Related papers: Relation between the Berry phase in quantum hermit…
Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry's transitionless driving algorithm or on dynamical invariants. We work out the basic…
Berry phases have long been known to significantly alter the properties of periodic systems, resulting in anomalous terms in the semiclassical equations of motion describing wave-packet dynamics. In non-Hermitian systems, generalizations of…
We develop a rigorous and highly accurate technique for calculation of the Berry phase in systems with a quadratic Hamiltonian within the context of the Kitaev honeycomb lattice model. The method is based on the recently found solution of…
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…
In Phys. Rev. Lett. {\bf 66}, 847 (1991), T. B. Kepler and M. L. Kagan derived a geometric phase shift in dissipative limit cycle evolution. This effect was considered as an extension of the geometric phase in classical mechanics. We show…
We have developed an adiabatic Abelian geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase-qubit systems. The fidelity of the designed quantum gate was…
A precise definition of an adiabaticity parameter $\nu$ of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator…
Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation.…
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 $T\gg1$ is…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
We study QED$_4$ in the adiabatic approximation, incorporating global topological effects associated with the $U(1)$ Berry connection. The Berry phase accumulated by the fermionic vacuum is given by $\Delta \alpha = \oint_{\mathcal{C}}…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
Quantum computing in terms of geometric phases, i.e. Berry or Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its implementation based on Zeeman coupling with a rotating field and isotropic Heisenberg interaction,…
It is shown that the non-adiabatic Hannay's angle of an integrable non-degenerate classical hamiltonian dynamical system may be related to the Aharonov-Anandan phase it develops when it is looked mathematically as a quantum dynamical…
We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schr\"{o}dinger equation, since the…
The Berry phase is analyzed for Weyl and Dirac fermions in a phase space representation of the worldline formalism. Kinetic theories are constructed for both at a classical level. Whereas the Weyl fermion case reduces in dimension,…
Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection…
We study the connection between Berry phases and quantum phase transitions of generic quantum many-body systems. Consider sequences of Berry phases associated to sequences of loops in the parameter space whose limit is a point. If the…
Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown…
The study of wavepacket revivals is extended to the case of Hamiltonians which are made time-dependent through the adiabatic cycling of some parameters. It is shown that the quantal geometric phase (Berry's phase) causes the revived packet…