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Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many...
I discuss the progress in the use of analytic techniques for low energy QCD, in particular as applied to kaon physics. These methods are becoming increasingly powerful and we have gained a good deal o...
We study (by an exact numerical scheme) the single-particle density matrix of ~103 ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to th...
Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable superfluid and insulating ground states with rich and nontrivial phase diagram. The structure of the grou...
We study properties of the supersolid phase observed for hard-core bosons on the triangular lattice near half-integer filling factor, and the phase diagram of the system at finite temperature. We find...
We study on-site occupation number fluctuations in a system of interacting bosons in an optical lattice. The ground-state distribution is obtained analytically in the limiting cases of strong and weak...
We analyze the interference pattern produced by ultracold atoms released from an optical lattice, commonly interpreted as the momentum distributions of the trapped quantum gas. We show that for finite...
We reveal a generic mechanism of generating sign-alternating intersite interactions mediated by strongly correlated lattice bosons. The ground-state phase diagram of the two-component hard-core Bose–H...
We construct a mapping between the two-dimensional toric code model in external magnetic fields, hz and hx, and the three-dimensional classical Ising system with plaquette interactions, which is equiv...
Phase transitions waves in atomic chains with double-well potential play a fundamental role in materials science, but very little is known about their mathematical properties. In particular, the only ...
We classify geometric blocks that serve as spin carriers into simple blocks and compound blocks by their topologic connectivity, define their fractal dimensions and describe the relevant transformatio...
We recently put forth a new fundamental lattice Hamiltonian based on an underlying picture of electrons and deuterons as elementary Dirac particles. Within this model there appears a term in which lat...
Abstract: Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$...
Abstract: In this paper we investigate anisotropic Union Jack lattice Ising model system in terms of the spontaneous magnetisation. Identification of disagreements in the theories published by Wu and ...
Direct Scaling Analysis of localization in disordered systems. II. Multi-particle lattice systems.

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