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# Questions tagged [boundary-conditions]

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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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### Diffusion equation with time-dependent boundary condition

I was trying to solve this 1D diffusion problem \begin{equation} \dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi} \end{equation} with ...
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### Quantization of Klein-Gordon field between two boundaries

Consider a real scalar $\phi(x,t)$ with mass $m$ in $1+1$ dimensional spacetime, described by the 2d free Klein-Gordon action. $\phi(x,t)$ lives on an interval $0 \leq x \leq L$, and is subject to ...
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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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### Self-adjoint extensions with 'teletransporting' boundary conditions

When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which (i) the probabilities teleport* between points on the boundary and (ii) boundary conditions ...
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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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### Dirac equation boundary conditions

In Schroedinger equation, which is second order differential equation, one normally, equates both $\psi(x)$ and $\psi'(x)$ across the boundary, as boundary conditions. However, the dirac equation ...
In the derivation of energy conservation, there is the transformation $q(t)\rightarrow q'(t)=q(t+\epsilon)$, whose end points are kind of fuzzy. The original path $q(t)$ is only defined from $t_1$ to $... 0answers 65 views ### Constraints vs Boundary Conditions I have a very broad question about how the mathematical framework that classical theories of physics utilize to solve problems. The question is: What are the intrinsic differences between the ... 1answer 132 views ### Symmetric potential well different solutions I have solved$H|\psi\rangle=E_{n}|\psi\rangle$with$V(x)=0$from$-a<x<a$and$\infty$otherwise. If I propose a solution of the form$\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$I arrive to the ... 1answer 88 views ### Deriving the path integral for periodic boundary conditions I'm thinking about path integrals with the Euclidean time formalism, where I have partition function$Z=\operatorname{Tr} e^{-\beta \hat H}$. I'm used to the following derivation of the path integral: ... 0answers 49 views ### Would Bekenstein bound disappear in some holographic models? In Holographic principle models there's a limit to the information that the system can store known as the "Bekenstein bound". In physics, the Bekenstein bound is an upper limit on the entropy S, or ... 0answers 47 views ### Property of surface Green function in electrostatic field Let's consider a 2D-square with 4 equal subsquares containing different dielectrics. Inside the square domain, the unknown electric potential function$\Phi$satisfies the Laplace equation: $$\nabla^... 1answer 89 views ### Boundary conditions for the numerical particle in a box example I want to solve the one-dimensional Schrödinger equation for the particle in a box example, and want to force the wavefunctions to zero on the boundaries. I am using the matrix, \begin{equation} \hat{... 1answer 407 views ### The derivation of the Planck distribution I am trying to understand the Planck distribution and black body radiation. In the Wikipedia derivation of the Planck distribution, the photons confined within a cubic box, are emitting from and ... 0answers 89 views ### Power in a wind turbine An wind turbine starts turning by a wind speed of v_b and it stops turning (rated wind speed, to prevent overloading) by a wind speed of v_g. By wind speeds between v_b<v<v_g, the power ... 0answers 106 views ### Boundary conditions for standing EM-waves My freshman course on waves uses Young and Freedman's University Physics. They seem to argue in the following fashion: An electric field induced by a static charge distribution is conservative. When ... 0answers 148 views ### Neumann boundary condition for Laplace's equation in 2D axisymmetric coordinates? I have the Laplace's equation, say, describing the density \rho(r,z) distribution in a 2D axisymmetric coordinate:$$\nabla^2 \rho=\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial \rho}{\... 0answers 113 views ### 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 ... 0answers 317 views ### 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 ... 0answers 102 views ### 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 ... 0answers 49 views ### 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 ... 1answer 292 views ### Why is the total force at a free surface zero? I am looking into waves on a free surface for which their are two main conditions: Kinematic condition: Particles on the surface remain on the surface. Dynamic condition: Forces acting on the surface ... 1answer 156 views ### Boundary conditions for Quantum Cascade Laser (QCL) The Quantum Cascade Laser (QCL) is a semiconductor device for the generation of radiation in the MIR region of the electromagnetic spectrum. One period of the device consists of two regions, the ... 0answers 421 views ### 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 $$\frac{\partial^2 u}{\partial t^2} = c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right)$$... 0answers 304 views ### 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 ... 0answers 81 views ### 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 ... 0answers 78 views ### “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 ... 0answers 247 views ### 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 ... 2answers 211 views ### What is the interpretation of a wave function of the Universe in Hawking's no boundary proposal? In the path integral formalism we have an in state$\Psi_{in}[\phi]$and and out state and we find the amplitude for going from one to the other:$$\Delta[\Psi_{in},\Psi_{out}] = \int \Psi_{in}[\phi]... 1answer 168 views ### Fixing time in Feynman phase space path integral The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed$q$endpoints and (as far as I'm aware) ... 0answers 121 views ### A classically charged point particle interacting with electromagnetism and gravity Consider a classically charged point particle interacting with electromagnetism and gravity. The relevant dynamical variables are$\chi^\mu (\tau)$of the particle, the electromangetic potential$A_\...
Lets say one has an infinitely long cylinder with some boundary heat terms on $r=r_0$ of the form $T(r=r_0, \phi,z)=T_0(\phi,z)$. What is the general solution for this type of equation? The general ...