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Dyck paths are classical Catalan objects. The peak distribution of Dyck paths is an important topic of combinatorics, and further the representation of symmetric groups.
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...
The full Kostant-Toda lattice defined on simple Lie algebras can be viewed as finite version of KP type hierarchies. In this talk I will show you how to explicitly construct (all) rational solutions o...
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological ...
NONPERTURBATIVE METHODS IN KAON PHYSICS (ASIDE FROM THE LATTICE)     Kaon physics  hadron       font style='font-size:12px;'> 2014/12/23
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 study the low temperature dynamics in films made of molecular magnets, i. e. crystals composed of molecules having large electronic spin S in their ground state. The electronic spin dynamics is med...
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...
We consider a three dimensional lattice U(1)×U(1) and [U(1)]N superconductors in the London limit with individually conserved condensates. The U(1)×U(1) problem, generically, has two types of intercom...
We perform a numeric study (Worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two- and three-dimensional optical lattices. At strong enough interactions and low enough tempe...

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