Related papers: Reflections on Virasoro circuit complexity and Ber…
The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct…
Phases arising from cyclic processes are fundamental in physics, bridging quantum and classical domains and providing deeper insights into the topology and dynamics of physical systems. This study investigates the accumulation of a…
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…
Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key…
For a time-dependent $\tau$-periodic harmonic oscillator of two linearly independent homogeneous solutions of classical equation of motion which are bounded all over the time (stable), it is shown, there is a representation of states cyclic…
One of the fundamental results of semiclassical theory is the existence of trace formulae showing how spectra of quantum mechanical systems emerge from massive interference among amplitudes related with time-periodic structures of the…
We consider in sufficient detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties…
Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations…
We consider the scattering of an atom by a sequence of two near-resonant standing light waves each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves and within the rotating…
We present an ab-initio real-time-based computational approach to study nonlinear optical properties in condensed matter systems that is especially suitable for crystalline solids and periodic nanostructures. The equations of motion and the…
Geometrical Berry phase is recognized as having profound implications for the properties of electronic systems. Over the last decade, Berry phase has been essential to our understanding of new materials, including graphene and topological…
The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…
In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations…
We study the quantum propagator in the semiclassical limit with hard-wall potentials. We show that, upon each reflection by the hard wall, a Berry phase $\pi$ is accumulated and leads to interferences between different classical…
We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how…
The dynamics of a molecule in a magnetic field is significantly different form its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of…
We expect black hole microstates to differ in their chaotic properties from states associated with other geometries. For supersymmetric black holes, ordinary level statistics cannot diagnose this distinction, since their energy levels are…
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…
We present both the gauge theoretic description and the numerical calculations of the Berry phases with the real eigenstates, involving one with a many-body system as a background and the other with no such background. We demonstrate that…
We establish an exact analytical relation between Zitterbewegung dynamics and the band geometry in two-dimensional Dirac systems. By identifying a time-independent antisymmetric observable-the \textit{areal rate of Zitterbewegung}-we show…