phase and quantum criticality in Yang-Baxter systems

Spin interaction Hamiltonians are obtained from the unitary Yang-Baxter -matrix. Based on which, we study Berry phase and quantum criticality in the Yang-Baxter systems.     

Phase space scars and quantum billiards

A semiclassical expression is derived for the spectral Wigner function of ergodic billiards in terms of a sum over contributions from classical periodic orbits. It represents a generalization of a similar formula by Berry, which does not immediately apply to billiard systems. These results are a natural generalization of Gutzwiller's trace formula for the density of states. Our theory clarifies the origin of scars in the eigenfunctions of billiard systems. However, in its present form, it is unable to predict what states will be dominated by individual periodic orbits. Finally, we compare some of the predictions of our theory with numerical results from the stadium. Within the limitations of numerical resolution, we find agreement between the two.     

Spin-orbit berry phase in a quantum loop

We have found a manifestation of spin-orbit Berry phase in the conductance of a mesoscopic loop with Rashba spin-orbit coupling placed in an external magnetic field perpendicular to the loop plane. In detail, the transmission probabilities for a straight quantum wire and for a quantum loop made of the same wire have been calculated and compared with each other. The difference between them has been investigated and identified with a manifestation of spin-orbit Berry phase. The non-adiabaticity effects at small radii of the loop have been found as well.     

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.     

Geometric phase induced by quantum nonlocality

By analyzing an instructive example, for testing many concepts and approaches in quantum mechanics, of a one-dimensional quantum problem with moving infinite square-well, we define geometric phase of the physical system. We find that there exist three dynamical phases from the energy, the momentum and local change in spatial boundary condition respectively, which is different from the conventional computation of geometric phase. The results show that the geometric phase can fully describe the nonlocal character of quantum behavior.     

Berry phase of many-body system: time-dependent representation method

In this paper, we investigate the Berry phase of many-body system in the time-dependent representation. The formula of Berry phase of many-body system calculating in the time-dependent representation is derived. In this scenario, the Berry phase can be decomposed into two terms, which have different physical meanings respectively. Using these formula, we calculated the Berry phase for the many-spin system coupled by the XXZ exchange interaction. The results show that the Berry phase consists of two contributions which can be interpreted as the flux of a nonquantized monopole and the flux of a Dirac ring respectively.     

Geometric aspects of phonon polarization transport

We study the polarization transport of transverse phonons by adopting a new approach based on the quantum mechanics of spin-orbit interactions. This approach has the advantage of being apt for incorporating fluctuations in the system. The formalism gives rise to Berry effect terms manifested as the Rytov polarization rotation law and the polarization-dependent Hall effect. We derive the distribution of the Rytov rotation angle in the presence of thermal noise and show that the rotation angle is robust against fluctuations.     

Geometric phase and non-stationary state

By investigating a particle motion in a three-dimensional potential barrier with moving boundary, we find that due to an alteration of boundary conditions, the wave function pick up an additional nonlocal phase factor independent on the dynamics of physical system. By compare the nonlocal phase with the geometric phase of the physical system, furthermore, we find that the nonlocal feature of quantum behavior can fully be described by its geometric phase.     

An Approach to Analyse Phase Synchronization in Oscillator Networks with Weak Coupling

We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system.     

Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角

研究了Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角, 通过理论计算得到了其表达式, 并讨论了这二者之间的半经典关系.结果表明, 这一量子Born-Oppenheimer复合系统的Berry相包含两部分: 第一部分与通常几何相的定义相同, 另一项则是由耦合造成的有效规范式引入的.这一量子修正可以被看作一个等效的Aharonov-Bohm效应.不仅如此, 其对应经典系统的Hannay角的定义中也存在类似的现象. 由此可见, 这一复合系统的Berry相与Hannay角之间也存在半经典关系, 并与文献[16] 中通常情况下的半经典关系相同.此外, 上述理论也可以运用于解决产生中性原子的人造规范势等物理问题. 关键词： Berry相 Hannay角 量子经典对应 Born-Oppenheimer近似     

Quantum particles from coarse grained classical probabilities in phase space

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.