All Questions
Tagged with non-linear-systems linear-systems
30 questions
3
votes
6
answers
2k
views
Why do people say the dynamics of quantum mechanics is always linear?
This statement seems false. An example of a non-linear equation governing the dynamics of a quantum system is the Gross-Pitaevskii equation.
- 3,295
1
vote
2
answers
161
views
Understanding linearity of Maxwell's equation compared to non-linarity of GR
In this post, it is mentioned that a linear equation means that the solutions 'do not interact with each other' or 'do not know' about each other. But we know that Maxwell's equations are linear ...
- 849
-6
votes
2
answers
79
views
Non-linear time and concurrent perceptions of reality [closed]
I am asking about what the fact that a photograph and a physical space can exist, in what we perceive to be different moments in linear time (with the photo being made from what we regard as our ...
0
votes
1
answer
62
views
Do all nonlinear systems store energy?
I would like to clarify, this question comes from my own curiosity while solving for nonlinear differential equations. I have noticed that I lack the fundamental understanding of linearity/...
- 3
0
votes
1
answer
53
views
Why for motion planning of quadrators the goal is to minimize the jerk/snap?
In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and ...
- 41
0
votes
0
answers
42
views
Concerete examples of physical systems that can be (approximately) modelled using a 2D triharmonic equation?
I have some experimental measurements of input-driven standing-wave resonances in a nonlinear, 2D medium. I think it's fair to assume that the dynamics are homogeneous and isotropic, and we can think ...
- 101
0
votes
1
answer
51
views
Problem identifying type of equation (linear/nonlinear)
I've looked at the answer to this Math.SE question, but I still can't know the answer to my question here.
The following is the equation of equilibrium: divergence of stress tensor that is the sum of ...
- 88
1
vote
1
answer
542
views
What is the difference between a linear and a non-linear perturbation?
Sometimes you will hear about the stability of certain solutions (black holes, solitons, etc) with respect to perturbations. Often they talk about linear vs. non-linear perturbations.
What is the ...
- 671
2
votes
2
answers
171
views
Is there a "measure of nonlinearity" that can be measured when testing quantum mechanics?
For context, I think the comparison to tests of general relativity here is apt. There is the post-Newtonian formalism that has some well-defined parameters that can discriminate between general ...
- 8,776
0
votes
0
answers
316
views
Two masses connected by spring moving in a plane
Is the 2-dimensional motion of two masses connected by a spring non-linear?
As far as I see it, the magnitude of the force on each mass is proportional to the spring's displacement from its ...
- 927
1
vote
2
answers
218
views
Can the phase portrait of SHO rotate counter-clockwise? or is it the case that there can be no physical motion corresponding to that?
Framing the question
In the case for Simple Harmonic Oscillation, we have the equation:
$$\ddot{x}+x=0 \tag{1} \label{1}$$
(say, we put all the coefficients to be 1)
Now, if we try to solve it in ...
- 57
1
vote
0
answers
193
views
Why must operators in QM be linear?
Why must all operators in QM be linear (and therefore able to be represented by matrices). What is the physical reasoning behind this?
Is it be possible that the non-unitary nature of quantum collapse ...
- 2,654
3
votes
1
answer
337
views
How does the linearity of the Schroedinger equation reflect the interactions?
There is a common lore that linear equations describe non-interacting systems, why non-linearities correspond to non-trivial interactions. My (loose) question is how is that compatible with the ...
- 1,594
1
vote
5
answers
1k
views
Are all systems really non-linear?
A few years ago I had a course on control and systems engineering. In one of the first chapters of the book we used, it was stated that "all physical systems are nonlinear".
When discussing ...
- 23
1
vote
1
answer
48
views
Linear Structure of Classical theory
I have been studying QFT from Timo Weigand’s lecture notes and in the chapter ‘Quantisation of spin-1 fields’, he describes the Feynman rules for QED and after some examples, there is subsection named ...
- 475
0
votes
2
answers
89
views
Linear system in polar coordinates [closed]
Unlike the Cartesian coordinates, I find navigating through polar coordinates difficult. Is the system defined by the following Lagrangian $L$ defined in polar coordinates linear?
$$L = \frac{1}{2} m \...
- 113
1
vote
1
answer
142
views
Is the quantum dynamics of a system of interacting particles linear or non-linear?
As I understand it, the linearity of quantum mechanics is considered to be an inviolable principle - e.g., this paper - because (among other things) causality would be violated or and/or superluminal ...
- 25k
0
votes
0
answers
35
views
Distinguishing a LTI from not with unknown inputs
Linear time invariant (LTI) systems are a staple of physics. They appear in many situations. But how do you know a system is a LTI?
In particular, if you are provided with a black box which ...
- 51.7k
1
vote
1
answer
175
views
Unpredictability, per definitions of chaotic behavior
Apparently I've been confused about the meaning(s) of "chaotic behavior". I always thought it meant that infinitesimal perturbations of a system parameter would lead to large changes in the system's ...
- 25k
2
votes
2
answers
628
views
Linear and non-linear systems
When I read about the superposition principle, it says that it works only on linear systems, my problem is that I cannot really understand the difference between a linear and a non-linear system. I ...
- 409
2
votes
2
answers
61
views
Is the trajectory of a particle with constant velocity (though its direction can change by collisions) always non-chaotic?
Suppose we have a particle that travels with constant velocity, without heat losses by friction, and no forces acting on it except for occasionally collisions with much bigger wall-like masses than ...
0
votes
1
answer
105
views
How to determine the linearity of a numerically simulated mass-spring system?
I did some numerical simulation of a mass-spring system, which is a 2D 1-degree-of-freedom spring-mounted cylinder vibrating due to moving fluid surrounding it.
The cylinder's motion may be described ...
- 161
1
vote
2
answers
1k
views
Is it a linear mass-spring system?
Please look at this equation representing a mass-spring system:
${\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+2\zeta \omega _{0}{\frac {\mathrm {d} x}{\mathrm {d} t}}+\omega _{0}^{\,2}x=F$
where ...
- 161
1
vote
2
answers
162
views
Why is stress linearly dependent on strain in elastic materials?
The displacement vector $\mathbf{u}(\mathbf{x}, t) = \mathbf{r}(\mathbf{x}) - \mathbf{x}$ is used to keep track of the motion of the material points in a material. Firstly, we take the gradient of the ...
- 284
1
vote
2
answers
709
views
a Non-linear Mass-spring system with different force and vibration frequency?
I got a classic mass-spring system with zero damp ratio, having weird behaviour.
The input frequency of external force is twice that of the output displacement results. While linear systems' input &...
- 161
2
votes
3
answers
339
views
Are all the quantum based equations linear?
I dont know much about the subject, but the wave equations (classical and modern) as well as classical equations of motion all seem to be inherently linear differential equations. Presumably this also ...
- 1,300
5
votes
5
answers
1k
views
How does non-linear behaviour arise from the inherently linear QM framework?
Quantum mechanics is a linear theory, living in a Hilbert space with built-in linearity. It has even been argued that introducing non-linearity in the quantum theory would allow for superluminal ...
- 858
4
votes
1
answer
380
views
Why linear wave equation does not have solitonic solutions?
As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
- 4,254
1
vote
2
answers
360
views
Linear quantization in quantum electrodynamics?
This is a continuation of this question.
What would be an example of linear quantization used on quantum electrodynamics? I ask this because QED is a nonlinear theory.
- 61
31
votes
5
answers
4k
views
Linearity of quantum mechanics and nonlinearity of macroscopic physics
We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are ...
- 2,017