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Derive partition sum for ideal gas (sum to integral)

Having the grand canonical partition sum: $$\mathrm{Z} = \sum_{\{n\}}\exp{\left(-\beta \{\varepsilon_n(N_n) -\mu\,N_n\}\right)}$$ how to arrive at: $$\mathrm{Z} = \sum_{N = 0}^{\infty} \dfrac{V^N}{h^{...
Leon's user avatar
  • 428
0 votes
1 answer
51 views

Statistical proof of the principle of least action

In statistical thermodynamics we can prove that the evolution of a system minimises some potential with units of energy (e.g. energy). This can be done purely statistically, by using the first two ...
pll04's user avatar
  • 77
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0 answers
22 views

Mean first passage time (MFPT)

I want to know the mean first passage time (MFPT) on a unit interval for two boundary conditions (please see attached figures a and b for your reference). This is in the context of the hydrodynamic ...
Curiosity's user avatar
-1 votes
0 answers
30 views

Is inside the eye of hurricane safe? [closed]

According to the pressure and velocity diagrams of a hurricane, can we say that inside the eye of the hurricane is somewhere safe?
Mohammad Javanshiry's user avatar
1 vote
1 answer
65 views

Would a black hole instantly form when a neutron star slips below the phantom event horizon?

So lets say we have a neutron star that is just few inches away from the phantom horizon and only needs 500 kg before collapsing. So lets say hypothetically that a ship that is designed to survive the ...
Milton the Cat's user avatar
1 vote
1 answer
32 views

An explicit form for the co-BRST operator?

Take a theory with 1st class constraints $M_{\alpha}$. We gave ghosts $c^\alpha$ and their conjugates $b_\alpha$ for every constraint. The BRST operator $\Omega$ has ghost number $+1$ and has an ...
dennis's user avatar
  • 459
0 votes
1 answer
40 views

Why electric potential at each point in a uniform electric field is not same?

why potential at any point in a uniform electric field is not same i.e. why potential difference between any two points in the uniform electric field is not zero? According to me if i bring a test ...
Sukriti Sharma's user avatar
0 votes
2 answers
45 views

Conservation of energy when 2 unequal forces are acting on a body [closed]

How will energy be conserved if two unequal and opposite forces (force1 &force2) are acting on a body, and the net force led the body to be displaced? What is the work done by force1 and force2 (...
Ali Hammad's user avatar
1 vote
2 answers
45 views

Moment of inertia of hollow body and solid body

I read in my textbook about the various results of moment of inertia for different geometrical shapes like solid and hollow cylinder, sphere, disc and ring etc. Something general I noted is that $M.I$ ...
Sarban Bhattacharya's user avatar
1 vote
3 answers
70 views

ELi5- How do pions hold nuclei together if they are so short-lived?

I need help understanding how particles do what they do and maintain the structures they maintain if so many of them exist for such a short time? In the case of the nucleus and pions, pions only exist ...
blacktopshaman's user avatar
3 votes
2 answers
63 views

Why is the alpha particle beam in the Rutherford experiment not affected by the electrons?

The force exerted by the nucleus on the alpha particles is electrostatic in nature. So, why does mass has an effect? How do we conclude that the electrons don't effect the alpha particles from the ...
Niladri Sarkar's user avatar
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0 answers
12 views

How is the specific impulse of a gridded ion thruster derived?

How is the specific impulse of a gridded ion thruster derived? I've searched and got a variety of answers and Bard gives a different answer each time I ask it. Too the best that I can reckon it's: 1/9....
Richard's user avatar
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0 answers
20 views

$6\times 6$ linearly independent matrices for Hamiltonian fourier expansion

I want to use the Slater-Koster method to Fourier expand a $6 \times 6$ Hamiltonian and for this, I need 36 linearly independent basis matrices. In two dimensions, we use Pauli matrices, and in 4 ...
Ali Rayat's user avatar
-1 votes
2 answers
93 views

Is signal photon independent of idle photon in Delayed Choice Quantum Eraser?

--The experiment of Kim et al. (1999) I want to know whether anything we do to the idler photon affects the landing position of the signal photon on the screen at $D_0$ in the Delayed Choice Quantum ...
Duke William's user avatar
-1 votes
0 answers
19 views

Solving a set of DE in any method, boundary conditions at $\rho\rightarrow -\infty$ [migrated]

I want to solve the following set: $$ y'(\rho) = y(\rho)*g'(\rho)+a $$ $$ f'(\rho) = -\frac{1}{a}*y(\rho)*f(\rho) $$ $$ g'(\rho)=-y(\rho)*\left[\frac{1}{a}f(\rho)^2 +a\right] $$ with the condition of $...
user897529's user avatar
1 vote
1 answer
30 views

Does off-shell graviton in 3+1D still have two degree of freedom?

