Related papers: Compressible $\nu=\frac{1}{2}$ state in a finite s…
Using the reduced formulation of large-N Quantum Field Theories we study strings in space-time dimensions higher than one. Some preliminary results concerning the possible string susceptibilities and general properties of the model are…
It is shown that conclusions regarding the statistical nature of multifragmentation, drawn by Botvina and Gross from experimental data, are unfounded. Imperfections of the experimental apparatus cannot restore information, once destroyed by…
We investigate the entanglement entropy in quantum states featuring repeated sequential excitations of unit patterns in momentum space. In the scaling limit, each unit pattern contributes independently and universally to the entanglement…
We show that previous correspondence between some (integrable) statistical field theory quantities and periods of $SU(2)$ $\mathcal{N}=2$ deformed gauge theory still holds if we add $N_f=1,2$ flavours of matter. Moreover, the correspondence…
In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result…
Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…
For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in…
Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
We present recommendations to improve reproducibility and replicability in condensed matter physics. This area of physics has consistently produced both fundamental insights into the workings of matter and transformative inventions. Our…
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems.
We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their…
We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary…
Quantum Gaussian states on Bosonic Fock spaces are quantum versions of Gaussian distributions. In this paper, we explore infinite mode quantum Gaussian states. We extend many of the results of Parthasarathy in \cite{Par10} and \cite{Par13}…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy…
We say that two (or more) state assignments for one and the same quantum system are compatible if they could represent the assignments of observers with differing information about the system. A criterion for compatibility was proposed in…
We study the typical behavior of the size of the ratio set $A/A$ for a random subset $A\subset \{1,\dots , n\}$. For example, we prove that $|A/A|\sim \frac{2\text{Li}_2(3/4)}{\pi^2}n^2 $ for almost all subsets $A \subset\{1,\dots ,n\}$. We…
By using extended bosonic coherent states, a new technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in literature. Finite-size…
This work provides a mathematical derivation of a quasi-stationary model for multimode parametric down-conversion, which was presented in [Gatti et al., Sci. Rep. 13, 16786] with heuristic arguments. The model is here derived from the 3D+1…