The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
3
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0answers
26 views
Lattice model completely constrained by boundary data
I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
2
votes
1answer
58 views
NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms
From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
1
vote
2answers
57 views
Energy dependent Maxwell-Boltzmann distribution
I'm having a bit of a problem figuring out the energy dependent Maxwell-Boltzmann distribution.
According to my book (Ashcroft & Mermin) they write the velocity dependent distribution as:
...
2
votes
2answers
56 views
What is the derivation for the exponential energy relation and where does it apply?
Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an ...
4
votes
3answers
161 views
Definition of entropy
In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
2
votes
0answers
38 views
What is the minimum non-integer dimension for which the XY model shows a phase transition? (if well-defined)
I know that XY statistical model for $d=2$ doesn't show a regular phase transition , while the $3d$ has, I was wondering what is the behaviour for $2< d < 3$.
If it is simpler one could ...
4
votes
2answers
77 views
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 ...
1
vote
4answers
84 views
The Preference for Low Energy States
The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been ...
2
votes
0answers
63 views
Ising Hamiltonian for relativistic particles
An Ising system is described by the simple Hamiltonian:
$$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$
Here the $x_i$ are spins (+1 or -1 in units ...
3
votes
4answers
187 views
If particles can find themselves spontaneously arranged, isn't entropy actually decreasing?
Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
1
vote
1answer
67 views
What is the interface tension between ordered and disordered phases of the Potts model?
I read in these papers(1,2) the concept of interface tension. I can't understand its definition. I can hardly imagine there is some tension in a model. Any help will be appreciated.
2
votes
1answer
40 views
Temperature of a small system
What is wrong if I define temperature of a small system (I mean, a system which has not a large number of particles) by
$$1/T = dS/dE$$
?
3
votes
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 ...
4
votes
2answers
83 views
Independent systems and Lagrangians
Definition 1:
The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
2
votes
0answers
28 views
Monte Carlo for Random Bond Ising ferromagnet
The set-up:
Consider the Ising model on an $L \times L$ square lattice, where the coupling of each bond is chosen to be $+J$ (ferromagnetic) with probability $(1-p)$ and $-J$ (antiferromagnetic) with ...
1
vote
3answers
68 views
Microscopic picture of an inductor
I have a good understanding of how inductors behave in electrical circuits, and a somewhat rough-and-ready understanding of how this behaviour arises from Maxwell's equations. However, what I don't ...
1
vote
0answers
27 views
Calculating the change in entropy in a melting process
I have a homework question that I'm completely stumped on and need help solving it.
I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
9
votes
3answers
223 views
Is there a way to obtain the classical partition function from the quantum partition function in the limit $h \rightarrow 0$?
One would like to motivate the classical partition function in the following way: in the limit that the spacing between the energies (generally on the order of $h$) becomes small relative to the ...
0
votes
0answers
39 views
Lambda transition data points of $\require{mhchem}\ce{^4He}$
I'm looking to get some data on the lambda transition of $\require{mhchem}\ce{^4He}$. I need the data points of the specific heat vs. temperature graph, if that makes sense.
0
votes
1answer
46 views
Number of particles in a microcanonical ensemble
Is it always assumed that, in a microcanonical ensemble, the number of particles is $N \gg 1$ ?
If no, are all the theorems related to the microcanonical description true even if the number of ...
7
votes
3answers
287 views
Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
I'm looking for an intuitive understanding of the factor $$e^{-E/kT}$$ so often discussed. If we interpret this as a kind of probability distribution of phase space, so that $$\rho(E) = ...
6
votes
1answer
73 views
Motivation for the Deformed Nekrasov Partition Function
I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the ...
2
votes
1answer
51 views
Error in variance
I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
2
votes
1answer
96 views
Energy density of a quantum mechanical ensemble
How do we determine the energy density of a given system? I have seen that the density operator
$$\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$
What does this mean exactly ...
1
vote
1answer
62 views
Basic energy calculation for N identical spin system
We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$.
My understanding: There is only one ...
2
votes
1answer
45 views
Bose-Einstein condensate for general interacting systems
There is Bose-Einstein condensate (BEC) for non-interacting boson systems. Can we prove the existence of BEC for interacting systems?
1
vote
0answers
28 views
Neutron scattering for a critical magnetic-ordering system : what about critical opalescence?
Liquid-gas transition critical point is believed to share the same universality class as the 3D Ising model.
We know that the liquid-gas transition is characterized by a phenomenon called critical ...
1
vote
1answer
33 views
How can I find the temperature of this system?
