# Questions tagged [mp.mathematical-physics]

Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

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### On the spectrum of fokker plank with linear drift

The paper by Liberzon and Brockett, "Spectral analysis of Fokker--Planck and related operators arising from linear stochastic differential equations." SIAM Journal on Control and ...
49 views

### Equilibrium position of $n$ free charges as polynomials roots

I asked the same question on here but received no answer. The classic problem of the electrostatic equilibrium positions of a linear system of $n$ free unit charges between two fixed charges is well ...
1 vote
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### "Classifying" causally closed sets in Minkowski space

Let $M = \mathbb R^{D+1}$ be Minkowski space. Recall that the causal complement of a set $A \subseteq M$ is the set $A^\perp \subseteq M$ where $p \in A^\perp$ there is no timelike path between $p$ ...
1 vote
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### K-finiteness of unitary representations of Poincaré-like groups?

$\DeclareMathOperator\SO{SO}\DeclareMathOperator\ISO{ISO}$I'd like to know if there are any papers that study the following problems: Determine when decomposing the unitary irreps of $\ISO(d,1)$ into ...
1 vote
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### How to numerically solve differential equations involving sines, cosines and inverses of the unknown function? [closed]

Crossposted at SciComp SE I'm very new to finite difference method and I am just introduced to methods of solving differential equation using finite difference method via sparse matrix method. I find ...
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### finding weak form of nonlinear differential equation for FEM simulation

The following is the well-known nonlinear differential equation for director's distribution at static equilibrium in liquid crystal displays(LCD). I want to obtain weak form of the given differential ...
96 views

### Solve the recurrence relation with 2 variables

We have the following recurrence relation: \begin{equation} f(n,m) = f(n-1,m) g_{\alpha, \gamma}(n,m) + f(n,m-1) g_{\beta, \gamma}(n,m) \\ g_{\alpha, \gamma}(n,m)= \sum^{n}_{i = 0} \sum^{m}_{j = 0} \...
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### Finding solutions to nonlinear wave equations with time-periodic boundary conditions (closed timelike curves)

Is it known how to solve nonlinear dispersive wave equations, such as the Klein-Gordon equation with a $\phi^4$ interaction with time-periodic boundary conditions? The motivation behind time-periodic ...
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### Express $Q_0 u + Q_1 \Delta u + Q_2 \Delta^2 u + Q_3 \Delta^3 u=0$ as a conservation law for $u(\vec x, t) : \mathbb R \times \mathbb R \to \mathbb R$

In the study of certain PDEs, it is beneficial to write them as a conservation law so that the energy of the system may be defined. More facts such as causality can be proven by considering surface ...
31 views

### Understanding the boundary condition of spherical waves in the flat spacetime

I am trying to understand one of the two boundary conditions one has to impose to find the solutions of the wave equation in the flat space-time inside a collapsing null shell. For the spherical wave, ...
31 views

### Fluctuation-dissipation theorem for Markov processes

In the context of particle systems of non-gradient types (see e.g. here, Step 2 on page 633), I recently encountered the concept of fluctuation-dissipation theorem (FDT). Since it is a major result in ...
158 views

### Physical intuition for curvature on higher order frame bundles?

$\DeclareMathOperator\SO{SO}$A priori: I apologize if this isn't up to Mathoverflow standards, I've had very little luck getting questions on this subject answered elsewhere. I'm looking for a physics ...