Related papers: The Geometric Phase in Supersymmetric Quantum Mech…
`Hypergeometric states', which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to…
We study Berry's connection potentials of many-body ground states of spin-one bosons with antiferromagnetic interactions in adiabatically varying magnetic fields. We find that Berry's connection potentials are generally determined by,…
Parametric Hamiltonians often exhibit point-like spectral degeneracies (diabolic points, or conical intersections), which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a…
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…
Non-Hermiticity can lead to the emergence of many intriguing phenomena that are absent in Hermitian systems, enabled by exceptional topological defects, among which Weyl exceptional rings (WER) are particularly interesting. The topology of…
We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a…
We study supersymmetric deformations of N = 4 quantum mechanics with a Kahler target space admitting a holomorphic isometry. We show that the twisted mass deformation generalises to a deformation constructed from matrix-valued functions of…
New results obtained within the recently developed approach to supersymmetric quantum mechanical systems are presented. The method does not suffer from the sign problem in any dimensions and is capable to provide any quantum observable with…
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…
Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming an existence of some adiabatic process which protects quantization of the Berry phase, non trivial Berry phase $\gamma=\pm 2\pi\rho$…
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…
Due to the frequent presence of a Berry phase, in most cases of dynamical Jahn-Teller systems the symmetry of the ground state is the same as that of the electronic state. However, the H x h icosahedral case, relevant for the physics of…
In the quantum-computation scenario, geometric phase-gates are becoming increasingly attractive for their intrinsic fault tolerance to disturbance. With an adiabatic cyclic evolution, Berry phase appears to realize a geometric…
This note addresses the question of the number of normalizable vacuum states in supersymmetric quantum mechanics with sixteen supercharges and arbitrary semi-simple compact gauge group, up to rank three. After evaluating certain contour…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. We…
Classical and quantum aspects of physical systems that can be described by Riemannian non degenerate superspaces are analyzed from the topological and geometrical points of view. For the N=1 case the simplest supermetric introduced in…
Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the…
Quantum oscillations can be used to determine properties of the Fermi surface of metals by varying the magnitude and orientation of an external magnetic field. Topological insulator surface states are an unusual mix of normal and Dirac…
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the…