Related papers: Liberation of Projections
We examine the statistical number of states, from which statistical entropy can be derived, and we show that it is an explicit function of the metric and thus observer dependent. We find a constraint on a transformation of the metric that…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow and thus Ornstein theory yielded the existence of a measure-preserving isomorphism…
We investigate the free convection processes in the vicinity of a spherical 1 kg mass standard by two- and three-dimensional direct numerical simulations using a spectral element method. Our focus is on the determination and suppression of…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
Let $x,y$ be freely independent selfadjoint elements in a $W^{*}$-probability space, where $y$ has free Poisson distribution of parameter $p$. We pursue a methodology for computing the absolutely continuous part of the Brown measure of $x +…
We present a constructive probabilistic proof of the fact that if $B=(B_t)_{t\ge0}$ is standard Brownian motion started at $0$, and $\mu$ is a given probability measure on $\mathbb{R}$ such that $\mu(\{0\})=0$, then there exists a unique…
The effects of a coupling between the quantized mechanical vibrations of a quantum dot and coherent tunneling of electrons through a single level in the dot are studied. The equation of motion for the reduced density operator describing the…
In this paper we introduce a method for creating a transparent computational boundary for the simulation of unidirectional propagation of optical beams and pulses using leaky modes. The key element of the method is the introduction of an…
This article, which is substantially motivated by the previous joint work with J. McKay [8], establishes the analytic analogues of the relations we found free probability has with Witt vectors. Therefore, we first present a novel analytic…
A density functional theory for a macroion suspension is examined, where the excess free energy corresponds to the macroion self energy arising from the polarisation of the supporting electrolyte solution. This is treated within a…
We consider the field concentration for the transmission problems of the homogeneous and inhomogeneous conductivity equations in the presence of closely located circular inclusions. We revisit these well-studied problems by exploiting the…
We study the transition of a particle between two points such that the particle takes discrete spatial steps in this transition. We analyze how the sum over histories interpretation of quantum mechanics can be implemented in this scenario.…
Starting with unitary quantum dynamics, we investigate how to add quantum measurements. Quantum measurements have four essential components: the furcation, the witness production, an alignment projection, and the actual choice decision. The…
We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we…
In this paper, we present a theoretical and numerical analysis of the free expansion of a Bose-Einstein condensate, where we assume that the single particle energy spectrum is deformed due to a possible quantum structure of spacetime. Also,…
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
We study the decoherence and thermalization of an Unruh-DeWitt detector linearly coupled to the free massless scalar field in flat spacetime of arbitrary dimensions ($d\geq 2$). The initial state of the detector is chosen to be a pure state…
Free field representations of vertex algebra in SL(2,R)/U(1) x U(1) WZNW model are constructed by considering a twisted version of the Bershadsky-Kutasov free field description of discrete states in the two-dimensional black hole CFT. These…