The phase-space tag has no wiki summary.
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What would happen if energy was conserved but phase space volume wasn't? (and vice-versa)
I'm trying to understand the relationship between the two conservation laws. As I understand, Liouville's result is a weaker condition: it relies merely on the particular form assumed by Hamilton's ...
4
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1answer
58 views
Peculiar Hamiltonian Phase space
I was solving an exercise of classical mechanics :
Consider the following hamiltonian
$H(p,q,t) = \frac{p^2}{2m} + \lambda pq + \frac{1}{2}m\lambda^2\frac{q^6}{q^4+\alpha^4}$
Where ...
3
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1answer
117 views
Phase space in quantum mechanics and Heisenberg uncertainty principle
In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state.
In my book about statistical physics ...
2
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1answer
129 views
Phase volume contraction in dissipative systems
I am confused about phase-volume contraction in dissipative systems. Please help me catch the flaw in my understanding. From a macroscopic point of view I understand that a dynamic system tends to go ...
4
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1answer
80 views
Postulate of a-priori probabilities
In Statistical Mechanics, we often postulate that for an isolated system, the phase-space density of all accessible microstates (i.e all microstates consistent with the energy) is the same. This is ...
4
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3answers
86 views
Other application of Liouville's theorem besides thermodynamics
Are there any other important practical and theoretical consequences of Liouville's theorem on the conservation of phase space volume besides the calculation of the microcanonical potential in ...
5
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1answer
208 views
Is there any uncertainty between mass and proper length or time?
I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
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0answers
33 views
Where can I find the Bohr Sommerfield condition?
I need to solve the Hydrogen Atom using the phase integral [Bohr Sommerfield Condition] but I don't know where can I find it. Help me please!
13
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1answer
181 views
Sympletic structure of General Relativity
Inspired by physics.SE: http://physics.stackexchange.com/questions/15571/does-the-dimensionality-of-phase-space-go-up-as-the-universe-expands/15613
It made me wonder about symplectic structures in ...
5
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4answers
218 views
Non-Integrable systems
Integrable systems are systems which have $2n-1$ time-independent, functionally independent conserved quantities (n being the number of degrees of freedom), or n whose Poisson brackets with each other ...
4
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3answers
281 views
number of microstates associated with two-level quantum systems
this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory
I'm trying to figure the number of simple quantum states (microstates) of ...
8
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1answer
195 views
Universality in Weak Interactions
I'm currently preparing for an examination of course in introductory (experimental) particle physics. One topic that we covered and that I'm currently revising is the universality in weak ...
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1answer
70 views
Is particle number a problem for formulating statistical physics in a mathematically rigorous manner?
Quantities like the chemical potential can be expressed as something like
$$\mu=-T\left(\tfrac{\partial S}{\partial N}\right)_{E,V}.$$
Now the entropy is the log some volume, which depends on the ...
1
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1answer
86 views
Where is the critical moment where the microcanonical ensemble enters the justification for the equilibium state?
As explained in many books, for the microscopic justification of the second law of thermodynamics (lets formulate it as the total entropy takes maximum among all possible exchanges of two systems), ...
4
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3answers
182 views
What are some mechanics examples with a globally non-generic symplecic structure?
In the framework of statistical mechanics, in books and lectures when the fundamentals are stated, i.e. phase space, Hamiltons equation, the density etc., phase space seems usually be assumed to be ...
2
votes
4answers
236 views
Books on Hilbert space and phase space?
Can you recommend books or papers that highlight or discuss extensively, or at least more than average, the similarites/differences between phase space and Hilbert space? I am primarily interested in ...
3
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2answers
178 views
Why doesn't phase space contain acceleration/forces?
I'm watching some Physics lectures on the internet by Leonard Susskind:
http://www.youtube.com/watch?v=pyX8kQ-JzHI&feature=BFa&list=PL189C0DCE90CB6D81&lf=plpp_video
In this lecture, and ...
0
votes
2answers
264 views
Phase space of a discrete dynamical system
Suppose a dynamical system of one variable $x$ with discrete time-steps. I've seen in some papers a type of graph in which $x(n+1)$ is plotted versus $x(n)$.
My questions are :
1/ Can this be ...
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0answers
139 views
What does it mean for a phase space trajectory to be “long” and “stable”?
What does it mean for a phase space trajectory to be "long" and "stable"?
I understand the concept of a trajectory in phase space but not how these adjectives can be applied to one.
Thanks.
