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

learn more… | top users | synonyms

1
vote
0answers
138 views

Understanding the product of partition functions by making sense of the maths and the physics

I have $N$ distinguishable particles in a 1D harmonic oscillator potential with 'proper' frequency $\omega$. The particles also have internal spin-$\frac12$ degrees of freedom in a magnetic field $B$ ...
1
vote
0answers
55 views

Condensate fraction and single-particle density matrix

In Bose–Einstein condensation (BEC), how to prove the largest eigenvalue of the single-particle density matrix $$\rho_{ij}=\frac{\langle\Psi|a_i^{\dagger}a_j|\Psi\rangle}{N}$$ is ...
1
vote
0answers
108 views

Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
1
vote
0answers
85 views

Is it possible to define a notion of temperature in a microcanonical ensemble?

I am thinking of a mircrocanonical ensemble as a finite system for which the number of particles, volume and the total energy is fixed. Is there a more refined view of this? Can I think of ...
1
vote
0answers
228 views

Boltzmann distribution: derivation from canonical distribution

I'm trying to understand the Maxwell-Boltzman Distribution, and in particular the derivation from the boltzman distribution for energy. I have successfully created an incorrect derivation, but I'm not ...
1
vote
0answers
60 views

What is conductivity?

I read that if we have spin $\frac{1}{2}$-particle, where a magetic force acts on, then the force is given by a drift speed times a conductivity. This conductivity is determined to be $\frac{kT}{D}$, ...
1
vote
0answers
159 views

Fugacity of the fermi gas

It can be shown that in the high temperature exploration of the Fermi gas, the Fermi function may be expanded to second order in $e^{\beta \mu}$, where $\beta = 1/kT$ and $\mu$ is the chemical ...
1
vote
0answers
38 views

Can the short-time dynamics of an open quantum system be approximately unitary?

Considering the physics of an open quantum system described by a Hamiltonian $H=H_S+H_E+H_{SE}$, where the subscript $S$ refers to the system of interest, $E$ to the environment and $SE$ to the ...
1
vote
0answers
170 views

The Maxwell and the Boltzmann distributions

I am trying to understand where the Boltzmann distribution comes from. I recently learned some interesting things of which my interpretation follows below. Did I interpret correctly? If so, is this ...
1
vote
0answers
83 views

Langevin equation

A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a harmonic spring, so that ...
1
vote
0answers
105 views

How does the Lennard Jones Potential changes for interaction between particles of different sizes?

I am interested in incorporating a Lennard-Jones potential in a simulation. When the interaction only involves the same type of particle, with same characteristics, we can use reduced units, scaling ...
1
vote
0answers
244 views

Free Energy of N Spin 3/2 Particles

This question is from the book "Introductory Statistical Mechanics" by Bowley and Sanchez. The question is as follows: Calculate the free energy of a system with N particles, each with spin 3/2 with ...
1
vote
0answers
59 views

Find out ground sates for large 2D classical spin model

Reaching the ground state of a large 2D classical spin model (e.g. classical Heisenberg model) might be a relatively difficult task while using conventional "flip/reject" Monte Carlo method. The ...
1
vote
0answers
178 views

Average number of spin up particles

In a paramagnetic system, where $N = N_\uparrow + N_\downarrow$ is fixed, how does one calculate the average number of spin-up particles $\langle N_\uparrow \rangle$? You can assume we have the ...
1
vote
0answers
40 views

Ergodicity Breaking in Supercooled Liquids

What is a ergodic system? What is Onset temperature of ergodicity breaking in super cooled liquids when we go towards lower temperature?
1
vote
0answers
88 views

Is there a systematic way to determine the relevant variables needed to describe a nonequilibrium system?

In strong nonequilirium, the statistical operator describing the system depends on an infinite number of variables (BBGKY-hierarchy), contains information about all the previous states starting from ...
1
vote
0answers
247 views

Peierls Argument for Absence of Long Range Order

I'm really confused about the argument in Cardy's book for why there can't be long range order in 1D for discrete models. Let me just copy it out, and hopefully someone can explain it to me. He ...
1
vote
0answers
117 views

Traditional Transfer Matrix on the Potts model — how it grows for strip lattices?

What is the transfer matrix size for a strip lattice of width $n$ vertices, with arbitrary $q$?? I am not sure if it is $q^n$ x $q^n$ or something else. Any reference is also welcome.
1
vote
0answers
198 views

Maxwell-Boltzmann distribution

The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function. What I currently need to solve is: ${{\mathcal{L}}^{\,\left( ...
1
vote
0answers
200 views

Maxwell-Boltzmann distribution for transport equations

I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for ...
1
vote
0answers
35 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 ...
1
vote
0answers
470 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 ...
1
vote
0answers
76 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 ...
1
vote
0answers
108 views

Statistical Mechanic

One can define entropy as $$S=k\log{\omega(E)},$$ where $\omega(E)$ is the numbers of states with energy equal $E$; and the canonical partition function for a set of N particles is defined ...
1
vote
0answers
189 views

helmholtz free energy of a polymer

You have a polymer chain of $N$ units, which is represented by $N$ independent springs in series. The springs are Hookean, with spring constant $L$, and the end to end vector is $\mathbf r$. So the ...
1
vote
0answers
161 views

Fock picture of bosonification in condensates

I want to understand how bosonification in a condensate must be interpreted in the Fock states picture Say i have uncoupled fermions in a set of states $E_1$, $E_2$ ... over the vacuum $E_0$. They ...
1
vote
0answers
110 views

What is meant by correlation propagation?

