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A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such…
We explore quantum localization phenomena in a system of two coupled tight-binding chains with incommensurate periods. Employing the inverse participation ratio as a measure of localization, we investigate the effects of geometric…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We extend the superconductor's free energy to include an interaction of the order parameter with the curvature of space-time. This interaction leads to geometry dependent coherence length and Ginzburg-Landau parameter which suggests that…
The influence of gravitational field on entanglement of bipartite states is investigated based on the recent idea of superposition states of gravitational field. Different from earlier considerations, we study the case where the…
In this thesis we investigate some aspects of quantum field theories from a holographic perspective. In the first chapters we examine in detail a one-paremeter family of three-dimensional gauge theories by means of their type IIA gravity…
Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…
We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that…
Position-deformed Heisenberg algebra with maximal length uncertainty has recently been proven to induce strong quantum gravitational fields at the Planck scale (2022 J. Phys. A: Math. Theor.55 105303). In the present study, we use the…
Within the new description of the polarization structure of quantum light (given in Part I) some types of generalized coherent states related to the polarization SU(2) group are examined. With their help we give a quasiclassical description…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
If reality has finite information content, space has finite fidelity. The quantum wave function that encodes spatial relationships may be limited to information that can be transmitted in a "Planck broadcast", with a bandwidth given by the…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth…
The Landau Hamiltonian, describing the behavior of a quantum particle in dimension 2 in a constant magnetic field, is perturbed by a magnetic field with power-like decay at infinity and a similar electric potential. We describe how the…
In this paper, we review two approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of…
A satisfactory theory of quantum gravity will very likely require modification of our classical perception of space-time, perhaps by giving it a 'foamy' structure at scales of order the Planck length. This is expected to modify the…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Quantum coherence could be sustained up to interstellar distances. It is shown that the photon mean free path in certain regions of the electromagnetic spectrum, such as within the radio or x-ray ranges, could allow sustaining of the…