von Neumann Lattices in Finite Dimensions Hilbert Spaces

The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can be viewed as two distinct degrees freedom. These, Schwinger's quantum degrees of freedom, are uniquely related to a von Neumann lattices in the phase space that characterizes the Hilbert space and specifies the simultaneous definitions of both (modular) positions and (modular) momenta. The area in phase space for each quantum state in each of these quantum degrees of freedom, is shown to be exactly $h$, Planck's constant.Comment: 16 page

Elucidation of role of graphene in catalytic designs for electroreduction of oxygen

Graphene is, in principle, a promising material for consideration as component (support, active site) of electrocatalytic materials, particularly with respect to reduction of oxygen, an electrode reaction of importance to low-temperature fuel cell technology. Different concepts of utilization, including nanostructuring, doping, admixing, preconditioning, modification or functionalization of various graphene-based systems for catalytic electroreduction of oxygen are elucidated, as well as important strategies to enhance the systems' overall activity and stability are discussed

Order parameter symmetry in ferromagnetic superconductors

We analyze the symmetry and the nodal structure of the superconducting order parameter in a cubic ferromagnet, such as ZrZn$_2$. We demonstrate how the order parameter symmetry evolves when the electromagnetic interaction of the conduction electrons with the internal magnetic induction and the spin-orbit coupling are taken into account. These interactions break the cubic symmetry and lift the degeneracy of the order parameter. It is shown that the order parameter which appears immediately below the critical temperature has two components, and its symmetry is described by {\em co-representations} of the magnetic point groups. This allows us to make predictions about the location of the gap nodes.Comment: 12 pages, ReVTeX, submitted to PR

Fractional Quantum Hall Effect and vortex lattices

It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special topologically nontrivial many-electron wave functions is considered. Their group classification indicates the special values of of electron density in the ground states separated by a gap from excited states

Simultaneous measurement of coordinate and momentum on a von Neumann lattice

It is shown that on a finite phase plane the $kq$-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number $M$ defining the size of the phase plane can be expressed as a product, $M=M_{1}M_{2}$, with $M_{1}$ and $M_{2}$ being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice.Comment: Published in EPL 83 (2008) 1000

Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. We identify $z_L$ with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian model. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing approach.Comment: 4 pages, 3 figure

Deformation of intrasalt beds recorded by magnetic fabrics

Funding Information Israel Science Foundation (ISF). Grant Number: 868/17 Israeli Government. Grant Number: 40706 Israel Science Foundation. Grant Number: 868/17Peer reviewedPublisher PD

Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.Comment: 12 pages, RevTe

Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result

In this paper we prove that any multi-resolution analysis of \Lc^2(\R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.Comment: Submitted to Journal Mathematical Physisc

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M