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Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our…
With the recent production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models for…
Based on the quasi-particle description of the QCD medium at finite temperature and density we formulate the phenomenological model for the equation of state that exhibits crossover or the first order deconfinement phase transition. The…
Strongly correlated materials exhibit exotic electronic states arising from the strong correlation between electrons. Dimensionality provides a tuning knob because thinning down to atomic thickness reduces screening effects and enhances…
We explore in detail the structural, mechanical and thermodynamic properties of a coarse-grained model of DNA similar to that introduced in Thomas E. Ouldridge, Ard A. Louis, Jonathan P.K. Doye, Phys. Rev. Lett. 104 178101 (2010). Effective…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer…
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
Field induced assembly of reconfigurable structures with complex hierarchical configurations has recently become an area of intense research with the promise for exciting applications in programmable self-assembly and nano/microstructure…
We have previously used inverse statistical-mechanical methods to optimize isotropic pair interactions with multiple extrema to yield low-coordinated crystal classical ground states (e.g., honeycomb and diamond structures) in d-dimensional…
We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied it reproduces many characteristic phenomena of liquids, glasses and colloidal systems such as ideal…
We study the structural and thermodynamic properties of patchy particle liquids, with a special focus on the role of "color", i.e. specific interactions between individual patches. A possible experimental realization of such "chromatic"…
Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these…
The paradigm of electrons interacting with a periodic lattice potential is central to solid-state physics. Semiconductor heterostructures and ultracold neutral atomic lattices capture many of the essential properties of 1D electronic…
We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear…
Fabrication of DNA nanostructures primarily follows two fundamental rules. First, DNA oligonucleotides mutually combine by Watson-Crick base pairing rules between complementary base sequences. Second, the geometrical compatibility of the…
We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, crystal, in characteristic relationship to each other. As the parameters of the model are varied one obtains characteristic patterns of phase…
We study Ising systems of spins with dipolar interactions. We find a simple approximate relation for the interaction energy between pairs of parallel lattice columns of spins running along the Ising spin direction. This relation provides…
We investigate the quenching process in lattice systems with short range interaction and several crystalline states as ground states. We consider in particular the following systems on square lattice: - hard particle (exclusion) model; - q…
The design of large-scale colloidal quantum dots (QDs) assemblies and the investigation of their interaction with their close environment are of great interest for improving QD-based optoelectronic devices' performances. Understanding the…