Generic solutions for some integrable lattice equations

We derive the expressions for $\psi$-functions and generic solutions of lattice principal chiral equations, lattice KP hierarchy and hierarchy including lattice N-wave type equations. $\tau$-function of $n$ free fermions plays fundamental role in this context. Miwa's coordinates in our case appear as the lattice parameters.Comment: The text of the talk at NEEDS-93 conference, Gallipoli, Italy, September-93, LaTeX, 8 pages. Several typos and minor errors are correcte

Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies

We discuss commuting flows and conservation laws for Lax hierarchies on noncommutative spaces in the framework of the Sato theory. On commutative spaces, the Sato theory has revealed essential aspects of the integrability for wide class of soliton equations which are derived from the Lax hierarchies in terms of pseudo-differential operators. Noncommutative extension of the Sato theory has been already studied by the author and Kouichi Toda, and the existence of various noncommutative Lax hierarchies are guaranteed. In the present paper, we present conservation laws for the noncommutative Lax hierarchies with both space-space and space-time noncommutativities and prove the existence of infinite number of conserved densities. We also give the explicit representations of them in terms of Lax operators. Our results include noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera, modified KdV equations and so on.Comment: 22 pages, LaTeX, v2: typos corrected, references added, version to appear in JM

Quantum states and linear response in dc and electromagnetic fields for charge current and spin polarization of electrons at Bi/Si interface with giant spin-orbit coupling

An expansion of the nearly free-electron model constructed by Frantzeskakis, Pons and Grioni [Phys. Rev. B {\bf 82}, 085440 (2010)] describing quantum states at Bi/Si(111) interface with giant spin-orbit coupling is developed and applied for the band structure and spin polarization calculation, as well as for the linear response analysis for charge current and induced spin caused by dc field and by electromagnetic radiation. It is found that the large spin-orbit coupling in this system may allow resolving the spin-dependent properties even at room temperature and at realistic collision rate. The geometry of the atomic lattice combined with spin-orbit coupling leads to an anisotropic response both for current and spin components related to the orientation of the external field. The in-plane dc electric field produces only the in-plane components of spin in the sample while both the in-plane and out-of-plane spin components can be excited by normally propagating electromagnetic wave with different polarizations.Comment: 10 pages, 9 figure

Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

The energy spectrum of spin-orbit coupled states of individual sub-surface boron acceptor dopants in silicon have been investigated using scanning tunneling spectroscopy (STS) at cryogenic temperatures. The spatially resolved tunnel spectra show two resonances which we ascribe to the heavy- and light-hole Kramers doublets. This type of broken degeneracy has recently been argued to be advantageous for the lifetime of acceptor-based qubits [Phys. Rev. B 88 064308 (2013)]. The depth dependent energy splitting between the heavy- and light-hole Kramers doublets is consistent with tight binding calculations, and is in excess of 1 meV for all acceptors within the experimentally accessible depth range (< 2 nm from the surface). These results will aid the development of tunable acceptor-based qubits in silicon with long coherence times and the possibility for electrical manipulation

Functional Tetrahedron Equation

We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a very general "block-matrix model" together with its algebro-geometric solutions, study its various particular cases, and also present a remarkably simple scheme of quantization for one of those cases.Comment: LaTeX, 16 page

Form factors of descendant operators: Free field construction and reflection relations

The free field representation for form factors in the sinh-Gordon model and the sine-Gordon model in the breather sector is modified to describe the form factors of descendant operators, which are obtained from the exponential ones, \e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra associated to the field $\phi(x)$. As a check of the validity of the construction we count the numbers of operators defined by the form factors at each level in each chiral sector. Another check is related to the so called reflection relations, which identify in the breather sector the descendants of the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi} for generic values of $\alpha$. We prove the operators defined by the obtained families of form factors to satisfy such reflection relations. A generalization of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor corrections; v4,v5: misprints corrected; v6: minor mistake correcte

Short-distance thermal correlations in the XXZ chain

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $- 1 < \Delta < 1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.Comment: 25 pages, 5 colored figure