Questions tagged [boundary-conditions]

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189 questions
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Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
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What are the boundary conditions for D4-branes ending on D8-branes?

In a recent paper by Cordova and Jafferis, they perform the physical derivation of the AGT correspondence. A crucial step is recognizing that the appropriate boundary conditions for the 5D super Yang-...
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Topological insulators: What does the scattering matrix at an topological edge tell about the Chern number?

In class we were briefly discussing, that one way to see if the edge of a TI carries a state is to consider the scattering of a lead that is attached to this edge. In fact the argument was more ...
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How are boundary consitions implemented correctly in time dependent hydrodynamics?

I posted this question more than one year ago and got an answer recently. This answer looks good to me, but indicates that something is wrong in my original approach to the problem. Can someone tell ...
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Eigenvalue problem $−\psi''(x) − (ix)^ N \psi(x) = E\psi(x)$ in complex plane

To find the eigenvalue in the complex plane of $x$ for one dimensional Schrodinger equation $$−ψ''(x) − (ix)^ N ψ(x) = Eψ(x).$$ where $N$ can be any real number, the boundary condition $ψ(x) → 0$ ...
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Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
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Variation of Gibbons-Hawking-York term. General boundary condition and total derivatives

It is actually a comment and question to the answer of Robert McNees in the following post: Explicit Variation of Gibbons-Hawking-York Boundary Term In deriving the variation of the extrinsic ...
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Current Density Boundary Conditions and its Implications

According to Ohm's Law, one can say $\overline{J} =\sigma \overline{E}$ if the field is in a conductor, and $\overline{J} =0$ if it's in empty space. Now if we take the surface of a conductor and ...
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How do I simulate a constant velocity flow in porous media

I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my investigation....
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Would Bekenstein bound disappear in some holographic models?

In Holographic principle models there's a limit to the information that the system can store known as the "Bekenstein bound". In physics, the Bekenstein bound is an upper limit on the entropy S, or ...
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1D wave equation with non-stationary boundary conditions

Consider a string with natural length $L$ with initial displacement $u(x, 0) = p(x) = 0$, and velocity $u'(x,0) = v(x) = 0$. Let the boundary conditions be $u(0, t) = f(t)$. This describes a string ...
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Solving Poisson's equation for an infinite grounded plane

I want to solve the Poisson equation for a thin slab of charge held above a grounded plane at $z=0$. The problem is somewhat reminiscent of the classical image problem of a point charge above an ...
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Conditions for allowed modes in Quantization of an EM Field

Usualy, when quantizing a free Electromagnetic Field, the first thing we do is solve the classical Maxwell Equations, to get a full set of modes (solutions of the equations) that are then used to ...
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Shooting Method for coefficient matching in holography

Usually when one is attempting to solve the equations of motion of a bulk field in the AdS/CFT framework the main goal is to understand if a corresponding boundary operator aqcuires a VEV (commonly ...
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Can d'Alembert's Formula for the Wave Equation in one dimension (1+1D) be used in three dimensions (3+1D)?

The 3+1D wave equation for spherically symmetric waves is $$\frac{\partial^2 u}{\partial t^2} = c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right)$$...
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Bound states in two and three dimensional delta potential in non relativistic QM

I would like to find bound state energies in let's say 2D delta function potential. So my eigenvalue equation is: $$(-\frac{1}{2}\Delta - g\delta(r)) \psi = -B \psi$$ and by the means of Fourier ...
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Perodic boundary conditions vs Dirichlet?

I have been working through several examples recently involving particles in boxes (when finding the partition function of an ideal gas for example or looking at photon gases). I have seen two ...
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“Simple” Variation of the gravity action with boundary

I'm concerned with the derivation of the quasi-local stress tensor (getting from eqn 2.4 to eqn 2.6 in this paper: http://arxiv.org/abs/hep-th/0508218). As is the case with all the references I have ...
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QFT with fixed boundary conditions

I am looking for references on the formulation of QFTs with fixed boundary conditions for the fields (typically $\phi(0)=\phi(L)=0$), and especially how to construct the corresponding perturbative ...
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Has this boundary condition been used in fluid flow?

I would like to know whether anyone has seen a boundary condition used in a fluid flow problem, of the following type. Suppose viscous incompressible fluid is to the left of a plane $x_1=a$, so the ...
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Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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Equivocal boundary conditions for Laplace equation of 2D “V”-shape conductor

A two dimensional infinite "V"-shape wedge conductor is earthed, wherein $\beta$ is the intersection angle. We can solve Laplace equation so as to get the electric potential inside the "V" zone, as is ...
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How is Poisson's Equation solved numerically?

This question is of pure interest. I would like to know, how a mixed boundary value problem like the following can be solved numerically: Lets say I have two conducting plates (not necessarily ...
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Differentiating D3 brane worldvolume theories with NS5 brane and NS5 antibrane boundary conditions

In 'Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory', Gaiotto and Witten derive boundary conditions for the worldvolume theory of the D3 brane. In particular the boundary conditions (...
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What are the “basic things” we need in physics to define any kind of energy, including “mass”?

After having commented an answer there: Relative potential energy vs Absolute potential energy, I realised that the energy concept may be much more subtle than what we usually believe, even if we ...