A system was given a small amount of thermal energy dE, and its number of states G grew by 25%. How can I find the system temperature?
The system contains gas particles, I know that $dE << ...
5
votes
1answer
75 views
Mean-field theory and spatial correlations in statistical physics
In statistical physics, mean-field theory (MFT) is often introduced by working out the Ising model and it's properties. From a spin model point of view, the mean-field approximation is given by ...
1
vote
1answer
54 views
Deriving the change in the Helmholtz free energy in the context of the free energy perturbation method
I am reading Free Energy Calculations: Theory and Applications in Chemistry and Biology by Chipot and Pohorille. At the beginning of the text (page 19, for example), the authors define the Helmholtz ...
0
votes
0answers
6 views
Hardware random number generator Vs. Pseudo random number generator in the battlefield of Markov Chain Monte Carlo processes [migrated]
I'm implementing a Markov Chain Monte Carlo process for a Quantum Monte Carlo routine, in every book and paper I've read so far the success of the routine and quality of the results strongly depends ...
0
votes
2answers
48 views
Has anyone studied a statistical scaling law for the universe? [closed]
How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the ...
0
votes
0answers
92 views
What is the condition for getting Bose-Einstein condensation? [closed]
Consider an ideal Bose gas in three dimension with energy-momentum relation E proportional to $p^s$ with $s>0$. Find the range of $s$ for which this system may undergo a Bose-Einstein ...
6
votes
0answers
63 views
Does quark color contribute to “spin degeneracy” for QGP calculations?
Like the title say, does quark color matter in counting contributions in a early universe plasma (QGP), as when adding up the total plasma energy density, or is it just spin? The book I have (Pathria) ...
2
votes
1answer
83 views
Accessible microstates of harmonic oscillator in microcanonical enemble
While reading up on statistical physics, I am going through the calculation of the partition function of the harmonic oscillator in the microcanonical ensemble. The result for the partition function ...
0
votes
1answer
72 views
Uncertainty and Thermodynamics
Dilemma
The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that
$\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
1
vote
1answer
62 views
Maximizing Multiplicity of Einstein Solid == (Temperature = $\infty$)?
If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ...
0
votes
0answers
26 views
Increase in number of micro states explanation or restatement of second law?
Is the boltzmann's expression of entropy as log of micro states leading to the formulation that system is more likely to be in a macrostate with more no. Of micro states really is an explanation or ...
3
votes
0answers
71 views
Spontaneous conversion of heat into work at negative temperatures
Consider a heavy macroscopic object moving in a gas. Friction causes its kinetic energy to be converted into heat. Thermodynamically, there is (effectively) no entropy associated with the kinetic ...
1
vote
2answers
132 views
Energy of particle in electric field
I'm taking a physics class and the professor teaches us really basic things in lecture and then gives homework way beyond what he taught in lecture. Obviously I need to find some resource other than ...
3
votes
1answer
115 views
Why the chemical potential of massless boson is zero? [duplicate]
In Bose-Einstein condensation, the chemical potential is less than the ground state energy of the system($\mu<\epsilon_g$). But why does the massless boson such as photon have zero chemichal ...
2
votes
0answers
150 views
Pauli paramagnetism for electrons with external magnetic field
Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $
$$
\chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)}
$$
...
2
votes
2answers
183 views
Does entropy really always increase (or stay the same)?
Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order.
While unlikely, ...
2
votes
1answer
65 views
classical quantum particles in grand canonical ensemble
To derive Bose-Einstein and Fermi-Dirac distribution, we need to apply grand canonical ...
1
vote
1answer
57 views
Differences between hard-core boson and fermion
Hard boson has strong repulsion with each other just like fermion. What is the differences between hard-cord boson and fermion. Which materials are hard-core bosons?
0
votes
1answer
72 views
Change of variables, Fermi Integral
This is a really basic question, but I'm kind of confused.
I have this integral
$$\int_{0}^{\infty}\frac{p^{2}dp}{e^{\alpha+\beta p^{2}/2m}+1}$$
where ...
3
votes
2answers
89 views
What is wrong with these ways of determining the mean occupation number?
Could anyone point out what went wrong in this argument?
Setup:
We have a system with 2 energy levels say with energies $0,e$ respectively.
We consider the grand canonical ensemble for the system ...
1
vote
0answers
26 views
Is there anything to prevent paired-up neutrons from a complete overlap
The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions.
However, assume I ...
2
votes
1answer
77 views
Local minima in Ising model in a Monte Carlo simulation
Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
2
votes
1answer
217 views
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 ...
