Related papers: Geometric potentials in quantum optics: A semi-cla…
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
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…
We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between…
It has been recently found that the equations of motion of several semiclassical systems must take into account anomalous velocity terms arising from Berry phase contributions. Those terms are for instance responsible for the spin Hall…
A fundamental problem regarding the Dirac quantization of a free particle on an $N-1$ curved hypersurface embedded in $N$($\geq 2$) flat space is the impossibility to give the same form of the curvature-induced quantum potential, the…
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a…
We study the magnetic Bloch oscillations performed by a quantum particle moving in a two-dimensional lattice in the presence of a strong (synthetic) magnetic field and a uniform force. An elementary derivation of the Berry curvature effect…
Geometric phases can manifest when a relativistic quantum particle moves cyclically along a loop in parameter space. The phase can be affected by the presence of a background field and can be accompanied by nontrivial topological features.…
We obtain the geometric phase for states of a particle in a spherical infinite potential well with a moving wall in two different cases; First, when the radius of the well increases (or decreases) monotonically. Second, when the radius…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
When a two-dimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the well-known geometric potential is induced by the kinetic energy operator, in fact…
The conservation of physical quantities under coordinate transformations, known as gauge invariance, has been the foundation of theoretical frameworks in both quantum and classical theory. The finding of gauge-invariant quantities has…
The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
We construct a semiclassical theory for propagation of an optical wavepacket in non-conducting media with periodic structures of dielectric permittivity and magnetic permeability, i.e., non-conducting photonic crystals. We employ a…
The evolution of a quantum system is governed by the associated Hamiltonian. A system defined by a parameter-dependent Hamiltonian acquires a geometric phase when adiabatically evolved. Such an adiabatic evolution of a system having…
We calculate Berry's phase when the driving field, to which a spin-1/2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g., the angular…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
In this work we consider a scale-tensor theory in which the space-time is endowed with a Weyl integrable geometrical structure due to the Palatini variational method. Since the scalar field has a geometrical nature (related to…
We introduce, and propagate wave-packet solutions of, a single qubit system in which geometric gauge forces and phases emerge. We investigate under what conditions non-trivial gauge phenomena arise, and demonstrate how symmetry breaking is…