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The relationship of local ordering and long-range order is studied for quasicrystalline tilings of plane and space. Two versions of the concept of local rules are introduced: strong and weak. Necessary conditions of the existence of strong local rules are found. They are mainly reduced to the constraints for irrational numbers related to… (More)

- Michael Lashkevich, Yaroslav Pugai, L. D. Landau
- 2008

A free field representation for the type I vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to expresses correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a nonlocal insertion. This new… (More)

- Vladimir N. Gribov, L. D. Landau
- 1994

We define a model of quantum computation with local fermionic modes (LFMs) — sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the… (More)

The dynamics of creation, annihilation, and transformation of topological defects in a closed system with a vector-type order parameter is studied both theoretically and experimentally. The particular case of a drop of a nematic with varying boundary conditions is considered. In the theoretical part, the concept of a continuously defined topological… (More)

- R. M. Kiehn, Lev Landau
- 2004

- G E Volovik, L D Landau
- 2008

Superconducting states with different internal topology are discussed for the layered high-T c materials. If the time inversion symmetry is broken, the superconductivity is determined not only by the symmetry of the superconducting state, but also by the topology of the ground state. The latter is determined the integer-valued momentum-space topological… (More)

The continuous spectrum and soliton solutions for the Boussinesq equation are investigated using the ¯ ∂-dressing method. Solitons demonstrate quite extraordinary behavior; they may decay or form a singularity in a finite time. Formation of singularity (collapse of solitons) for the Boussinesq equation was discovered several years ago. Systematic study of… (More)

In this talk we solve continuum and discrete elasticity problems in infinite domains by introducing exact artificial boundary conditions (ABCs) that can be applied at a planar interface below which there are no forces. The problem domain is assumed to be composed of a large regular domain, which can be handled analytically, and a small irregular region,… (More)

- G E Volovik, L D Landau
- 2003

The problem of cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, the vacuum energy is important for the Universe even in the absence of gravity , i.e. in the case when the Newton constant G is exactly zero, G = 0. We discuss the response of the vacuum energy to the perturbations of the quantum… (More)