The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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3
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2answers
210 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
29 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
153 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 ?
3
votes
1answer
472 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 ...
0
votes
1answer
200 views

Math for Thermodynamics Basics

I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ...
4
votes
2answers
206 views

Erogodicity in a Monte Carlo simulation

Q1: What is the ergodicity and ergodicity breaking in a Monte Carlo simulation of a statistical physics problem? Q2: How does one ensure that the ergodicity is maintained ?
0
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2answers
140 views

Probabilistic vs Statistical interpretation of Double Slit experiment

Why is it assumed that the results seen in the double slit experiment are probabilistic and not just a statistical result of some unknown variable or set of variables within the system.
2
votes
1answer
241 views

How to define the order parameter of the q-state Potts model?

The order parameter of Ising model can be defined as $m=\frac{N_1-N_2}{N}$, if $N$ is the total number of lattice points, $N_1$ and $N_2$ is the number of lattice points spin up and down respectively, ...
4
votes
3answers
417 views

Is there a mechanism for time symmetry breaking?

Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
3
votes
1answer
211 views

Third-order phase transition in Landau theory

$F=\frac{a}{2}m^2+\frac{u}{4}m^4+\frac{v}{6}m^6-hm$, where F is the free energy, m is the order parameter, h is the external field, $a=a_0(T-T_c)$, and $a_0>0,u>0$ and $v>0$.We know this free ...
4
votes
2answers
382 views

Dispersion relation and Heat Capacity

I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation $\omega = c_sk$. It is said that for temperatures much less than ...
4
votes
1answer
101 views

Semi-conductors

Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
3
votes
1answer
384 views

Intuition behind classical virial theorem

I am continuing to brush up my statistical physics. I just want to gain a better understanding. I have gone through the derivation of the classical virial theorem once more. I have thought about it, ...
2
votes
1answer
101 views

Interacting particles

We are familiar with the grand partition function for the grand canonical ensemble. This makes me wonder: what kinds of modifications would be required if the particles interacted? Thanks.
1
vote
1answer
106 views

microcanonical distribution

We know that in an isolated system, the density matrix is the microcanonical distribution matrix. That this the possibility for all the states with energy in a certain interval is a constant? But how ...
1
vote
2answers
223 views

Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation

Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
1
vote
0answers
248 views

Rotational Constant and Moment of Inertia of Fluorine gas

I have come across some homework question on thermodynamics which needs me to calculate $B$ of $F_2$ My attempt: $B= \frac{h}{8\pi^2cI}$ where $I=\mu r^2=\frac{m_1m_2}{m_1+m_2} r^2$ Atomic mass of ...
2
votes
0answers
126 views

Deriving the “total” Bose Einstein density of states, including the condensate

Is is possible to derive the Bose-Einstein density of states containing the delta function representing the BE condensate?
6
votes
0answers
80 views

Does the Standard Model plasma develop a spontaneous magnetisation at finite temperature?

Reference: arXiv:1204.3604v1 [hep-ph] Long-range magnetic fields in the ground state of the Standard Model plasma. Alexey Boyarsky, Oleg Ruchayskiy, Mikhail Shaposhnikov. The authors of this paper ...
2
votes
3answers
326 views

Results of Statistical Mechanics first obtained by formal mathematical methods

I have a question that seems natural in Physics and Mathematics mainly in Statistical Mechanics of Equilibrium. Results that are proven by formal mathematical methods that were already seem intuitive ...
0
votes
0answers
179 views

Ground and first excited state of non interacting spin system Hamiltonian

For a non interacting spin system containing two $\frac{1}{2}$ spin particles I am trying to determine its Hamiltonian. If the energy of a up spin is $+\mu {\bf B}$ and a down spin is $-\mu {\bf B}$, ...
0
votes
1answer
237 views

Ground states of the Hamiltonian of a two spin system

For the spin system shown in this graph (http://i.stack.imgur.com/3lg1R.png), the Hamiltonian is $$S^{(1)}_z\cdot S^{(1)}_z=\frac{1}{4}\begin{pmatrix} 1 & 0 &0 &0 \\ 0&-1 &0 ...
2
votes
1answer
109 views

Eigenvalues of a mean correlation matrix (integral over correlation matrices with arbitrary density)

Consider a stationary dynamic system with state $s(t)$ and correlation structure described by $C_{ij}(\tau)=\mathbb{E}[(s_i(t+\tau)-\bar{s_i})(s_j(t)-\bar{s_j})]$. Given an arbitrary density function ...
0
votes
1answer
382 views

Pure state - density matrix - real life example of boxes in warehouse

So if there are a billion boxes in a warehouse, I would like to know conceptually how to tell if it is in a pure state. I know that if it is in a pure state (not mixed) that the density matrix has ...
1
vote
2answers
2k views

The number of degrees of freedom of a monatomic gas

Suppose that I have a monatomic gas sample consisting of $N$ atoms (e.g., $N$ argon atoms); thus there are no vibrations or rotations. How many degrees of freedom does the system have? Does the ...
1
vote
1answer
125 views