What is meant by correlation propagation in physics? I have an intuitive understanding but are there any introductory notes ( more mathematical oriented) and with some physical examples?
1
vote
0answers
94 views

usage of partition function in some number of particles in one-dimensional axis

I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case: Suppose there are three particles in ...
1
vote
0answers
182 views

Does the spin glass corresponding to a restricted Boltzmann machine have a characteristic timescale?

From what I gather, a Boltzmann machine can be identified with a spin glass. Though I don't know the details yet (and would welcome any references within the last 5 years--not, e.g. MacKay, etc.), I ...
1
vote
0answers
213 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.
0
votes
0answers
22 views

bose einstein phase transition

From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is $$ \ln(Z) = ...
0
votes
0answers
18 views

Making Pudding; A complicated non-equilibrium statistical process?

There are a lot of non-equilibrium processes examples given in physics literature. But some processes that are present in everyday life are not treated. As an example, the formation of pudding can be ...
0
votes
0answers
15 views

Ewald summation without repeating one particle periodically?

I need to perform an Ewald summation for a Brownian Dynamics simulation. In the normal Ewald summation procedure, all particles in the simulation box are periodically repeated in the neighbouring ...
0
votes
0answers
27 views

Can I measure the volume of a locked room by pumping gas through keyhole and measuring its entropy?

Suppose that I have a locked room and a keyhole in the door and I want to measure the room's volume. Suppose also that I have some "magical" "artificial" inert gas A that doesn't interact with ...
0
votes
0answers
56 views

Equipartition theorem and virial theorem differences?

The classical virial theorem and the classical equipartition theorem are clearly related. A version of the virial theorem is, \begin{equation} \bigg\langle \sum ^{3N}_{i=1} x_i\frac{\partial ...
0
votes
0answers
27 views

Mean-field solution of Potts model

The mean-field equation for the three-state Potts model $H= -J∑δσiδσj$ can be derived as follows using this: a) show that $H$ is equivalent to $-J∑Si.Sj$ where, $Si=(1 0) , (-1/2 √3/2 ) , (-1/2 ...
0
votes
0answers
46 views

About the factorial N! in the partition function

After reading these posts: Why is the partition function divided by $(h^{3N} N!)$? , What is the resolution to Gibb's paradox?, and some of these: http://arxiv.org/abs/1012.4111 , ...
0
votes
0answers
36 views

Non-trivial integral with the Bose-Einstein distribution and Cosine function

When I consider the Casimir interaction between an atom and a perfect conducting slab I find the following non-trivial integral: $$\int\limits_0^\infty {\frac{{\cos \left( mx \right)}}{{x + ...
0
votes
0answers
26 views

What is normal fluctuation?

I was reading Statistical Mechanics (second edition) by Kerson Huang. On page 146, after equation 7.14, there is a reference to normal fluctuation. What is it? Here is the relevant part from the ...
0
votes
0answers
30 views

Problem in deriving the second term in perturbation expansion the quantum ising model

So I'm trying to derive the perturbation expansion for one particle states in the quantum ising model (Sachdev 2011 QPTs which this is derived from ) $$ H_I= - J g \sum_i \sigma_i^x - J ...
0
votes
0answers
46 views

Finding the phase space density of $N$ harmonic oscillators

Consider a system of $N$ identical harmonic oscillators in 1d. The Hamiltonian will be given by $$\mathcal{H}_N=\sum_{i=1}^N \frac{p_i^2}{2m}+\frac{m\omega^2}{2}q_i^2$$ Now supposedly the Hamiltonian ...
0
votes
0answers
71 views

Density matrix in Quantum Statistical Mechanics

What is the connection between the density matrix in quantum statistical mechanics and the probability of being a particular state in classical statistical mechanics? It would seem that the elements ...
0
votes
0answers
32 views

What are the limitations of simulating grand unification theories of elementary particles in condensed matter settings?

What are the limitations of simulating grand unification theories of elementary particles in condensed matter settings? I know that condensed matter systems can be constructed to be described by any ...
0
votes
0answers
38 views

What is the justification for the minimum image convention in periodic boundary condition?

As the distance between first particle-second particle and first particle-image of the second particle are not same. How is it justified to use the distance from the nearest image to compute ...
0
votes
0answers
45 views

Internal energy of ideal gas in the grand canonical ensemble

I am reading through Pathria/Beale StatMech and I have a problem to understand the calculation of the internal energy of an ideal gas in the grand canonical ensemble, i.e. the derivation of the ...
0
votes
0answers
48 views

Canonical or microcanonical ensemble?

What of this ensembles is more honest with natural thermal equilibrium? In microcanonical ensemble the sample is isolated, and we don't now the precise value of energy. By this considerations we have ...
0
votes
0answers
23 views

Formula for computing macrostates

I'm trying to figure out how to arrange 3 particles across 5 energy level from 0E to 4E and obtained 5 macrostates (this could be wrong). While it is possible to do so for small number of n particles, ...
0
votes
0answers
61 views

Construction of free energy based on Landau theory

Consider an Ising model system where the total energy is $E = −J \sum_{<ij>} S_iS_j $, $S_i = \pm 1$ and $< ij >$ implies sum over nearest neighbours. For $J < 0$ the ground state of ...
0
votes
0answers
11 views

When obtaining the thermodynamic entropy (e.g. by differentiating F) the average entropy is being found. In what sense is this an average?

If I have some expression of the entropy (or another thermodynamic quantity of a system (e.g. pressure) obtained from the Helmholtz free energy, F. Is this the mean (average) or the modal (most ...
0
votes
0answers
22 views

Singularities across the critical isotherm in Landau's phenomenological theory of phase transition

Why don't we encounter any singularities when crossing the critical isotherm when $h \neq 0$ or $m\neq0$, where $h$ is the ordering field and $m$ is the order parameter.