Related papers: Quantum mechanics in the noncontractible space
We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
We elaborate on the distinction between geometric and dynamical phase in quantum theory and show that the former is intrinsically linked to the quantum mechanical probabilistic structure. In particular, we examine the appearance of the…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum…
We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space.…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
We introduce a pedagogical discussion on Bohmian mechanics and its physical implications in connection with the important role played by the quantum phase in the dynamics of quantum processes. In particular, we focus on phenomena such as…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
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…