All Questions
Tagged with dof or degrees-of-freedom
473 questions
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Law of equipartition of energy, shouldn't kinetic energy per molecule by $(3/2)kT/f$
I study that according to the law of equipartition of energy the average kinetic energy associated with each degree of freedom is equal to $(1/2)kT$. But shouldn't it be $\frac{(3/2)kT}{f}$
where $f$ ...
- 581
2
votes
2
answers
136
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Is this a gauge symmetry?
Imagine a hypothetical action:
$$S=\int \left(\frac{\partial}{\partial t}\phi(x,t)\right)^2 d^3x dt$$
Now we have a symmetry of the action: $$\phi(x,t)\rightarrow \phi(x,t)+\chi(x).$$
At time $t$, $\...
user84158
11
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1
answer
11k
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Counting independent components of the Riemann curvature tensor
In 4D spacetime, we may choose a locally inertial frame at point P, that is we always have a transformation such that $g_{{\mu'}{\nu'}}(P) = \eta_{{\mu'}{\nu'}}$ and its first derivatives vanish. ...
user243050
2
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1
answer
2k
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Non-holonomic constraints, degree of freedom and generalized coordinates
If a system has $N$ coordinates and $M$ number of holonomic constraints then number of degree of freedom $=N-M$ and generalized coordinates $=N-M$ too. But if there are $k$ non-holonomic constraints ...
- 362
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1
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178
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Does a "gimbal hinge" have the same degrees of freedom as a ball-and-socket joint?
I am trying to design a joint to 3D print and considering different models. One model was a traditional spherical ball-and-socket joint. However, due to production issues, I am considering other ...
- 4,241
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87
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Degree of freedom in ideal and real case
what will be the degree of freedom of a massless rod, moving freely in space with a particle which is constrained to move on it? What is meaning of massless rod?
- 362
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2k
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Infinite number of degrees of freedom
In a system with a finite number of degrees of freedom $\eta_i$, $i=1,\ldots, N$
, the partition function depends on the N external fields that may couple linearly to the $\eta_i$ in the Hamiltonian
$...
- 1,048
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vote
1
answer
643
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Some counting of field degrees of freedom for a classical spin-1/2 Dirac field
A classical real scalar field admits a decomposition $$\phi(x)\sim a_pe^{-ip\cdot x}+a_p^*e^{+ip\cdot x}$$ which tells that at each $x$, there exists a real number i.e., one degree of freedom at each ...
- 12.3k
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1
answer
2k
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Einstein solid degree of freedom
I was studying from Schroeder's thermal physics book. When it talks about Einstein solids it says that they have 2 degrees of freedom thus $U=NkT$
However, I thought when we talk about Einstein ...
- 153
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102
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Physical degree of freedom and gauge fixing?
I'm confused with the gauge fixing in the Higgs mechanism.
So if we have an action like
$$S=\int |D\phi|-\frac{1}{4}F^2 -V(\phi) ~ ,\tag{1}$$
then expand around some non-trivial vacuum, then we have ...
- 311
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1
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3k
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Degeneracy in Landau Levels
A subsection from "Landau Levels" from pg 21 from Lectures on Quantum Hall effect by David Tong.
He shows and derives the energy of a charged particle in a planar surface under the action of a ...
- 55
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1
answer
1k
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How many degrees of freedom does a spring pendulum have? [closed]
I've been looking at a spring pendulum system, but I'm not sure how many degrees of freedom it has.
- 11
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0
answers
161
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Rigorously define degrees of freedom
I want to understand if there is truly a rigorous definition for the degrees of freedom in a system. Say all of a system's physical states are contained in some set $S$. A seemingly acceptable (and I ...
2
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1
answer
565
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Why do we have redundant degrees of freedom?
Preliminaries: Consider the homogenous Maxwell's equations
$$\partial_\mu F^{\mu\nu}=0.$$
and
$$\partial_{\sigma} F_{\mu \nu}+\partial_{\mu} F_{\nu \sigma}+\partial_{\nu} F_{\sigma \mu}=0$$
Since ...
- 4,820
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2
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283
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How to know the number of constants of a free particle?
Landau-Lifshitz Mechanics says that there are $2s-1$ constants of a system with $s$ degrees of freedom (beginning of the second chapter on Conservation Laws). If this is true, for a single free ...
- 108
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174
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Equipartition theorem - concerning the square dependence of energy
So the equipartition theorem states that if the energy dependence is square
($\langle\,E\,\rangle= as^2$ + ...(something not dependent on $s$))
then each variable (degree of freedom) contributes ...