In general relativity, on-shell spin 2 graviton has 2 degree of freedom in 3+1D due to gauge symmetry, which is because of einstein equation, however, for off-shell graviton, does it still have 2 ...
feng lin's user avatar
  • 509
2 votes
0 answers
34 views

The difference between $E-k$ diagram and simplified Energy band digram

I know form the the Kroning-Penny Model the $E-k$ diagram solution which something like this or like this but While dealing with semiconductors we always draw this energy band diagram My question ...
amin's user avatar
  • 525
0 votes
0 answers
28 views

Can Newton’s system of particles be used to solve this constrained motion? How? [closed]

Thanks the picture from quora. No friction on pulley. I would like to know how to solve detailly with the Cartesian coordinate and vectors clearly.
Kanokpon Arm's user avatar
0 votes
2 answers
65 views

What happens to those parts of the amplitude that are not inside the black hole? [closed]

Assuming that a sinusoidal wave with an amplitude a million times bigger than the diameter of a black hole enters a black hole, what happens to those parts of the amplitude that are not inside the ...
dsa's user avatar
  • 1
0 votes
0 answers
40 views

Why does the transverse delta function appear in the definition of the free photon propagator?

I'm working on the coupling of electron and photon kinetics in the non-equilibrium Green's function formalism. When modeling such a systems, something you encounter are the non-interacting propagators ...
vetschn's user avatar
1 vote
0 answers
34 views

Wald: 2-dim Covariant Derivative for Null Hypersurfaces

On pp. 221-222, Wald introduces the 2-dim "hatted" manifold of null geodesics. He moves from 9.2.30 to 9.2.31 and he is allowed to do so because the tensors have the special properties that ...
mster8390's user avatar
0 votes
0 answers
30 views

How to derive the general Horndeski's action?

I have seen that Horndeski's theory can be written in terms of an action as : $$ S\left[g_{\mu \nu}, \phi\right]=\int \mathrm{d}^4 x \sqrt{-g}\left[\sum_{i=2}^5 \frac{1}{8 \pi G_{\mathrm{N}}} \mathcal{...
guizmo133's user avatar
0 votes
0 answers
67 views

Schrödinger equation is also not exact/breaks down? [closed]

we know for sure that Maxwell's equations are incorrect in detail - the model only works in the classical limit and linearised approximation. Deviations from it are experimentally known. My question ...
Mantu Das's user avatar
3 votes
1 answer
58 views

The relation between $F^2=f_{\mu\nu}f^{\mu\nu}$ and $H^2=H_{\mu\nu\lambda}H^{\mu\nu\lambda}$

there are two papers https://arxiv.org/abs/hep-th/0411105 and https://arxiv.org/abs/hep-th/9406216. What is relation between the $H^2=H_{\mu\nu\lambda}H^{\mu\nu\lambda}$ in the second paper and $F^2=...
mina ahmadi's user avatar
9 votes
2 answers
1k views

Reverse blood flow in an IV

When the IV drip for a patient is completed, the patient's will flow back. This is apparently due to the pressure difference. However, IV needles are inserted into veins in the direction of blood flow....
Starlight's user avatar
  • 245
2 votes
3 answers
96 views

Shouldn't Electric Potential energy be $U=2kQq/r$?

Let's take 2 charges $Q$ and $q$ a meter apart. Say you want them to collide. You'll have to apply force $F$ on charge $q$ (which I know is changing with distance). I know we integrate this force and ...
Maddy's user avatar
  • 31
2 votes
0 answers
42 views

Deriving the FLRW metric from the cosmological principle?

I was reading some notes (page 10/54 of pdf or page 214 of document) which state: A more formal approach to the derivation of the spatial FLRW metric from the cosmological principle starts with the ...
More Anonymous's user avatar
0 votes
3 answers
50 views

Is it possible for a single torque to rotate a sphere of uniform density at rest from one arbitrary orientation to another?

If I had an object at rest in some arbitrary rotational position, is it possible to apply a single force to it in order to rotate it to a second rotational position? This would be assuming the object ...
Patrick McCaffrey's user avatar
0 votes
1 answer
36 views

Light wave/photon doppler effect

So I understand the explanation/derivation of doppler effect from the perspective of wave crests emission being stretched out as the source moves. But how does this work from the photon point of view? ...
ABC's user avatar
  • 141
0 votes
0 answers
13 views

Sky coverage plot using Python/Astropy

I want to recreate a plot where the area that is not visible from a certain point on earth (latitude and longitude) trough a full year. An example of this plots for example can be: Where in white is ...
Euler's user avatar
  • 479
0 votes
2 answers
53 views

Proving that $y$-component of the electric field of a uniformly charged ring is zero without using symmetry

It seems this case is always worked out by means of symmetry in standar Physics textbooks: arguing that for any two opposite segments in the ring, their perpendicular electric field components cancel ...
MazapanDeKilo's user avatar
0 votes
1 answer
31 views

Hamilton's Principle extended to deal with non-conservative forces [closed]

I have seen both authors stating that there is an extension of Hamilton's Principle to systems with non-conservative forces, and others stating that there is no variational principle available for ...
jvf's user avatar
  • 235
0 votes
1 answer
24 views

SETI: Are there holes in the EM spectrum that are quiet enough to communicate at decently large distances?

So this is a variant of this other question. I know stars are big, they radiate a lotta energy, they have spectral lines. But how dense are these spectral lines and is there a noise floor at ...
robert bristow-johnson's user avatar
2 votes
1 answer
106 views

Derive 2d wave equation on a membrane: why my result is wrong?

