Questions tagged [steady-state]
52 questions
17
votes
3 answers
Reversibility = non-causality. Can this be right?
I read yesterday the Norton Dome's paper, which shows that some Newtonian systems can be non-causal, based on specific solutions of Newton's laws. The author justifies the solutions in very nice, logically consistent ways, that made me unable to…
The Quantum Physicist
- 3,517
14
votes
1 answer
Difference between steady state and equilibrium?
In semiconductor physics, what is the difference between steady state and equilibrium. How analysis of devices varies in these processes?
johndaniel
- 323
6
votes
1 answer
Why are the Navier-Stokes equations inconsistent in this case?
Consider the case of a one-dimensional incompressible, non-viscous fluid flowing down a vertical pipe under the influence of gravity. Since we assume the flow is constant along the cross section of the pipe from the one dimensional assumption, let…
Chandrahas
- 1,797
6
votes
1 answer
Fokker-Planck equation with time-dependent potential
Consider a Fokker-Planck (FP) equation where the advection term is a function of time, i.e.
\begin{align}
\frac{\partial P ( x , t )}{\partial t}
=
-\nabla \cdot \left[ -\mu \, P \, \nabla U (x,t) - D \nabla P \right]. \qquad\qquad ({\rm…
SaMaSo
- 538
6
votes
1 answer
Steady state solution to density matrix
A density matrix follows the dynamics
$$
\dot{\rho} = \mathcal{L}\rho,
$$
where $\mathcal{L}$ is the Liouvillian super-operator. If put in Lindblad form, it can be written as
$$
\mathcal{L}\rho = -i[H,\rho] + A\rho A^\dagger -…
Vladimir Vargas
- 1,039
6
votes
3 answers
General Definition of Steady State
According to many sources (including Wikipedia, Stephani&Kluge, D.J. Acheson) a steady state ist:
In systems theory, a system in a steady state has numerous properties that are unchanging in time. This means that for those properties $p$ of the…
Kuhlambo
- 950
3
votes
3 answers
In heat conduction, what does it actually mean to be in the steady state?
I have read about the method of heat conduction and I have some questions related to this topic:
If I consider a metal bar and supply heat in one end, the heat will flow through the bar and if I consider the bar to consist of many layers then each…
user101134
- 741
- 14
- 26
2
votes
0 answers
Is the Long-Time energy in a generic spin-Boson model independent of the dephasing?
I am considering spin-Boson model with the total Hamiltonian given by
\begin{align}
\hat{H}_{SE} &= \hat{H}_S + \hat{H}_E + \hat{H}_I.
\end{align}
where
\begin{align}
\hat{H}_S &= \frac{\Omega}{2}\hat{\sigma}_3, \\
\hat{H}_E &= \sum_k…
Prem
- 2,356
2
votes
0 answers
Vanishing terms in $G^<$ Dyson equation for steady state
The exact Dyson equation of the lesser Green function $G^<$ reads $$G^< = (1+G^\mathrm{r}\Sigma^\mathrm{r}) g^< (1+\Sigma^\mathrm{a}G^\mathrm{a}) + G^\mathrm{r} \Sigma^< G^\mathrm{a} \qquad(*)$$
with $g$ the undressed Green function. This can be…
xiaohuamao
- 3,971
2
votes
1 answer
Steady-state wave equation
I know that for the heat equation $u_t=\nabla^2u$, the steady-state condition $u_t=0$ suggests we need to solve $\nabla^2u=0$ (i.e. Laplace's equation), which yields the equilibrium temperature distribution after a considerable amount of…
whitenoise
- 121
2
votes
2 answers
Helmholtz decomposition of flow at non-equilibrium steady state
I'm trying to work through Karl Friston's mathematical derivation of the Free Energy Principle from Langevin Dynamics (see this paper). I'm confused about the part at the end of page 8 where he uses the Ao/Helmholtz decomposition to rewrite the…
Ariel
- 31
2
votes
1 answer
Quantum systems with steady states: does a system always approach the steady state as it evolves?
Say we have a quantum system whose dynamics results in there being a steady state. For example, it may be described by a Linblad master equation with several opposing dissipators. It is obvious that given that enough time has passed, the…
hendlim
- 856
2
votes
1 answer
Do the Euler equations always converge to a steady solution if the boundary conditions are steady?
I'm considering the compressible euler equations without any heat addition, body forces, energy addition, etc. In other words, i'm using the following equations with the assumption of an ideal gas.
$$
\begin{split}
…
Thomas Wagenaar
- 310
2
votes
2 answers
How does one get this steady-state solution?
I am studying the concept of a "gain medium" inside a laser cavity. The active atoms are taken to have the two levels $a$ and $b$, separated by energy $\hbar \omega$ and represented by a density matrix $\rho$. The atoms are stationary.
The equation…
The Pointer
- 939
2
votes
1 answer
Jim's Simple Physics Issue #i: The Big Bang Theory and Inflation
this is Jim again with another of my Simple Physics installments. This time I want to cover the much misunderstood concepts of the Big Bang theory and cosmological inflation. Like many of my other installments, there are plenty of posts out there…
Jim
- 24,676