Questions tagged [probability]

For questions about probability, probability theory, probability distributions, expected values and related matters. Purely mathematical questions should be asked on Math.SE.

160 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
14
votes
0answers
257 views

Renormalisation and the Fisher-Rao metric

The renormalisation group (I'm talking about classical, statistical physics here, I'm not familiar with field theory too much) can be though of as a flux in a space of possible Hamiltonians for a ...
8
votes
0answers
661 views

How is conditional probability handled in quantum mechanics?

In ordinary probability theory the conditional probability/likelihood is defined in terms of the join and marginal likelihoods. Specifically, if the joint probability of two variables is $\mathcal{L}(...
7
votes
1answer
511 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by $f(x)=\left|\psi(x)\right|^2$....
5
votes
0answers
38 views

“Synchronization” Probability of Multiple Waves with Varying Frequencies

Update 1: I've done some digging and I think this is related to signal coherence, namely, that I'm seeing a coherence time of ~3 σ, which is consistent with the definition where Ct=1/Δv where Δv is ...
5
votes
0answers
102 views

What properties would a physical biased die have?

Imagine a physical biased six-side die. How much and what kind of bias we could possibly introduce by moving it's center of mass? What would be the exact mechanism describing the relation of center of ...
5
votes
0answers
328 views

Free probability in Physics

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with ...
5
votes
0answers
2k 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 ...
4
votes
1answer
56 views

Ehrenfest theorem and correlation among observables at the quantum scale

I am studying quantum mechanics and I encountered the famous Ehrenfest Theorem, which states that given an observable $A$, its expectation value time evolution is governed by $\partial_t\langle A\...
4
votes
0answers
120 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
votes
0answers
134 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 ...
4
votes
0answers
313 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 ...
3
votes
0answers
41 views

What do marginalised or marginalised error mean? Contours and posterior

I am curently working on Forecast in cosmology and I didn't grasp very well different details. Forecast allows, wiht Fisher's formalism, to compute constraints on cosmological parameters. I have 2 ...
3
votes
1answer
61 views

How to evaluate the probability when a particle is detected?

Everyone knows the standard probability interpretation of the quantum mechanics. For example, the wave function of some particle at some time $t$ is $\psi (x,t)$. Therefore, if the particle is ...
3
votes
0answers
46 views

Is there an open quantum system analogue of the equilibration time bounds for classical ergodic Markov chains?

Background For classical ergodic discrete Markov chains, we can bound the time taken to reach the stationary distribution to the spectral properties of the transition matrix. I will outline this ...
3
votes
1answer
142 views

In statistical mechanics, why do we consider number of states of a system in energy interval?

In statistical mechanics,when we go for calculating the no. of accessible micro states of a system, I notice that we always calculate the no. of micro states of that system in some energy interval say ...
3
votes
0answers
64 views

A proof for this equivalent version of the Infrared Bound/Gaussian Domination

Consider the Ising Model in the $d$-dimensional discrete torus with side lengh $L$, denoted by $\mathbb{T}_L $, with nearest neighbors interaction (with interaction parameter $J$, no magnetic field, ...
3
votes
1answer
329 views

Cosmological fluctuations: what is gaussian?

When we are speaking about gaussianity and non-gaussianity in a cosmological context, what is gaussian or non-gaussian in the CMB? What would a non gaussian CMB look like compared to a gaussian one? ...
3
votes
0answers
168 views

What can I expect to see in a oscillator exhibiting bifurcation?

I have a program which aims to simulate a Josephson Bifurcation Amplifier. I am currently trying to obtain a plot of the probability of bifurcation as a function of the ratio between the driving and ...
3
votes
0answers
110 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 ...
3
votes
0answers
201 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 ...
2
votes
1answer
49 views

Inequality for quantum probability

Let $H$ be a separable Hilbert space for a quantum mechanical system then $$w (x, y) = {{\langle y \mid x\rangle\langle x \mid y \rangle} \over \langle x \mid x \rangle\langle y \mid y \rangle}$$ is ...
2
votes
0answers
34 views

List of Replica Symmetry results for different models?

Does anyone know of a good source that might have a list of problems or models along with what kind of replica symmetry they are conjectured to have? I am aware of some of the more famous results, e....
2
votes
0answers
36 views

Calculating the probability of one particle being in a certain state in two-particle system

Let's say I have the two-particle state $$|\psi\rangle=\frac{|H\rangle_a|H\rangle_b+|V\rangle_a|V\rangle_b}{\sqrt{2}}$$ where $H$ is horizontally polarized and $V$ is vertically polarized. And I ...
2
votes
1answer
31 views

Probability of a system in the canonical ensemble

In the canonical ensemble, we have the state of system $x_s$ and the state of the environment $x_e$. The probability of the total system is $$P(x_s,x_e)= const.$$ and that is independent of the states ...
2
votes
1answer
55 views

Finding total flux of probability current through a sphere

For a wavefunction: $$\Psi(\textbf{x}) = e^{ikz} + \dfrac{f(\theta)}{r}e^{ikr}$$ Where $z = r\cos(\theta)$. The probability current $J$ is then given by: $$J(\textbf{x}) = J_1(\textbf{x}) + J_2(\...
2
votes
0answers
51 views

Probability at temperature in system has energy

Salutations, I'm starting in statistical mechanics and reviewing some related studying cases I would like to understand what occurs in small systems with normal modes of vibration, for example, a ...
2
votes
0answers
30 views

Discrepancy regarding Husimi Probability distribution calculation

I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state. To carry out the projection onto coherent states I have proceeded ...
2
votes
0answers
100 views

Time and Quantum Mechanics

my question is about the nature of time across classical/macro and quantum scales. I understand that the 2nd law of thermodynamics and entropy increase has a lot to do with our understanding of time ...
2
votes
0answers
50 views

given an AC field, how many photons are there?

