相关论文: Perturbed lattice crosses and Heisenberg uniquenes…

Let $\Gamma$ be the hyperbola $\{(x,y)\in\mathbb R^2 : xy=1\}$ and $\Lambda_\beta$ be the lattice-cross defined by $\Lambda_\beta=\left(\mathbb Z\times\{0\}\right)\cup\left(\{0\}\times\beta\mathbb Z\right)$ in $\mathbb R^2,$ where $\beta$…

Given a curve $\Gamma$ and a set $\Lambda$ in the plane, the concept of the Heisenberg uniqueness pair $(\Gamma, \Lambda)$ was first introduced by Hedenmalm and Motes-Rodr\'{\i}gez (Ann. of Math. 173(2),1507-1527, 2011, \cite{HM}) as a…

Let $\Lambda$ be a set of lines in $\mathbb{R}^2$ that intersect at the origin. For $\Gamma\subset\mathbb{R}^2$ a smooth curve, we denote by $\mathcal{A}\mathcal{C}(\Gamma)$ the subset of finite measures on $\Gamma$ that are absolutely…

A Heisenberg uniqueness pair is a pair $\left(\Gamma, \Lambda\right)$, where $\Gamma$ is a curve and $\Lambda$ is a set in $\mathbb R^2$ such that whenever a finite Borel measure $\mu$ having support on $\Gamma$ which is absolutely…

Let $X(\Gamma)$ be the space of all finite Borel measure $\mu$ in $\mathbb R^2$ which is supported on the curve $\Gamma$ and absolutely continuous with respect to the arc length of $\Gamma$. For $\Lambda\subset\mathbb R^2,$ the pair…

We describe a general method for constructing Heisenberg uniqueness pairs $(\Gamma,\Lambda)$ in the euclidean space $\mathbb{R}^{n}$ based on the study of boundary value problems for partial differential equations. As a result, we show, for…

Let $\Gamma$ be a smooth curve or finite disjoint union of smooth curves in the plane and $\Lambda$ be any subset of the plane. Let $\mathcal X(\Gamma)$ be the space of all finite complex-valued Borel measures in the plane which are…

In this paper we study the Heisenberg uniqueness pairs corresponding to finite number of parallel lines $\Gamma$. We give a necessary condition and a sufficient condition for a subset $\Lambda$ of $\R$ so that $(\Gamma,\Lambda)$ becomes a…

Two measurable sets $S, \Lambda \subseteq \mathcal{R}^d$ form a Heisenberg uniqueness pair, if every bounded measure $\mu$ with support in S whose Fourier transform vanishes on {\Lambda} must be zero. We show that a quadratic hypersurface…

The phase transition in frustrated spin systems is a fascinated subject in statistical physics. We show the result obtained by the Wang-Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple…

We discuss on Heisenberg uniqueness pairs for the parabola given by discrete sequences along straight lines. Our method consists in linking the problem at hand with recent uniqueness results for the Fourier transform.

We generalize the study of Heisenberg uniqueness pairs considered in earlier work with Alfonso Montes-Rodriguez. We also find the critical density in the case of one branch of the hyperbola. In the critical case there is non-uniqueness for…

A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic $1 + 1$-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to…

In this paper, we convert the lattice configurations into networks with different modes of links and consider models on networks with arbitrary numbers of interacting particle-pairs. We solve the Heisenberg model by revealing the relation…

(Presented at conference on Fundamental Problems in Physics - UMBC - June 1994) It is shown that among the orthogonal sets of EPR (completely entangled) states there is a unique basis (up to equivalence) that is a also a perfectly resolved…

We obtain new Fourier interpolation and -uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa, and by the second author. We show that the only Schwartz function which, together with its…

The notion of a Heisenberg Uniqueness Pair (HUP) is introduced. This amounts to asking which collections of exponentials are weak-star fundamental in $L^\infty$ on a planar curve. In the case when the curve is a hyperbola, we can give a…

In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods and lattice Ward…

An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact…

We consider a two-dimensional periodic Schr\"odinger operator $H=-\Delta+W$ with $\Gamma$ being the lattice of periods. We investigate the structure of the edges of open gaps in the spectrum of $H$. We show that under arbitrary small…