Neumann Definition and 81 Threads

Is anyone thoroughly familiar what von Neumann was trying to say in his von Neumann Chain concept where one can locate anywhere the observer and the observed? I've been reading the original and analyzing it for hours and can't seem to completely get the context in light of present day concept...

Density matrix and von Neumann entropy -- why does basis matter? I'm very confused by why I'm unable to correctly compute the von Neumann entropy S = - \mathrm{Tr}(\rho \log_2{\rho}) for the pure state | \psi \rangle = \left(|0\rangle + |1\rangle\right)/ \sqrt 2 Now, clearly the simplest...

Von Neumann wrote in a major physics book decades ago that consciousness was what collapse the wave function.. how could he stated this bizaare statement and the facts remain up to this day? Is the interpretation been refuted already by the latest discovery of Decoherence? I can't find...

I'm playing with the PDE toolbox in Matlab and solving Laplace's equation, ∇2V = 0, for various electrostatic geometries. I say 'playing' because I started in the wrong end (or right end, depending on how you look at it) by simple trial and error until the solutions looked like something...

I am new to differential equations, any help would be great. I have a ODE of the second order u''x = e^x over the domain [1, 1] where u'(0) = 0 is a Neumann boundary on the ODE. I am trying to approximate the solution using the finite differences method, I can do Dirichlet boundaries with...

From Partial Differential Equations: An Introduction, by Walter A. Strauss; Chapter 1.5, no.4 (b). Homework Statement "Consider the Neumann problem (delta) u = f(x,y,z) in D \frac{\partial u}{\partial n}=0 on bdy D." "(b) Use the divergence theorem and the PDE to show that...

hi all, I am trying to solve this PDE by separation of variables, it goes like this: \frac{\partial u}{\partial t} = \alpha\frac{\partial ^2 u}{\partial z^2} for 0\leq z\leq infty the initial condition I have is: t=0; u = uo. the boundary condtions: z=0; \frac{\partial...

The Von Neumann entropy is \mathcal{S}(|\psi\rangle) = -Tr[\rho_a ln \rho a] . The linear entropy S_L = \frac{l}{l-1}(1 - Tr[\rho_a^2]) For l =2 the linear entropy is written 4Det(\rho_A) which is also called the tangle \tau. I understand this just fine, I can show that. Now it says the Von...

Hello everybody, I've been puzzling over something (quite simple I assume). Take S^1. Now consider the action of a Z_2 which takes x to -x, where x is a natural coordinate on the cylinder ( -1< x <1). Now we mod out by this action. The new space is an orbifold: smooth except at x=0. It...

(a) Let α and β be two von Neumann ordinals. Show that α ⊂ β if and only if α ∈ β. (b) Show that the Axiom of Foundation implies that a transitive set which is linearly ordered by ∈ is an ordinal I can't seem to follow through this properly, any help?

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

Hi everyone, What's the difference between these two boundary conditions? Why are they important to know?

I am confused by the definition of the Von Neumann entropy. In Nielson and Chung's book page 510, the Von Neumann entropy is defined as S (\rho) = - tr(\rho \log \rho) where \rho is the density matrix. What is the definition of the logrithm of a matrix? Is it some series expansion of a...

Hi, it's been a while since I touched mathematics and I'm a little rusty... I'm looking at a problem right now that I find difficult to understand, conceptually. Any insight would be greatly appreciated. (A direct solution would help immensely as well, not only because that's what I need to...

Does Quantum Mechanics forbid some type of Von Neumann machine for the Universe?

Hi all, I need to solve the heat equation (Ut=C*Uzz) with the following boundary conditions: U(max z,t)=0 and Uz(0,t)=-B. where B is a constant. My initial condition is U(z,0)=Uo where Uo is a constant. I know how to solve the equation for simple 0 boundary conditions. The Neumann BC...

"Helmholtz equation" Neumann and divergence Hello, I'm trying to solve the following elliptic problem : S = B - \mu\nabla^2 B Where S(x,y) and B(x,y) are 3 component vectors. I have \nabla\cdot S = 0 and I want B such that \nabla\cdot B = 0 everywhere. I'm using finite differences on a...

I just wanted to run this working by some of you. Simplest Greenberger-Horne-Zeilinger state (entagled) state is: \mid GHZ \rangle = \frac{1}{\sqrt{2}}\left(\mid 0 \rangle_{A}\mid 0 \rangle_{B}\mid 0 \rangle_{C}+\mid 1 \rangle_{A}\mid 1 \rangle_{B}\mid 1 \rangle_{C}\right) density matrix is...

Hi all, I have tried to solve the heat equation with a Fourier-Bessel approach but I fail to implement the boundary condition, which is a Neumann condition. Every textbook that I have available treats the corresponding Dirichlet problem but not the Neumann one. Below I have tried to summarize...

So for an assignment I have to write a program to find the roots of the Neumann function N_{n}(x). However the only Neumann function I have in my class notes is: Which is not overly helpful, and its the only one that was "boxed" in class. Any hints on how I can incorporate that into a...

We have a hyperbolic pde (in fact the 1d wave equation) with indep vars X, T We use the central difference approximations for the second derivatives wrt X, T to get [phi(Xn, Tj+1) -2phi(Xn, Tj) + phi(Xn, Tj+1)]/(dT^2) = [c^2][phi(Xn-1, Tj) -2phi(Xn, Tj) + phi(Xn=1, Tj)]/(dX^2) where dX...

I'm trying to find the analytical solution to the following equation: c1*d2p/dz2-dp/dt = -c2*cos(omega*t) where - p is a function of spatial z and time t, p=p(z,t) - d2p/dz2 is the second derivative of p wrt z - dp/dt is the first derivative of p wrt t c1, c2 and omega are...

I tried to solve laplace equation for the steady state temperature over a rectangle with both neumann and dirichlet boundary conditions. For the part of the rectangle with neumann boundary condition(normal derivative = 0) i used U(k,p)=(2*U(k+1,p)+U(k,p+1)+U(k,p-1))/4 Is this correct...

[SOLVED] Measurement Issues: POVM, Neumann and generalized What is a POVM measurement? How is it different from Nuemann measurement theory and what would be the most general measurement formulation? Please keep things discrete and not continuous. -KM

What's the difference between thermodynamic entropy and von Neumann entropy? In particular, how is temperature related to the von Neumann entropy? Also, what has information got to do with these two entropies?

Hi all...need a little help with this one... I need to find the Green's function for the half space Neumann problem in the domain z>0. i.e. Laplacian u=f in D, du/dn=h on the boundary of D. Any ideas?

Let P be a density matrix. Then the von neumann entropy is defined as S(P) = -tr(P*log(P)) But how is log(P) defined ? --edit-- found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.

Could somebody please explain or give me a link to an explanation of the idea about measerument that von neumann put forward. That is that a system interacts with a pointer state associated with the measurering device with the hamiltonian H:=c * d(t) * A (X) * P where d(t) is diracs delta...

I wonder If someone could state the mean ergodic theorem von neumann without using meassure spaces ? I have studied normed spaces, banach spaces and hilbert spaces, that is complete normed inner product spaces. Could someone state and explain the theorem for me? :smile:

When you foretell that will be sent the first Von Neumann probe?

Several papers have appeared in the last few months suggesting a development in the quantum theory of general relativity which is analogous to the Stone-von Neumann theorem of 1931. The clearest and most representative of the bunch is probably the Okolow-Lewandowski paper dated February 2003...