- 649
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54
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Degrees of freedom [duplicate]
Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space.
In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$
...
- 25
1
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answers
173
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Explicit counting of gauge field degrees of freedom
Consider a connection on a principal $U(1)$-bundle $A_\mu$ over the flat base manifold $M_4$. The action of the theory is described in terms of the curvatures of such connection coupled to some source ...
- 315
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2
answers
102
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Dimensionality of the quantum space of states
I don't understand what is the dimension of the space of the states because it looks different dependently on the base that I choose, for example:
If I use the position representation (the base are ...
- 1,978
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3
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90
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Constrained Curve in 3 Dimensions [closed]
I have a particle in a 3D space that moves on a curve of the function $$r(x)=\begin{bmatrix}x \\ x\sin(x) \\ \exp(x^2)\end{bmatrix}$$
I know that there must be 1 degree of freedom left thus $S = 3N-P$...
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1
answer
368
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Goldstone bosons when SSB potential has two fields
A theory consists of two complex scalar fields $φ_0$ and $φ
_1$ with a symmetry-breaking potential $$V(|φ_0|^2 + |φ_1|^2).$$ How many Goldstone particles will there be in the theory?
- 81
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2
answers
1k
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Degrees of freedom in a mechanical system
Here our professor told that the degree of freedom of the system is 2 as we just need 2 angles shown in the figure to completely specify the configuration of the system but this system with a given ...
- 53
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160
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Non-relativistic E&M Lagrangian: number of dynamical variables greater than 6
There is an argument I do not understand given in "Introduction to quantum electrodynamics" by Cohen-Tannoudji (page 111 for the French version of the book).
We are dealing with the non-relativistic ...
- 1,560
1
vote
0
answers
109
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Field degrees of freedom from equations of motion and higher spin
It is my understanding that we compute the number of degrees of freedom of a quantum field as the number of its components minus the number of non trivial equations we get by taking the divergence of ...
- 1,914
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vote
1
answer
2k
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Why we fill dU/dT value in Cv(specific heat at constant volume) only and why not in Cp?
According to equipartition of energy, the energy ossociated with each degree of freedom is $\frac{K_{b}T}{2}$ for one molecule .
For 'x' molecule which has degree of freedom f it's energy is given by ...
- 13
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166
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Can kinetic energy broken down into its components ? Even if it is scalar?
I'm confused while reading about degrees of freedom. According to what I read the number of degrees of freedom (DOF) of a monoatomic gas is 3 at low temperature. My question is: is that
1) because the ...
1
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4
answers
648
views
How is the relationship of the value $kT$ and a degree of freedom derived?
Sources that discuss the derivation of the Maxwell-Boltzmann Statistics end up with two unknown constants ($\alpha$ and $\beta$) through the Lagrange Multipliers, of which $\alpha$ is derived by ...
- 471
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69
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Query about working out the Specific heat ratio of a gas
The specific heat ratio for $\rm CO_2$ at room temperature is $1.28$ according to my tables.
Since $C_V= \left.\frac{\partial U}{\partial T}\right|_V$ and $C_P=\left.\frac{\partial U}{\partial T}\...
- 1,545
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1
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2k
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How many degrees of freedom for $\rm N_2O_2$?
From my reading, I have understood examples a diatomic molecule to be $\rm N_2$ or $\rm O_2$, however, the below seems to suggest that $\rm N_2O_2$ is also diatomic. Is this correct and can someone ...
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29
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Why don't asymmetric molecular orbitals and lone pairs in linear molecules lead to an additional degree of rotational freedom?
For example, in CO2, the molecule is linear and thus rotation about the intermolecular axis leads to an identical molecule. But if you consider the pi molecular orbitals, which are radially ...
3
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1
answer
387
views
Is there only one vacuum solution of the Einstein equations?
I am thinking about this: A vacuum solution means vanishing Ricci tensor. The Ricci tensor is a contraction of the Riemann, which itself involves contains second derivatives of the metric. Thus they ...
- 33
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1
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712
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How to determine whether a set of coordinates are independent and sufficient to determine the system completely?
In Analytical mechanics, when we formulate our principles, in general, it is assumed that we start with a cartesian coordinate system, and then find some generalised coordinates $q_j$s they are all ...
- 2,313
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4
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929
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Question about holonomic constraints
Goldstein says that when a system of $N$ particles is subject to $k$ holonomic constraints, the positions $\mathbf{r}_1, \dots, \mathbf{r}_N$ can be parameterized by $3N - k$ independent coordinates $...
user113773
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2
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88
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Why the notion of degree of freedom is correct?
