All Questions
Tagged with semiclassical statistical-mechanics
19 questions
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2
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118
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Why Normalise by $h$ in the Partition Function for Classical Harmonic Oscillator?
I was wondering if anyone could explain the reasoning behind the $h$ normalization constant when calculating the partition function for a classical harmonic oscillator.
I know that the partition ...
- 31
2
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1
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62
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Intution for the physical meaning of high energy limit of a quantum states and uniform distribution in phase spacehow of a particle
Zeev Rudnick state in his talk Quantum Ergodicity for the Uninitiated (around 12 minute 40 second mark at the last text section of the slide) that a "a possible interpretation of the statement ...
- 125
1
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0
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158
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Region of validity of classical statistical mechanics
Consider the argument (attached below) from Reif for the domain of validity of classical statistical mechanics, as applied to some fixed homogeneous substance. I am confused in particular with why the ...
- 1,271
2
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0
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124
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Single particle density of states for non-free particle
I am trying to find the single particle density of states in terms of the energy, for a system with the single particle 2D Hamiltonian:
$$H=\frac{p^2}{2 m}+\alpha x \text { with } 0<y<L, x>0$$...
- 21
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152
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Response Functions in Field Theory - Subtleties?
The definitions I saw of response functions, e.g. in Landau & Lifschitz (SP Sec. 125), or in Altland & Simons (Ch.7), are given in terms of expectation values of some physical quantity $\...
- 1,657
1
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1
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363
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The connection between classical phase space and quantum multiplicity
I am aware of the relationship $N = V/h^n$ where $N$ is the quantum multiplicity, $n$ is the number of position (or momenta) degrees of freedom, $V$ is the volume of classical phase space and $h$ is ...
- 395
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22
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Quantum corrections for protons in hydrogen bonds (even at high temperatures?)
Consider a proton transfer reaction in some biomolecule at approximately room temperature. There are hundreds of examples of such reactions in enzymes, DNA, clusters of waters,... The energetic ...
- 1,264
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1
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61
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Relation of Corresponding principle and law of large numbers
Is it possible that Corresponding principle can be derived from the law of large numbers? Also is the principle a postulate of Quantum Mechanics?
- 1,688
2
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1
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772
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Volume of state in phase space free particle
I have to how a quantum state of a free particle between 0 and a occupies an area of $h$ in the phase space.
What I did was to calculate $\Delta x \Delta p$ and show that it was of order $h$, but I ...
0
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0
answers
610
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The classical limit of QM as a Hamilton-Jacobi equation?
I'am having difficulties to understand the so-called classical limit in quantum mechanics. There is a popular method to transform the Schrödinger equation into two coupled equations that are the ...
- 733
2
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2
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712
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Negative probabilities with Wigner quasi-probability distributions
I was toying with Wigner corrections to thermodynamic equilibrium. The semiclassical correction for the position probability density to second order in $\hbar$ is:
$$P(x)= \text{e}^{-\beta V(x)}\left(...
- 1,264
3
votes
2
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833
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Least action principle in imaginary time
In quantum mechanics, the amplitude of wave function propagation can be found using the Feynman's path integral
$$
\langle z'|e^{-itH/\hbar}|z\rangle=\int\limits_{x(0)=z\\x(t)=z'} Dx(t')\:
\exp\left\{\...
- 2,393
2
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0
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117
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How to rigorously take the classical limit of a thermal correlation function
I am interested in how one formally takes the classical limit of:
$$ \langle A(x_0)B(x_t)\rangle = \mathrm{Tr}[e^{-\beta \hat{H}}A(\hat{x})e^{i \hat{H}t/\hbar}B(\hat{x})e^{-i \hat{H}t/\hbar}]$$
i.e. ...
- 418
11
votes
1
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605
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Statistical path integral normalization
So I am looking at a statistical path integral, meaning that I work with an Euclidean action. The propagator of my (Wiener) path integral is given by:
$$
K(x_T,T|x_0,0)=\int\limits_{x(0)=0}^{x(T)=x_T}\...
- 3,132
2
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0
answers
59
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Non-equilibrium electronic distribution in the time-relaxation approximation - Which is the boundary condition?
In Chapter 13 of Ashcroft-Mermin - "Solid State Physics", the following non equilibrium electronic phase-space distribution for the semiclassical electrons in a periodic crystal is derived: $...
- 4,744
1
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2
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1k
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Phase space derivation of quantum harmonic oscillator partition function
I would like to derive the partition function for the quantum Harmonic oscillator from scratch:
$$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$
The free particle appears in many textbooks. $H = p^2$...
- 788
1
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1
answer
883
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Semiclassical Approximation
In many books I read about semiclassical approximation applied to the field of Bose-Einstein condensation.
But I don't understand what it really means.
For example I read that an expression like this
...
- 417
9
votes
2
answers
4k
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Bohr-van Leeuwen theorem and quantum mechanics
Preamble:
If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
- 7,400
25
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1
answer
1k
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How is the logarithmic correction to the entropy of a non-extremal black hole derived?
I`ve just read, that for non-extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that
$$S = \frac{A}{4G} + ...
- 9,691