# Tagged Questions

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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### How can we define the distance for a pair quantum states in phase space?

In condensed matter physics, we know that two degenerate ferromagnetic ground states $|\uparrow\uparrow ...\uparrow \rangle$ and $|\downarrow\downarrow...\downarrow\rangle$ are far from each other in ...
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### Confusion about the use of the term “Phase Space” in Strogatz text

I've just started learning about Hamiltonian mechanics, and from the definition given in Taylor's classical mechanics, phase space must always have an even dimension. However, I recall from reading ...
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### Wigner functions, symmetry

I'm trying to get more insight into quasiprobability distributions, as for example the Wigner function. There are some Wigner functions, which are symmetric. Symmetric: Fock state Thermal states ...
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### Density of states of classical harmonic oscillator in phase space

Since all classical harmonic oscillators are ellipses in phase (position-momentum) space, and since the entire phase trajectory of a given system (with a fixed rigidity and mass factor) can be ...
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### When is an attractor meaningful?

Iâ€™m originally a computer scientist; so I hope my question is not trivial. Iâ€™m working with time series and want to reconstruct the phase space from the time series based on time-lagged versions of ...
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### Why Liouville's theorem is obvious?

In Florian Scheck's Mechanics, he stated the local form of Liouville's theorem as follows: Let $\Phi_{t,s}(x)$ be the flow of the differential equation $$-J\frac{d}{dt}x=H_{x}.$$ Then for all $x,t,s$ ...
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### Motivation for covariant phase space

The covariant phase space idea, in one sentence, is that there is a natural symplectic structure on the space of the classical trajectories of a system and that the usual $(q,p)$ coordinates just ...
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### How to show period is defined by $T=dS/dE$ (V.I. Arnold Mathemtical Physics)
I'm looking at a book by VI Arnold on mathematical physics and I've hit a roadblock pretty early on. I'll quote the question: "Let $S(E)$ be the area enclosed by the closed phase curve ...