# Questions tagged [phase-space]

A notional even-dimensional space representing all relevant states of a dynamical system; it normally consists of all components of position and momentum/velocity involved in that unique specification. Use for both classical and quantum physics.

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### Area of Phase Space and Dependence on Energy

The phase curve for a system is made for some configuration, for example - The Harmonic Oscillator. Now as we increase the energy, the phase curve enlarges i.e. area enclosed by the curve increases. ...
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### A problem understanding primary constraints meaning

I have some problems understanding the meaning of a function that vanishes weakly. As far as I can understand, when somebody writes that a function $F$ in the phase space vanishes weakly, that means ...
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### The equivalence of the Stosszahlansatz and the usual Boltzmann entropy arguments?

Question Below I show one can use the Boltzmann Stosszahlansatz to independently arrive at the Maxwell Boltzmann distribution without using the usual phase space arguments (Assuming $*$ equation has a ...
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### A rule for when phase-space orbits may cross

Note: in this question when I talk about "phase space," I will be refering to velocity vs. position space, which can also be correctly referred to as "state space." Many sources (...
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### Why is the action an adiabatic invariant in a unidimensional oscillator?

I'm reading Rax's "Méchanique Analytique" but I can't understand a particular step. We consider a unidimensional oscillator system with a potential that depends on a parameter $\lambda(t)$ ...
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### Phase space of $\phi$-Meson decay

A $\phi$-Meson can decay into an electron-positron-pair or a pair of Kaons. In which decay is the phase space bigger?
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### Classifying canonical transformation and scaling transformation

Lets assume we have a very simple transformation in 1 Dimension from $(x, p_x)\rightarrow (y,p_y)$ given as \begin{aligned} y &= cx \\ p_y &= c^{-1} p_x \end{aligned} Is this a strictly ...
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### The different generators of canonical transformations

Consider the phase space of a one degree of freedom mechanical system. We can pass from one phase space coordinates to another phase space coordinates via a canonical transformation. I want to focus ...
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### Potentials that prevent the phase flow of the system [closed]

I am trying to solve a question that my professor gave. When a particle moves in one dimension $x$ in a potential $U(x)$ , the resulting motion over a very short time interval is specified by Newton’...
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### In Hamilton-Jacobi theory, how is the new coordinate $Q$ time-independent when Hamilton's principal function separates?

Following the notation in Goldstein, the solution to the Hamilton-Jacobi equation is the generating function $S$ for a canonical transformation from old variables $(q,p)$ to new variables $(Q,P)$ ...
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### Liouville's Theorem & Flows in Phase Space for Particle in a Box

A Hamiltonian system of $100$ interacting oxygen atoms, each of mass $16$ $m_p$, is confined within a cubical box of sides $1 m$. The average initial speed of each particle is $300 ms^{-1}$. Estimate ...
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### Liouville's theorem on the tangent bundle [duplicate]

One interpretation of Liouville's theorem is the determinism and reversibility of classical mechanics, i.e. the mechanical states can't converge or diverge. The theorem is often formulated on the ...
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