The Dirac operator d+ δ on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L2μΩ, [A,A ] acts as multiplication by a positive constant on excited states if and only if the logarithm of the measure density of dμ satisfies a pair of equations. The equations are equivalent to the existence of a harmonic distance function on M . Under these c...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

Motivated by formal similarities between the continuum limit of the Ising model and the Unruh effect, this paper connects the notion of an Ishibashi state in boundary conformal field theory with the Tomita–Takesaki theory for operator algebras. A geometrical approach to the definition of Ishibashi states is presented, and it is shown that, when normalisable the Ishibashi states are cyclic separ...

The functional state of the human operator is critical to optimal system performance. Degraded states of operator functioning can lead to errors and overall suboptimal system performance. Accurate assessment of operator functional state is crucial to the successful implementation of an adaptive aiding system. One method of determining operators' functional state is by monitoring their physiolog...

Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4n-dimen...

We identify the puncture operator in c = 1 Liouville gravity as the discrete state with spin J = 1 2. The correlation functions involving this operator satisfy the recursion relation which is characteristic in topological gravity. We derive the recursion relation involving the puncture operator by the operator product expansion. Multiple point correlation functions are determined recursively fr...

We present a very simple model for numerically describing the steady state dynamics of a system interacting with continua of states representing a bath. Our model can be applied to equilibrium and nonequilibrium problems. For a one-state system coupled to two free electron reservoirs, our results match the Landauer formula for current traveling through a molecule. More significantly, we can als...

We extend the real time process algebra of [BB91a] with the state operator of [BB88]. We show the usefulness of this extension in several examples. We use concepts from (classical) real space process algebra of [BB91b] in order to deal with different locations.

Abstract. In this paper we present a generalized description of the Grover operator, employed in a quantum database search algorithm. Our purpose is to employ an operator to find the proper solution(s) originated from an arbitrary initial state in the two dimensional vector space, where the orthogonal basis vector system are rotated in such a way where the result is obtained with a probability ...