Say you are applying a time varying potential across double quantum dots in the form of $V_{ac}$cos($2\pi f t$). We know that each photon has an energy $E_{photon}= hf$. Is it correct to say that ...
2
votes
1answer
46 views

Particle ensemble performing shm, calculate amplitude pdf

Consider the shm for a single particle. Then the particle's position is given by (assume zero initial phase): $$x = a \times \sin(\omega t)$$ The infinitesimal probability of finding a particle ...
2
votes
0answers
243 views

Shift a Galton board's distribution by manipulating pegs

My question is related to this one but is simpler and more specific. It's also related to this this question which doesn't answer my question. In a standard Galton board, balls are dropped onto a ...
2
votes
0answers
66 views

Reconstruct quantum state from probabilities

Given a quantum state, the Born rule lets us compute probabilities. Conversely, given probabilities, can we reconstruct the quantum state? I think the answer is almost trivially positive but how ...
2
votes
0answers
94 views

Does Bell's theorem have anything to say about the locality or realism of Quantum Mechanics?

In the original paper written by Bell, it's clear to me that what he's really trying to answer is what class of Classical Theories (that obey the laws of classical probability theory) can replicate ...
2
votes
0answers
306 views

Probability density to find the end of a double pendulum

Given infinite time, is there a way to find the probability to find the end of a double pendulum at a given position? I am looking at a system with no damping (constant energy). The bobs are point ...
2
votes
1answer
187 views

Normalized probability distribution from the Coulomb/Rutherford scattering amplitude?

My question appears elementary, but I have been pretty vexed trying to answer it precisely. Can one use the Rutherford/Coulomb scattering amplitude to get a finite, normalized momentum-space ...
2
votes
0answers
225 views

Examples of “Ordered state from disordered state”

A thought experiment - Imagine two containers joined to each other with a stopcock between them. One container initially has only two molecules of a gas and other is empty. Now, if we open the ...
2
votes
0answers
179 views

Is 'interpretation' in quantum mechanics the same as 'interpretation' in probability?

I heard all 'interpretations' of quantum mechanics give exactly the same answer to every measurement so they are all equally correct. Is that the same 'interpretations' as in probability? Context: ...
2
votes
0answers
119 views

Interpretation of Characteristic function of probability density function for a classical system

Can the characteristic function ( fourier transform ) of a probability density function in position space for a classical system be related to its momentum space probability density function in any ...
2
votes
0answers
210 views

Why are isoprobabilty contours circles for uncorrelated functions and ellipse for correlated functions? Kindly explain.

I would like to know how to understand these and to learn how to go from a scatter plot to the isoprobabity contour plots. Thanks is advance!
2
votes
0answers
92 views

Measure-theoretic maths behind Born's probabilistic interpretation of Schrodinger's equation

I was reading a bit about Quantum Mechanics, Schrodinger's equation and its probabilistic interpretation (found this very insightful intro here https://plus.maths.org/content/schrodinger-1), my ...
2
votes
1answer
71 views

Any fractal physical model that generates time series which demonstrate heavy-tailed (non-Gaussian) behavior in some form?

I know that fractal structures have power-laws in various forms "hidden" in them. I am looking for the most simple fractal model that I can find that generates time series with, say, Pareto-...
2
votes
0answers
132 views

Applicability of perturbation theory

Consider some system in some initial state $|k^{(0)}\rangle$. The probability that such a state makes a transition to some other state $|m^{(0)}\rangle$ can be computed to various orders in time ...
2
votes
0answers
275 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 ...
2
votes
0answers
3k views

Finding the probability that a $1s$ electron in ${}^3$H remains in the $1s$ state after beta decay to ${}^3$He with the sudden approximation

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 \...
2
votes
0answers
576 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 ...
2
votes
0answers
99 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 ...
1
vote
0answers
45 views

The PDF obtained through diffusion equation turns out to be negative for some values?

I am trying to find out the probability density function (PDF) of diffusive molecules in a rectangular closed environment with one reflecting and rest absorbing walls. I am using the equation: $$\frac{...
1
vote
0answers
38 views

Analytical solution to damped harmonic oscillator - Fokker-Planck equation

In the paper "Numerical solution of two dimensional Fokker-Planck equations" (available at: https://doi.org/10.1016/S0096-3003(97)10161-8), the authors quote an analytical solution to the damped ...
1
vote
0answers
49 views

How does $H^2$ effect on the probability of photon detection?

Lets consider an electromagnetic wave, between two ideal conductive plates. Maxwell's theory predicts appearance of a standing waves(of $\textbf{H}$ and $\textbf{E}$), at that nodes($\textbf{E} = 0$)...
1
vote
0answers
39 views

Converting a discrete statistical energy distribution to a continuous version

The probability of finding a particle at a particular energy level when energy is considered discrete is according to Boltzmann: $$P(E_j) = \frac{g_j\cdot e^{-\beta E_j}}{\sum_{j=1}^\infty g_j \cdot ...