Hamiltonian of a simple graph

I have a spin system: As shown in the picture, there are two spins S1 and S2, and a pair of interactions between them. One is a ferromagnetic interaction and the other is anti ferromagnetic ...
2
votes
0answers
140 views

Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
2
votes
2answers
560 views

Absolute zero and Heisenberg uncertainty principle

I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and ...
1
vote
1answer
560 views

Significance of the the Lagrange multipliers in statistical mechanics

In classic thermodynamics one can derive the Maxwell Boltzmann statistics by solving a Lagrange multipliers equation. In this process a new parameter $\beta$ is introduced to take account of the total ...
2
votes
2answers
363 views

Why the temperature is getting lower when the universe is expanding

As we know, if an ideal gas expands in vacuum, as its energy is unchanged, the temperature remains the same. An ideal gas's energy does not depend on volume. In general, the energy is $kT$ times the ...
1
vote
1answer
113 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
3
votes
1answer
209 views

Classical blackbody radiation 'solution'

I never understood how the equipartition theorem was applied electromagnetic waves inside the metallic blackbody. As hyperphysics puts it ...
5
votes
2answers
416 views

Is there a formal definition of a macroscopic variable in statistical mechanics?

Intuitively it's easy to accept that the usual variables like temperature, internal energy, etc. are 'macroscopic', but does there exist a formal definition of a macroscopic variable? In other ...
4
votes
1answer
298 views

Renormalization Group and Ising with d=1 and D=1

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...
3
votes
2answers
387 views

Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is: $$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$ The ...
1
vote
0answers
70 views

Partition function for multidimensional scaling energy

Let $D_{ij}$ a random matrix with i.i.d positive coefficients. One can take for instance $D_{ij}$ uniformly distributed in [0,1]. We consider the following energy function $H(x)$ defined for ...
7
votes
0answers
314 views

Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?

According to professor Wen's string-net theory, electrons can be viewed as the elementary excitations of string-net objects. Just like the phonons and magnons are the elementary excitations of ...
5
votes
0answers
148 views

Drawing the RG flow diagram

In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a ...
3
votes
0answers
67 views

Question about the derivation of an equation in full replica symmetry breaking solution

Using replica method and saddle point method, the free energy of a magnetic system can be expressed as $$-\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
4
votes
1answer
859 views

The definition of Density of States

The density of states (DOS) is generally defined as $D(E)=\frac{d\Omega(E)}{dE}$, where $\Omega(E)$ is the number of states. But why DOS can also be defined using delta function, as ...
2
votes
2answers
604 views

Why is there a Global Minimum for the Morse Potential?

For Diatomic molecules, the Morse potential describes their potential energy as a function of separation distance between the two particles. My question is, what is the explanation of of the dip ...
1
vote
3answers
730 views

Why do we need different ensembles in statistical mechanics?

Why do we study these different ensembles, microcanonical, canonical, grand canonical ensemble ? Are they used for studying different physical system or scenarios?(e.g. in some system you can only ...
2
votes
1answer
115 views

How can dQ/T be interpreted as a system's level of disorder?

Long before statistical mechanics, entropy was introduced as: $dS = \frac{dQ}{T}$ At the time when entropy was introduced in this manner, was it known that entropy represents how "disordered" a ...
2
votes
0answers
167 views

Why is the free energy minimized by the Boltzmann distribution?

Can someone show me, without glossing over anything, why $F = E - TS$ is minimized when $p_i = e^{-U_i/k_bT}/\sum_ie^{-U_i/k_bT}$? I understand it conceptually, but am having difficulty showing it ...
2
votes
0answers
84 views

Spin Glass Transitions in Random Bond Ising Model (RBIM)

In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its ...
2
votes
1answer
301 views

Maxwell-Boltzmann velocity PDF to CDF [closed]

I asked on Math.SE and was advised to try here instead. I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
2
votes
1answer
312 views

ultrarelativistic gas

Consider the ideal ultrarelativistic gas Hamiltonian $\mathbf{H = }\sum_{i = 1}^N \mathbf{c |\vec{p_{i}}|}$, now if we let molecules to interact with a potential term like $\mathbf{d|\vec{q_{i}}|}$; ...
14
votes
4answers
343 views

Comments on entropy and the direction of time in Landau and Lifshitz's Statistical Mechanics

In Landau and Lifshitz's Stat Mech Volume I is the comment: However, despite this symmetry, quantum mechanics does in fact involve an important non-equivalence of the two directions of time. ...
1
vote
2answers
979 views

Molecular Dynamics (MD) Simulation: energy fluctuations in NVE ensemble

I'm writing my first MD simulation (ever) for liquid Argon. The code is up and running. I am supposed to do the calculations in the NVE ensemble. Having implemented a 4th order symplectic integrator ...
0
votes
0answers
117 views

Number of microstates of discretized paths

Let us consider a square grid, which has been rotated by 45deg. On this grid we define a path, the directed polymer, which starts at the origin ($t = 0$) and extends in the positive $t$-direction ...