All Questions
Tagged with classical-mechanics statistical-mechanics
188
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Diffusive momentum transport as overlap of acoustic peaks?
In the context of molecular dynamics simulations of soft or hard spheres in the fluid phase (e.g., with Lennard-Jones interactions), it is known that the velocity autocorrelation function (VACF) ...
- 895
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1
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46
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Why the interaction between system and thermal bath does not affect the energy levels of the system?
When we write down the full Hamiltonian of a system in contact with a thermal bath, it is as follows:
$$H_{\text{total}} = H_{\text{system}} + H_{\text{system+bath}} + H_{\text{bath}}.$$
As our focus ...
- 1,068
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Is the Virial Theorem dependent on the classical Equipartition Theorem?
The Wikipedia entry for the Virial Theorem states:
"*The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems ....
- 5,571
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Temperature as a frequency
In Arnold's Mathematical Methods of Classical Mechanics, he leaves as an exercise to show that if $S(E)$ is the area enclosed by a closed phase curve of energy $E$, then $T:=S'(E)$ is the period of a ...
- 873
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The specific heat of an EM wave in classical physics
I'm reading Dirac’s Principles of Quantum Mechanics and, in the first chapter, he states:
… There must certainly be some internal motion in an atom to account for its spectrum, but the internal ...
- 1,080
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2
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91
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Does time average induce phase space propability distribution?
Lets say we have a trajectory (positions and momenta) $(x(t), p(t))$ that is the solution of the equation of motion for a system with Hamiltonian $H(x,p)$. For some function $A(x,p)$, the time average ...
- 21
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2
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Why Normalise by $h$ in the Partition Function for Classical Harmonic Oscillator?
I was wondering if anyone could explain the reasoning behind the $h$ normalization constant when calculating the partition function for a classical harmonic oscillator.
I know that the partition ...
- 31
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What is the connection between energy in classical mechanics and thermodynamics
In classical mechanics the concept of energy is very simple. If I have a bunch of particles $r_1$...$r_n$. Then the total energy is:
$$E=\frac{1}{2}m(\dot r_1^2+...\dot r_n^2)+U(r_1...r_n)$$
Now in ...
- 29
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178
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Why do stones in a garden rise to the surface?
Why do stones in a garden rise to the surface?
I haven't done my own research on the subject, but experienced gardeners seem to suggest that, even if the garden is cleaned from stones, they reappear ...
- 59.6k
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Relation between hamiltonian perturbation theory (classical) and the Fokker Planck drift and diffusion coefficients?
Suppose I have a hamiltonian of the form
$$
H(q,p) = H_0 + \epsilon H_1(q,p)
$$
In perturbation theory we approximate the solution to the equations of motion as a power series in $\epsilon$:
$$
q(t) = ...
2
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1
answer
559
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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 \...
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153
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Is the entropy for the classical microcanonical ensemble defined... up to an infinite number?
In the microcanonical ensemble all states $(p, q) \in \Gamma$ (where $\Gamma$ is the phase space of a system with $3N$ coordinates) with the same energy have the same probability density. I would ...
- 1,290
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53
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Understanding the use of Capstan Equation
I'm currently working on the analysis of a current capstan, I want to analyze this system using the capstan equation.
The current capstan I'm working on has been built on the following parameters
...
- 1
5
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In statistical mechanics, why is one "allowed" to treat classical systems probabilistically?
Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental ...
- 161
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237
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Connection Helmholtz free energy and $H,M,B$ fields
Consider a magnetic system subject to a magnetic field. Here we work with the fields $H,M,B$.
Now, how does a change in the Helmholz free energy depend on $H,M,B$? I have three sources that seem to ...
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