We employ projection operator techniques in Hilbert space to derive a continuous sequence of effective Hamiltonians which describe the dynamics on successively larger length scales. We show for the case of φ theory that the masses and couplings in these effective Hamiltonians vary in accordance with 1-loop renormalization group equations. This is evidence for an intimate connection between Wils...

Bloch and Okounkov introduced an n-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible ĝl ∞ -modules of level one. These correlation functions have been generalized for irreducible integrable modules of...

In a superlattice containing a finite number of periods, the allowed values of the Bloch wave number form a discrete set, and the dynamics of an electron through k-space under the influence of an external force is necessarily that of a superposition wave packet composed of multiple Bloch waves. The present paper investigates this dynamics for a particularly simple class of “kcompact” wave packe...

By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass. §

Quantizing the motion of particles on a Riemannian manifold in the presence of a magnetic field poses the problems of existence and uniqueness of quantizations. Both of them are considered since the early days of geometric quantization but there is still some structural insight to gain from spectral theory. Following the work of Asch, Over & Seiler (1994) for the 2–torus we describe the relatio...

To enhance the optimization ability of quantumbehaved particle swarm optimization algorithm, some improvement measures are proposed. First, we propose a encoding approach based on qubits described on Bloch sphere. This approach makes each particle contain three groups of Bloch coordinates of qubits, and all three groups of coordinates are regarded as approximate solutions describing optimizatio...

The scientific community is becoming more and more interested in the research that applies themathematical formalism of quantum theory tomodel human decision-making. In this paper, we expose the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These foundations rest on the results of two decade studies on the axiomatic and operational-realistic approac...

In this paper, we characterize those holomorphic symbols u on the unit ball B and holomorphic self-mappings φ of B for which the weighted composition operator uCφ is bounded or compact from Bloch-type space to H∞ space. Mathematics subject classification (2010): Primary 47B33; Secondary 47B38.

The boundedness of the weighted differentiation composition operator from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0 . An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

We present wannier90, a program for calculating maximally-localised Wannier functions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWF in real space. This is done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point. As a result, wannier90 is...