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We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment…
Recent work of Fili and the author examines an ultrametric version of the Mahler measure, denoted $M_\infty(\alpha)$ for an algebraic number $\alpha$. We show that the computation of $M_\infty(\alpha)$ can be reduced to a certain search…
Finite temperature properties of a non-Fermi liquid system is one of the most challenging probelms in current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liquids is in one dimension,…
A general expression for the temperature of a finite-dimensional quantum system is deduced from thermodynamic arguments. At equilibrium, this magnitude coincides with the standard thermodynamic temperature. Furthermore, it is well-defined…
Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent…
In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…
We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding…
A previous analysis of scaling, bounds, and inequalities for the non-interacting functionals of thermal density functional theory is extended to the full interacting functionals. The results are obtained from analysis of the related…
The sine-Gordon model serves as a foundational $1+1$-dimensional quantum field theory with numerous applications in condensed matter physics. Despite its integrability, characterizing its finite-temperature behavior remains a significant…
A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to non-linear static density response functions in quantum many-body systems. Within this framework, explicit expressions…
We investigate the set of invariant idempotent probabilities for countable idempotent iterated function systems (IFS) defined in compact metric spaces. We demonstrate that, with constant weights, there exists a unique invariant idempotent…
We study conformal Ward-Takahashi identities for two-point functions in $d(\geq3)$-dimensional finite-temperature conformal field theory. We first show that the conformal Ward-Takahashi identities can be translated into the intertwining…
In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation values and correlation functions at finite…
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…
We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual…
Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $\alpha$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times…
We investigate a density-functional theory (DFT) approach for an unpolarized trapped dilute Fermi gas in the unitary limit . A reformulation of the recent work of T. Papenbrock [Phys. Rev. A, {\bf 72}, 041602(R) (2005)] in the language of…