The intuitional definition for number of degrees of freedom is following: it is the minimal amount of numbers which allows us to describe the system's configuration correctly.
For example, for dot ...
- 331
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2
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986
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Why doesn't a monoatomic particle have 6 degrees of freedom? [duplicate]
A monoatomic particle can move in three directions: $x$, $y$, and $z$. So the number of degrees of freedom (DOF) for translation is 3. The particle can also rotate around three axes. So the number of ...
2
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0
answers
384
views
Relation between spin degrees of freedom and the dimensions of Hilbert space
I came across a question which reads
"Suppose the spin degree of freedom of two particles (nonzero rest mass and nonzero spin) is described completely by a Hilbert space of dimension twenty one. ...
- 475
5
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2
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672
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Duality transformations, such as between a massless scalar field and the Kalb-Ramond field
There is a kind of duality transformations between antisymmetric tensor fields which I learnt from a series of lectures by Gia Dvali on quantum field theory. I have not been able to locate a source ...
- 2,646
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2
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How many degrees of freedom in a massless $2$-form field?
Consider the Kalb-Ramond field $B_{\mu\nu}$ which is basically a massless $2$-form field with the Lagrangian
$$
\mathcal L = \frac{1}{2}P_{\alpha\mu\nu}P^{\alpha\mu\nu}\,,
$$
where $P_{\alpha\mu\nu} \...
- 2,646
2
votes
2
answers
599
views
Computing the spin degrees of freedom for a massless particle in $D$ dimensions
According to the paper A Lagrangian formulation of the classical and quantum dynamics of spinning particles, a relativistic spinless particle in $D$ spacetime dimensions can be described by the ...
- 105k
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2
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696
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Degrees of freedom of gas molecules
What is the degrees of freedom of a three dimensional polyatomic molecule when only one vibrational mode is excited?
- 369
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118
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A problem on degree of freeedom?
[The problem is roughly]
Toy “Supermag” makes it possible to construct, among others, polyhedrons — e.g. tetrahedrons, cubes, and many irregular polyhedrons, where the edges
of the ...
- 181
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40
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What is degree of freedom in thermodynamics? [duplicate]
I have read a lit bit of degree of freedom in classical mechanics and hope to understand as if the number of variable used to describe a system in the configuration space. But in thermodynamics I read ...
- 181
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68
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What is the formal definition of Degree of Freedom? [duplicate]
Is the degree of freedom defined in classical mechanics same as the degree of freedom in thermodynamics?
If not what is the formal definition of degree of freedom in thermodynamics?
- 181
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2
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210
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Why does Maxwell's equations $\partial_{\mu} F^{\mu \nu} = 0$ have 3 independent components (DOF) in $D = 4$?
And how can we generalize this to the statement that it has $D-1$ independent components in dimension $D$?
I know that $F_{\mu \nu}$ has six independent components (because of antisymmetry), how do ...
- 11
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1
answer
28
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Kelvin and kinetic theory of gases
I know that the degree of freedom increase by 2 when the temperature is high and decrease by 2 when the temperature is low. A dumb question here, what temperature is considered as 'high temperature' ...
- 11
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0
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75
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Are singularities' behaviour really unpredictable?
If a real/true singularity existed our models and theories would become useless to predict what would happen in that singularity.
For example if naked singularities really existed, we could not ...
user198758
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249
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Notion of 'functional degrees of freedom' for the metric function in GR?
I have read through the numerous questions on 'degrees of freedom' in the metric tensor, and won't list them all here. However none of them address my question on 'functional' degrees of freedom in ...
- 4,067
5
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1
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268
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Why is $4=3\oplus 1$? What are propagating modes? Etc
In Schwartz's QFT book, he said that the vector representation of the Lorentz group, $V_\mu$ that is four-dimensional, is the direct
sum of two irreducible representations of $SO(3)$: a spin-0 ...
- 302
1
vote
3
answers
382
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Why does gauge invariance in electrodynamics mean that there are redundant degrees of freedom? [closed]
It is possible to choose different gauges in electrodynamics. I am familiar with two of them: Coulomb gauge and Lorenz gauge. Let us stick to the Coulomb gauge. It sets $$\nabla\cdot\vec{A}=0.$$ The ...
- 12.3k
4
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1
answer
622
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Degrees of freedom in General Relativity and well-posedness of the EFE
I would like to understand what are the degrees of freedom in GR. I have read a few previous posts already, but none of them really help me. Below, I will try to write down the entangled web of ...
- 377