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Fermi-Dirac Statistics

In Fermi-Dirac statistics the probability of being in a certain energy state is $$f(E) = \left[1 + \exp\left(\frac{E-E_F}{k T}\right)\right]^{-1}$$ In the area that I'm looking at the texts always ...
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1answer
93 views

Random walks on resistive network

I have been referring to a paper http://arxiv.org/abs/physics/0405135 to determine the effective resistance using random walks for an infinite square resistive lattice Though the author seems to ...
2
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1answer
101 views

Probability density of detection of collinearly emitted photons in two detectors

Update: As proposed by @dmckee, I added equation numbers and improved the display of some equations. The answer by @Trimok inspired me to look at coordinate systems which are not specific to the ...
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1answer
37 views

Proof of Liouville's theorem: Relation between phase space volume and probability distribution function

I understand the proof of Liouville's theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of ...
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1answer
47 views

What do matrices in the Gaussian orthogonal ensemble look like?

I've been reading a fair amount about quantum chaos, and random matrix theory comes up a lot. I get that they're looking at the distribution of eigenvalues from an ensemble of random matrices, but I ...
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1answer
252 views

Fermi's golden rule and Probabilities in QM

In Fermi's golden rule $$P_{ab}(t)=2\pi t/\hbar \left|\langle\psi_b|V|\psi_a\rangle\right|^2 \delta(E_f-E_i)$$ for transition probability from state $a$ to $b$, how can the probability grow with ...
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0answers
37 views

Help with deriving an asymptotic expression

Note: I don't know if this is the best place for this question, because it is very specific. However, I'm not sure of a better place to go (apart from one of the other SE's). If you have a ...
4
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0answers
215 views

Electron hopping among molecules - Marcus equation

I'm running out of professors to talk to, and I need to clarify a couple of things for the sake of making a realistic model of electron travel through a mesh. This is about calculations of electron ...
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0answers
87 views

Are frequency and likelihood the same across the multiverse?

My probability text distinguishes between two interpretations of probability values: the frequency of occurrence "as percentage of success in a moderately large number of similar situations" (coin ...
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0answers
67 views

Probability density of Klein-Gordon equation

This may, perhaps, stir some healthy debate; at least I am having some "fun" thinking about it, hopefully I can solicit some outside views too. It is often regarded that the Klein-Gordon equation ...
2
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0answers
62 views

Reference for stochastic processes which helps moving from a basic level to a measure theory one

I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains). I've ...
2
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0answers
60 views

Statistical Mechanics: Most probable orientation of grain particle in gas chamber?

I'm in an introductory statistical mechanics course, and we've been posed the following situation: Long-shaped dust particle (so imagine something like a grain of rice) is placed in a gas chamber (so ...
2
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0answers
83 views

How to explain Tsirelson's inequality using extended probabilities?

How to explain Tsirelson's inequality using extended probabilities? Some people have tried explaining the Bell inequalities using extended probabilities. For instance, a pair of entangled photons ...
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0answers
47 views

Probability and the propagator

Due to the Wiki article, "...In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to ...
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0answers
49 views

tritium beta decay - probability of being in 1s state

Hydrogen-like wavefunctions have the form: $$R_{10} = \left(\frac{Z}{a_0}\right)^{\frac{3}{2}} 2\space e^{-\frac{Zr}{a_0}}$$ $$Y_{00} = \frac{1}{\sqrt {4\pi}} $$ where $a_0 = \frac{4\pi \epsilon_0 ...
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0answers
39 views

Deriving probability distributions from the Wigner distribution

I know that I can calculate the probability distributions of $x$ and $p$ from the Wigner quasiprobability distribution, and I can calculate the probability distributions of other operators by ...
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0answers
47 views

Quantum Rigid Rotor Perturbation

As the title says, I have a rigid rotor with a perturbation given below $$H=\frac{L^2}{2I}-\alpha B L_z.$$ So I know that the eigenvalues of $H$ will be $\ell(\ell+1)/2I -\alpha B m$ where $m$ is our ...
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0answers
67 views

Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
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0answers
70 views

Equivalence of simple formulations of qubit entanglement

I'm reading some very elementary treatments of quantum computation and am unsure about the correspondence among "definitions" of qubit entanglement. One definition states that (1) the bits of a ...
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0answers
56 views

Modeling the probability of a photodiode measuring photons targets at a neighbor

In current digital cameras, sensors are arrays of photodiodes which "transform" photons energy to electrons. I am aware that the probability of a photon to generate an electron is modeled by a Poisson ...
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0answers
58 views

Quantum mechanics and probability

I've done an intro course on QM and I'm now hoping to understand exactly how to use probability theory rigorously in solving problems. My question is: How do I do the same thing, or the closest thing ...
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0answers
24 views

Stochastic process corresponding to Schrödinger evolution

In probability theory, the Fokker-Planck equations governs the trajectory of a sample path of a stochastic process -- say the heat equation in the case of a Wiener process. Consider a Gaussian ...
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9 views

Conceptual questions about chaotic signals

Are chaotic signals stationary or non stationary signals? They are ergodic and ergodic signals are a kind of stationary signals. But, from statistics point of view, are chaotic signals classified as ...
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0answers
36 views

Measurement of the amplitude

I want to ask how do we actually measure the probability amplitude that appears in Schrödinger equation. From what I read in quantum mechanics textbooks, it appears that after the measurement, the ...
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0answers
27 views

How do I overlap this two-particle symmetric wavefunction?

Suppose we have a symmetric wavefunction that composed of a two-particle system: $$ \psi_s = \frac{1}{\sqrt 2} \left(|u,A\rangle|v,B\rangle + |v,A\rangle|u,B\rangle\right)$$ where $u_{(x)}$ and ...
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57 views

Notation for Propability Amplitudes

I've recently stumbled upon a certain piece of notation that doesn't quite seem clear to me. When discussing the amplituhedron, my teacher mentioned the relation between the volume and the amplitude ...
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0answers
50 views

What is the probability that all the air ends up in the upper right corner of the room and we suffocate

Since someone commented this on this question(What is the probability of ice in boiling water?), I would like to ask what is the probability that all the air ends up in the upper right corner of the ...
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0answers
81 views

How to use The Schwarzchild Metric formula to get distribution representing “free-fall”

Given formula: How I can use to calculate distribution of points in space, so if i choose path which contains most of the points I get path that close to "free-fall path". As far as I know i should ...
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0answers
63 views

The meaning of $p_{i}$ and $\rho^{i}$ as probabilities and densities in Quantum Mechanics

The question I have concerns the actual meanings of $p_{i}$ and $\rho^{i}$ Now $p_{i}:Meas_{I} \times D(H) \rightarrow [0,1]$, so for a particular set of Measurement matrices M and Density matrices ...