Related papers: Statistical Mechanics and Quantum Fields on Fracta…
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
The fractal property stipulates that the same physical laws apply for different scales of a given physics. This property is applied to particles and nuclei, in order to study the possibility to use it to help for determination of unknown…
The fractal character of some quantum properties has been shown for systems described by continuous variables. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing,…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
Simple considerations about the fractal characteristic of the quantum-mechanical path give us the opportunity to derive the quantum black hole entropy in connection with the concept of fractal statistics. We show the geometrical origin of…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of…
We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions.…
This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schr\"{o}dinger Equation and provides insights into its consequences. The study presents a General Solution for…
Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features…
In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated…
The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in…
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular…
Dynamical symmetry breaking in an expanding nuclear system is investigated in semi-classical and quantum framework by employing a collective transport model which is constructed to mimic the collective behavior of expanding systems. It is…