On finite-size scaling in the presence of dangerous irrelevant variables

A scaling hypothesis on finite-size scaling in the presence of a dangerous irrelevant variable is formulated for systems with long-range interaction and general geometryL ^d–d× ^d . A characteristic length which obeys a universal finite-size scaling relation is defined. The general conjectures are based on exact results for the mean spherical model with inverse power law interaction.     

How irrelevant operators affect the determination of fractional charge

We show that the inclusion of irrelevant terms in the Hamiltonian describing tunneling between edge states in the fractional quantum Hall effect can lead to a variety of nonperturbative behaviors in intermediate energy regimes and, in particular, affect crucially the determination of charge through shot noise measurements. We show, for instance, that certain combinations of relevant and irrelevant terms can lead to an effective measured charge nue in the strong backscattering limit and an effective measured charge e in the weak backscattering limit, in sharp contrast with standard perturbative expectations. This provides a possible scenario to explain the experimental observations by Comforti et al. [Nature (London) 416, 515 (2002)]], which are so far not understood.     

Luttinger liquids with a source of backscattering: finite size analysis of irrelevant operators and transport properties

We perform a numerical analysis of the low energy spectrum and transport properties of large finite size Luttinger liquids with a single source of backscattering. The renormalization group trajectory from weak to strong coupling is followed in a numerically accurate way. A precise exploration of irrelevant perturbations and their manifestation in transport is carried out by studying the size dependence of the low energy region. We consider the interplay between the two irrelevant operators: particle hopping across the impurity and charge oscillations, investigating their influence on the temperature and frequency dependence of the conductance.     

On spectral properties ofq-oscillator operators

The property of self-adjointness of the operatorQ =a ₊ +a _- in three types ofq-oscillator algebras is considered. Spectral measures and generalized eigenfunctions ofQ are found in the cases when this operator is bounded. Generalized eigenvectors are expressed in terms ofq-Hermite polynomials. If the operatorQ is unbounded, then its closure is not self-adjoint. However, in this case, admits self-adjoint extensions. Deficiency subspaces are one-dimensional. These subspaces are explicitly found.     

On some operators in multichannel scattering

We investigate the strong limit of an operator valued sequence used in other form in the nonrelativistic theory of multichannel scattering, and also some of its consequences.     

On isospectral sets of Jacobi operators

We consider the inverse spectral problem for a class of reflectionless bounded Jacobi operators with empty singularly continuous spectra. Our spectral hypotheses admit countably many accumulation points in the set of eigenvalues as well as in the set of boundary points of intervals of absolutely continuous spectrum. The corresponding isospectral set of Jacobi operators is explicitly determined in terms of Dirichlet-type data.     

On finite approximations of Cp-class operators

It is shown under which conditions $\text{C}$_p-class operators may be approximated in the p-norm by their projections on finite dimensional subspaces.     

关于构造阶梯算符

给出有关构造阶梯算符的定理,提供了构造阶梯算符的一种规范方法。     

On the domains of generalized operators

The domains of generalized operatorsT: _–+ on rigged Hilbert spaces _– H ₊ are investigated. We introduce an equivalence relation for operators with different domains. Arguments are given for taking ₊ to be the weak quasi-completion of _– and for _– to be Mackey quasi-complete. For domains of closed symmetric Hilbert space operators we give a representation for ₊ and provide certain elements in the equivalence class of the corresponding operator.     

On the first-order operators in bimodules

We analyse the structure of the first-order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules, thereby generalizing several proposals.Laboratoire associé au Centre National de la Recherche Scientifique — URA D0063.     

On the relativistic spin projection operators

In the Rarita-Schwinger formalism, the relativistic spin projection operators are discussed with the help of the Pauli-Lubanski four-vector. It is shown that this approach is equivalent to the conventional one, but moreover, it enables one to derive recurrence relations for the spin projection operators. Such relations can be useful in practical applications.     

On Mpc-structures and symplectic Dirac operators

We prove that the kernels of the restrictions of the symplectic Dirac operator and one of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute these kernels explicitly for complex projective spaces and show that the remaining Dirac–Dolbeault operator has infinite dimensional kernels on these finite rank sub-bundles. We construct injections of subgroups of the symplectic group (the pseudo-unitary group and the stabiliser of a Lagrangian subspace) in the $M{p}^c$ group and classify $G$-invariant $M{p}^c$-structures on symplectic manifolds with a $G$-action. We prove a variant of Parthasarathy’s formula for the commutator of two symplectic Dirac-type operators on general symmetric symplectic spaces.     

On the level order for Dirac operators

We start from the Dirac operator for the Coulomb potential and prove within first-order perturbation theory that degenerate levels split in a definite way depending on the sign of the laplacian of the perturbing potential.     

On the representation of linear evolution operators

We give a proof that any two parameter evolution operator may be represented as a Kossakowski's dynamical semigroup in a suitable Banach space.     

On the coherent state representation of linear operators

It is shown that the possibility of representing every operator, acting on a vector space, irreducible under SU(2), in the form f|>G()<| d [1], where {|>} is a set of Bloch (atomic) coherent states, can be generalized to compact semi-simple Lie groups.Supported by the Swiss National Science Foundation.