Related papers: Quantization dimension for self-similar measures o…
Symmetry plays a fundamental role in quantum many-body physics, and a central concept is spontaneous symmetry breaking, which imposes crucial constraints on the possible quantum phases and their transitions. Recent developments have…
We study cold atomic gases in a disorder potential and analyze the correlations between different systems subjected to the same disorder landscape. Such independent copies with the same disorder landscape are known as replicas. While in…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
For a self-similar set in $\mathbb{R}^d$ that is the attractor of an iterated function system that does not verify the weak separation property, Fraser, Henderson, Olson and Robinson showed that its Assouad dimension is at least $1$. In…
We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets, we assume that the sets satisfy certain separation…
The multifractal spectrum of a Borel measure $\mu$ in $\mathbb{R}^n$ is defined as \[ f_\mu(\alpha) = \dim_H {x:\lim_{r\to 0} \frac{\log \mu(B(x,r))}{\log r}=\alpha}. \] For self-similar measures under the open set condition the behavior of…
We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking and superconducting (Cooper pair condensates) phases at large-N. At zero temperature and density, the model can be solved…
We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that, for a given strongly local, regular symmetric…
We explore the relationship between symmetrisation and entanglement through measurements on few-particle systems in a multi-well potential. In particular, considering two or three trapped atoms, we measure and distinguish correlations…
Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern…
We show that if $X$ is a uniformly perfect complete metric space satisfying the finite doubling property, then there exists a fully supported measure with lower regularity dimension as close to the lower dimension of $X$ as we wish.…
Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…
With the example of a Stern-Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse - for example, the singleness (or mutual exclusivity) of…
For a self-affine measure on a Bedford-McMullen carpet we prove that its quantization dimension exists and determine its exact value. Further, we give various sufficient conditions for the corresponding upper and lower quantization…
Until recently, it was an important open problem in Fractal Geometry to determine whether there exists an iterated function system acting on $\mathbb{R}$ with no exact overlaps for which cylinders are super-exponentially close at all small…
Weak measurements performed between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this…
In this paper, we study the statistical mechanics within the polymer quantization framework in the semiclassical regime. We apply a non-canonical transformation to the phase space variables. Then, we use this non-canonical transformation to…
The damage spreading method (DS) provided a useful tool to obtain analytical results of the thermodynamics and stability of the 2D Ising model --amongst many others--, but it suffered both from ambiguities in its results and from large…
We show that any equicontractive, self-similar measure arising from the IFS of contractions $(S_{j})$, with self-similar set $[0,1]$, admits an isolated point in its set of local dimensions provided the images of $S_{j}(0,1)$ (suitably)…