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

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184 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 ...
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34 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 ...
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421 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 ...
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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 ...
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106 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 ...
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178 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 ...
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152 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 ...
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108 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?
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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 ...
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154 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 ...
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208 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.
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10 views

Why 'free energy' can contain different amount of information in different settings, and what's their connection to phase transition?

I have seen 'free energy' arising from several contexts in very different forms, and each contains different amount of information (as a number, 1D function, 2D surface, etc). For example free ...
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10 views

Mean value of number of molecules of a gas inside a volume

I'm trying to solve this problem in Statistical Mechanics but I'm not sure if my reasoning is right. The problem is as follows: we have a certain region with volume $V_0$ containing $N_0$ molecules of ...
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15 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, ...
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24 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 ...
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30 views

Particles with spin and probability theory

I'm studying Statistical Mechanics but I'm not being able to understand some points on how probability theory ideas are being applied so I'm going to ask on the context of a particular problem that is ...
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7 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 ...
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16 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.
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46 views

Thermodynamics and Axioms and the like

Can thermodynamics and any important related information be expressed as a set of axioms with various 'rules of manipulation'?
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30 views

Magnetic susceptibility in ising model as magnetization change

Let's say I have a standard 2D Ising model with $$ H(\sigma) = - \sum_{<i~j>}\sigma_i \sigma_j - h\sum_{j} \sigma_j $$ With the metropolis algorithm, I can compute various things like energy ...
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22 views

how will the distribution of the no. of particles be in a system ,(N,V,E) if N tends to infinity?

MB distribution is followed if there are N no. of non interacting and distinguishable particles. But if N tends to infinity why does the no. of micro states reduces? Is there any peak in the graph?
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26 views

Does spin degeneracy affect ideal Fermi gases in any way as T->Infinity?

In other words, given any system comprised of an ideal Fermi gas, in the high-temperature (classical) limit, are there any observable thermodynamic quantities (pressure, volume, energy, density, etc.) ...
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32 views

Reference for Non-Hamiltonian treatment of Liouville's theorem

Does anyone know of any good books /lecture notes that include a section on Liouville's theorem with regard to non-Hamiltonian dynamics/systems, i.e. those with $\frac{d\rho}{dt} \neq 0$. Examples ...
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34 views

Number of particles in a box at thermal equalibrium

Consider a cube box of volume $V$ in thermal equilibrium at temperature $T$. We have 3 pieces of information: The probability of finding a particle of mass $m$ in the box having momentum in ...
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40 views

What is the use of Schwinger-Keldysh formalism?

In non-equilibrium statistical mechanics, there is this formidable formalism, called the Schwinger-Keldysh formalism. I have read about it, and I understand what it is. However, what I what to know ...
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22 views

Time evolution of the density of phase points for an ensemble

I want to calculate the time evolution of the density of phase points for an ensemble of N harmonic oscillators. However, I intended to do so without using the Liouville equation. Sure, I want to ...
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46 views

Corrections to the Equipartitio theorem

Does anyone know why sometimes $E = \frac{3}{2}k_{b}T $ is written as $E = \pi k_{b}T$. Where does this come from?
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31 views

Difference between molecular dynamics and direct simulation Monte Carlo

I just started studying about rarefied gases and I came across the concepts of Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC); so here is my question: How are these two fields ...
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29 views

How to understand the Bose glass phase has infinite superfluid susceptibility?

The Bose glass phase is characterized by a gapless excitation spectrum, exponential decay of superfluid correlations, finite compressibility and infinite superfluid susceptibility. The disordered ...
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47 views

Calculating the heat transfer into CO$_2$ gas at a constant pressure

I am having trouble with a homework question and I am just not sure how to attack it. We have not covered how to deal with non-ideal gases yet, and we are expected to answer this question without that ...
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35 views

What are the Fermi and Debye temperature constants?

What are the Fermi temperature and Debye temperature constants? We were discussing these in class and I don't fully understand what these constants are or why we have them. Can anyone explain?
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39 views

Is any phase associated with some fixed point in Renormalization Group?

