All Questions
Tagged with adiabatic classical-mechanics
16
questions
2
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563
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Question about Landau's derivation of the energy relation in Statistical Physics (Vol 5)
In Statistical Physics (Vol 5 of Landau's books) section 11, Landau derives an important relation: $\overline{\frac{\partial E(p, q;\lambda)}{\partial \lambda}} = \left(\frac{\partial E}{\partial \...
- 35
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0
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71
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Order $\epsilon^2$ mean rate of change in action variable for adiabatic oscillator
In adiabatic theory of classical mechanics, considering a linear oscillator with a slowly changing frequency $\omega=\omega(t)$, Percival and Richards's nice book (pp. 144-147) discusses how it is ...
- 632
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51
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Why is the action an adiabatic invariant in a unidimensional oscillator?
I'm reading Rax's "Méchanique Analytique" but I can't understand a particular step.
We consider a unidimensional oscillator system with a potential that depends on a parameter $\lambda(t)$ ...
- 111
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2
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Is this set up a reversible process and is the adiabatic equation of state applicable here?
I had this question in a recent test:
My teacher while discussing this question used the adiabatic equation of state PV^gamma=constant to solve for length L (options C and D). And used work energy ...
- 105
5
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1
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167
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Adiabatic Invariant when forcing is at the natural frequency of a classical simple harmonic oscillator
Consider a simple harmonic oscillator of unit mass, natural frequency $\omega_0$, given by the Hamiltonian
\begin{align}
H_0(q,p)=\frac{1}{2} \left[ p^2 + \omega_0^2 q^2 \right] \ .
\end{align}
Now ...
- 73
2
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0
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49
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Adiabatic invariance of a particle with negative energy [closed]
Given a particle with negative total energy in the potential $$V=-\frac{V_0}{\cosh^2({\alpha}x)}$$
with $\alpha > 0$, I must show that under small and slow variations of $V_0$, the quantity $$\frac{...
- 160
2
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105
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Sound waves as an adiabatic process and defining pressure inside vibrating columns of air
In a MIT OCW video a professor goes on to derive the sound wave equation.
For this he takes a horizontal air column and assumes a pressure difference at its end which drives the gas column to the ...
- 1,270
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98
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Adiabatic invariants for rigid bodies
I Landau & Lifshitz I mechanics introduces adiabatic through Hamiltonian that is dependent on some slowly changing parameter $\lambda$. After some derivation they got
$$I=\frac{1}{2\pi}\oint pdq=...
1
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1
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189
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Adiabatic Invariant in Variable Mass Oscillator
Suppose you have an harmonic oscillator whose mass is adiabatically changing such that $T\frac{dm}{dt}\ll m$ where $T$ is the period of the motion. It could for example be an ice ball slowly melting ...
- 193
2
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466
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Plane pendulum at an angle (Goldstein 12.11) [closed]
I am struggling not only to come up with action/angle variables for the system, but more generally an appropriate Hamiltonian that takes into account the tilt of the plane. The system is as follows:
&...
- 1,031
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Adiabatic invariance regime
Consider a system executing a finite motion, described by its hamiltonian $H$ and characterized by some parameter $\lambda(t)$ being varied over time.
Reading Landau & Lifshitz (Mechanics, ...
- 193
1
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1
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217
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Tilting a water glass so that you can run faster without spilling water (counter-diabatic driving Hamiltonian)
In this paper, there is an interesting figure:
Every attempt I've made to search online to confirm whether or not waiters/waitresses actually do this, has been unsuccessful.
Is there really an ...
- 324
1
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0
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158
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Slowly Varying Functions for Adiabatic Invariants - The Same as Karamata's?
In section 49 (and 50) of Landau and Lifschitz's "Classical Mechanics", adiabatic invariants are discussed, which are related to functions which vary adiabatically or "slowly" with time.
Admittedly ...
- 544
3
votes
1
answer
188
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Simplest Live Demonstration of Adiabatic Transport
I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original ...
- 2,107
9
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Adiabatic invariant and Liouville's theorem
It appears that many people have tried to show adiabatic theorem from Liouville's theorem, e.g., Li's note, or at least tried to find some relations, e.g., Rugh, Adib and Tong's lecture notes Sec. 4.6....
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