I am trying to derive the 2d wave equation on a membrane. Instead of considering a small $\Delta x\times \Delta y$ rectangle around $x_0$, I consider a small circle with radius $r$ around $x_0$. But I ...
user112758's user avatar
0 votes
0 answers
31 views

How does strong nuclear force hold hydrogen vs xenon? does the strong nuclear force have variable distance? [closed]

My understanding is that the strong nuclear force holds the protons and neutrons together as well as the surrounding electrons. give too many electrons and it becomes an unstable isotope due to ...
Franklin Montez's user avatar
0 votes
1 answer
50 views

Equating 2 sides of EFE

Can we say if the covariant derivative is zero, the partial derivative is also zero because locally covariant derivative reduces to partial derivatives (since locally spacetime is flat)? Because, in ...
Nayeem1's user avatar
  • 715
1 vote
1 answer
38 views

Does the formula $ V =\omega r$ holds in angular frequency

$ V =\omega r$ can I use that formula if $\omega$ is angular frequency instead of angular velocity? V is velocity
SirMrpirateroberts's user avatar
2 votes
0 answers
37 views

QED theta term as pullback of a volume form

The well-known QED theta term is $S_\theta = \frac{\theta}{4\pi} \int d^4 x F \wedge F $ where $F=dA$ is the field strength 2-form. Altland and Simons (p.547) introduce a more general category of $\...
catalogue_number's user avatar
0 votes
0 answers
25 views

Are excited states broader?

Consider the 1D Schroedinger equation with some potential $V(x)$. Let the ground state $\psi_0$ be centered around $x = 0$. If $\psi_1$ is the first excited state, is it true that for all potentials $$...
K. Sadri's user avatar
  • 232
-1 votes
0 answers
43 views

Could Dark Matter have negative pressure?

Is it possible for dark matter to have negative (but negligible) pressure? How small should it be to fit with observations? Dark matter pressure is actually known and measured?
Antonio Peña's user avatar
3 votes
0 answers
43 views

Renormalizability of massless Gross-Neveu theory

We have the following Lagrangian density: $$ \mathcal{L} = \bar{\psi}_i i \gamma^\mu \partial_\mu \psi_i + \frac{g^2}{2} \left( \bar{\psi}_i \psi_i \right)^2 $$ which corresponds to the two-...
MicrosoftBruh's user avatar
3 votes
4 answers
196 views

On the non-quasistatic transfer of heat

Suppose we have two bodies at different temperatures, and we let them interact thermally in such a way that the process is not quasistatic (e.g. two different metal spheres touching). Do we arrive at ...
EE18's user avatar
  • 942
0 votes
0 answers
15 views

In non-metals, does low specific heat capacity correlates with good thermal conductivity and vice versa?

As i understand, when heat transfers by conduction, there are two main mechanisms that can take place: either by the vibrations of the lattice (mostly non-metals) or with the movement of free ...
CaptainAmerica Whyso's user avatar
0 votes
1 answer
38 views

Dependence of Klein-Gordon solution only on spatial coordinates

I am studying QFT with the Peskin and Schroeder textbook, and I am new to this area of physics. I'm struggling with the solution of the Klein-Gordon equation using Fourier integral as a continuum set ...
Andrey's user avatar
  • 11
1 vote
1 answer
24 views

Which dimensions do self-dual even Lorentzian lattice exists?

I am reading page 499 of Peter West's Introduction to Strings and Branes where he stated 'Self-dual even Lorentzian lattices only exist in dimensions $8n+2$, $n=1,2,...$, the simplest such lattice is ...
Rescy_'s user avatar
  • 639
1 vote
1 answer
36 views

Determining the location of light receivers using signals propagating in anisotropic media

Problem. I have a set of $16$ light receivers with entirely unknown locations, and a pair of light transmitters with exactly known locations. One light transmitter is stationary, and located near to ...
MomentumEigenstate's user avatar
0 votes
1 answer
58 views

Why should this thermodynamics problem be indeterminate?

Callen asks us to consider the following A cylinder of length $L$ and cross-sectional area $A$ is divided into two equal-volume chambers by a piston, held at the midpoint of the cylinder by a ...
EE18's user avatar
  • 942
2 votes
1 answer
52 views

Why is sequential Stern-Gerlach experiment a complete surprise?

In page 5 of his Modern QM , Sakurai block $S_z-$ from first S-G experiment and sends $S_z+$ atoms to next S-G experimen in $x$-direction. Then sends the result of second experiment to third S-G ...
moshtaba's user avatar
  • 1,169
0 votes
0 answers
8 views

Viability of generators and electromagnetics based solely on ionic liquids

The background to this question lies in the science fiction novel "The Day the Machines Stopped" by Christopher Anvil (1964), where somehow an experiment gone wrong causes the laws of ...
Ron Kaminsky's user avatar
-2 votes
0 answers
40 views

Why Tree branches only grow "upwards"? [closed]

Here is a Tree This is a genuine questions. Sunlight may not be the reason. Pika-chu!!!
Pika-Chu's user avatar

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