Neumann Definition and 98 Threads

Homework Statement Solve the heat equation ut=uxx on the interval 0 < x < 1 with no-flux boundary conditions. Use the initial condition u(x,0)=cos ∏x Homework Equations We eventually get u(x,t)= B0 + ƩBncos(n∏x/L)exp(-n2∏2σ2t/L2) where L=1 and σ=1 in our case. B0 is...

Homework Statement From a previous exercise (https://www.physicsforums.com/showthread.php?t=564520), I obtained u(r,\phi) = \frac{1}{2}A_{0} + \sum_{k = 1}^{\infty} r^{k}(A_{k}cos(k\phi) + B_{k}sin(k\phi)) which is the general form of the solution to Laplace equation in a disk of radius a. I...

So I'm reading through Jackson's Electrodynamics book (page 39, 3rd edition), and they're covering the part about Green's theorem, where you have both \Phi and \frac{\delta \Phi}{\delta n} in the surface integral, so we often use either Dirichlet or Neumann BC's to eliminate one of them. So for...

According to John von Neumann’s interpretation of QM, consciousness is why the wave function collapses. Copenhagen is on the same general idea, but does not mention it that categorically. Multiverse interpretation of QM says there is no wave function collapse, therefore the observer or...

I'm trying to get to the bottom of things concerning the shaping of an optical pulse(change of state) with linear optics. Using linear optical apparatus we can shape the pulse of a photon in such methods as cavity dumping. You feed an optical cavity with near monochromatic(short bandwidth)...

Hi guys! I'm to find the solution to \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} Subject to an initial condition u(x,0) = u_0(x) = a \exp(- \frac{x^2}{2c^2}) And Neumann boundary conditions \frac{\partial u}{\partial x} (-1,t) = \frac{\partial...

***EDIT: This is nonsensical. I'm new to density matrices, and I had a sign error that led to some confusion. In addition... this just doesn't make sense, reading it over. I apologize for the post. I'd appreciate it if a moderator removed this, please. I'm reading about the von Neumann entropy...

Homework Statement U_t = u_{xx} - 4U u_x (0, t) = 0, u_x (\pi, t) = 1 u(x, 0) = 4cos(4x) Find a steady state solution to the boundary value problem. Homework Equations n/a The Attempt at a Solution Well I'm quite comfortable solving dirichlet/ mixed boundary value...

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...

I wrote a program that uses the FEM to approximate a solution to the heat conduction equation. I was lazy and wanted to test it, so I only allowed Neumann boundary conditions (I will program in the Dirichlet conditions and the source terms later). When I input low values for the heat flux, I...

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...

Hi, I am trying the solve the Poisson equation in a domain with curved boundaries using the Finite Difference Method (second order accurate). I need to apply the Neumann condition on the curved boundary. I have used bilinear interpolation to do this but this causes the resultant scheme to be...

Hi, I am trying the solve the Poisson equation in a domain with curved boundaries using the Finite Difference Method (second order accurate). I need to apply the neumann condition on the curved boundary. I have used bilinear interpolation to do this but this causes the resultant scheme to be...

Can anyone help me out with von Neumann entropy please?? I've been wondering if I could be able to calculate the entropy of a system which is part of a bigger system. For example, let's say that there's a cavity and two atoms(atoms are two-level system). The hamiltonian of the system would...

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...

Homework Statement Use finite difference central method to approximate the second-order Ordinary Differential Equation U''(x) = e^x over domain [0, 1] where: u(1) = 0 (Dirichlet Bound) U'(0) = 0 (Neumann Bound) Homework Equations let 'h' be the change in x direction The Attempt...

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...

The problem statement is: Solve the Neumann problem for the wave equation on the half line 0<x<infinity. Here is what I have U_{tt}=c^{2}U_{xx} Initial conditions U(x,0)=\phi(x) U_{t}(x,0)=\psi(x) Neumann BC U_{x}(0,t)=0 So I extend \phi(x) and \psi(x) evenly and get...

(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?

Homework Statement Solve Laplace's equation inside a circular annulus (ring) (a < r < b) subject to the BCs: \frac{\partial{u}}{\partial{r}}\left({a,}\theta\right)&={f}\left(\theta\right) \frac{\partial{u}}{\partial{r}}\left({b,}\theta\right)&={g}\left(\theta\right) Homework...

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...

Hi all, I'm trying to analytically solve the heat equation with a heat source and Neumann B.C. The source term is creating some problems for me as I cannot determine the coefficients in the series that builds up the solution. If someone could could help me or at...

"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...

Dear all, I am a new member of this forum. I saw it many and I found it very interesting. I am solving a 2d transport equation. I discretized it in space with an upwind scheme and in time with Backward Euler difference. Hence, if I want to solve the problem I have to solve a linear system of...

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...