In Wilson's paper I found a lot of discussion in expansions near a fixed point. He suggested that each fixed point is associated with a regime of the system. Like the fixed points of Anderson's Model, ...
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49 views

Ising Model with All Spins Interacting with All Other Spins

I am studying the Ising model with all spins interacting with all other spins and have formulated $Z$. I am trying to understand what it means to study at large N but not infinite N. I know that at ...
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31 views

Phase separation - density functional theory

I would like to get the equilibrium density profile $\rho(x)$ of a non ideal gas that has phase separated. I start by defining a simple free energy density. The total free energy $F[\rho]$ is a ...
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39 views

Partition function for a two state system

We have a system of two energy states and we treat classical distinguishable and indistinguishable particles respectively. For the distinguishable case I thought that all in the left one one left ...
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20 views

Dimension of the Hilbert space of the restricted surface-on surface (RSOS) model

Right now I'm reading a paper on inversion identities for RSOS models, which you can find here. To give you a short introduction: The RSOS model is a face model, with a height variable assigned to ...
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34 views

What is the central charge of the disordered $q$-state Potts model, for large $q$?

The central charge of a model, is, heuristically related to the number of microscopic degrees of freedom. Is there a simple argument for the asymptotic behavior of the central charge for the ...
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48 views

How to find Entropy of system in terms of Magnetic Field and Temperature

I'm studying for final exams and I have a question about how to find the entropy of a particular system. The system is a lattice of paramagnetic atoms fixed to the lattice sites, with an external ...
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32 views

How can one approximate integral def. of Z by the max value of the integrand?

I am taking a course in statistical physics, and while reviewing my notes from the lectures I came across something that I cannot get my head around. We arrive at an integral expression for the ...
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20 views

Volume in NVT ensemble

While solving a problem of ideal gas in canonical ensemble, I got stuck into this one. It may sound silly though- Why $$\int d^{3N}q$$ equals to $V^N$ but not $V^{3N}$
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53 views

Schottky Anomaly - Heat Capacity

I'm having a little bit of a difficulty understanding the origins of the schottky anomaly at low temperatures in the heat capacity of certain materials with restricted energy levels. As I understand, ...
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37 views

Independent boson model with an arbitrary finite-dimensional impurity

The independent boson model consists of the following Hamiltonian: $$ H_s = E \sigma^z $$ $$ H_b = \sum_k \omega_k b^{\dagger}_kb_k $$ $$H_{sb} = \sigma^z \sum_k (g_k b_k + g_k^{\ast}b^{\dagger}_k).$$ ...
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36 views

Johnson Noise: Source of thermal fluctuations

I've read a lot online about Johnson noise being caused by thermal fluctuations, and the Wikipedia page of thermal fluctuations attributes this to the fact that particles don't all have the same ...
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30 views

Examples of systems with linear response behavior

I've checking the linear response theory and there are 3 fundamental assumptions. 1) Linearity of the response of the system to an external excitation, 2) Stationary response function: ...
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31 views

Mean square velocity of an ideal Bose gas

I'm trying to find the mean square velocity of a particle in an ideal Bose gas. The equation is given by: $\langle v^2 \rangle = \dfrac{1}{N}\displaystyle\sum_{\vec{k}}(\hbar ...
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10 views

How is the pattern of the decay of cluster expansion coefficient

For cluster expansion applied in material prediction. Is there some general trends how the ECIs should decay? Thank you.
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19 views

Ising Monte-Carlo and Three point functions

I'm looking for literature on the calculation of three points function in the 2d Ising Model using numerical methods, especially around the critical point. By $Z_2$ symmetry, three spin insertions is ...
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57 views

Is entropy related to Poincare recurrence time?

One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after ...
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26 views

Many body quantum rotors

I'm stuck on a particular problem about quantum rotors. Suppose we have $N$ such rotors and they are connected to a thermal reservoir of temperature $T$. Neglecting any center of mass motion, I'm ...
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27 views

Coupling a ferromagnet to an antiferromagnet

Consider a system composed of a thin film of FM material on top of an AFM material. From my research I found that pinning of the FM material occurs when we cool the system from $T_N<T<T_C$ to ...