Related papers: The Geometric Phase in Supersymmetric Quantum Mech…
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.…
Adiabatic time evolution of degenerate eigenstates of a quantum system provides a means for controlling electronic states since mixing between degenerate levels generates a matrix Berry phase. In the presence of spin-orbit coupling in…
We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfine states of the BEC.…
We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a non-trivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that…
Strong coupling between matter and quantized electromagnetic fields in a cavity has emerged as a possible route toward controlling the phase of matter in the absence of an external drive. We develop a faithful and efficient theoretical…
We have discussed a consistency condition of Berry phases defined by a local gauge twist and spatial symmetries of the many body system. It imposes a non trivial gap closing condition under the gauge twist in both finite- and infinite-size…
We propose a pair of the complex Berry curvatures associated with the non-Hermitian Hamiltonian and its Hermitian adjoint to reveal new physics in non-Hermitian systems. We give the complex Berry curvature and Berry phase for the…
Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of…
The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a…
The standard quantum mechanical electronic state calculations for molecules and solids uses the Schroedinger representation where the momentum conjugate to the coordinate $q_r$ is given by $-hbar {partial over {partial q_r}}$. This…
We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
Bose gas on a two-leg ladder exhibits an interesting topological phase. We show the presence of a bosonic symmetry-protected-topological (SPT) phase protected by $Z_2\times Z_2$ symmetry. This symmetry leads to $Z_4$ fractional quantization…
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…
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric…
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity…
Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of 2pi [K. S. Novoselov et al., "Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene", Nature Phys. 2,…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
The phase relation between quantum states represents an essential resource for the storage and processing of quantum information. While quantum phases are commonly controlled dynamically by tuning energetic interactions, utilizing geometric…
We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type, where the time 't' is also an operator. An effective commutative description of the system gives a time dependent…