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0
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2answers
55 views

Why is a circuit of linear elements itself linear?

A resistor's voltage is proportional to it's current. V=iR. And a source maintains a constant voltage or current. So these are linear, time independent relations. If I put combinations of them in a ...
4
votes
1answer
96 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
-1
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1answer
148 views

Meaning of Eigenvalues/Eigenvectors of a linear system of equations

I have a 41x41 system of linear equations (inhomogen) which I derived with Eureqa by describing the timecourse of fMRI haemodynamic data from a brain area as a function of the timecourses of 40 other ...
4
votes
0answers
88 views

Is there a classification scheme for linear classical field theories?

Central to a mathematical understanding of the Bogolyubov transformation is the study and classification of linear lattice field theories. What follows might be familiar to many people, but I just ...
3
votes
0answers
90 views

Multiple meanings of polarizability?

There's a concept in linear response theory called the polarizability $\chi$ $$\tag{1} \rho_{ind}=\int \chi(\vec{r},\vec{r}',t-t') V_{ext} \: d\vec{r}' dt' $$ where $\rho_{ind}$ is the induced charge ...
1
vote
0answers
161 views

Is strictly harmonic 2D lattice made of Hooke springs possible?

If we connect a set of point masses in a 1D lattice with Hooke springs and consider longitudinal oscillations, we'll have a strictly harmonic system, for which there exist eigenmodes and the frequency ...
1
vote
0answers
373 views

linear response for a simple harmonic oscillator

Really sorry for this simple question, but I think it will be useful/interesting in general. Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$ Calculate $\...
0
votes
0answers
35 views

Generalized Eigenvalue Problem from linear stability analysis

I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to ...
0
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0answers
28 views

Initial conditions for second order ODE with complex stiffness

I tried this on Math Stack Exchange. I'm trying to find initial conditions to ensure systems of the form stay bounded $$\ddot{x}_i+\sum_{j=1}^N k_{ij} x_j = 0, \quad k_{ij} \in \mathbb{C}.$$ For ...
0
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0answers
89 views

Berry curvature and linear response functions

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...
0
votes
0answers
103 views

How to get general relativity from linear gravity theory?

I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the self-interaction(...