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

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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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26 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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23 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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26 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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9 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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18 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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32 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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23 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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22 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 ...
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29 views

Chemical potential related with quantum and classical limit in ideal gas

For ideal gas we have chemical potential $\mu = \tau \ln \left(\frac{n}{n_Q}\right) $ where $n = N/V$ number density and $n_Q = \left(\frac{M\tau}{2\pi \hbar^2}\right)^{\frac{3}{2}} $ Note we call ...
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17 views

Pressure components in a film

I am performing molecular-dynamics simulations of a polymer near a crystalline substrate (polymer film). I am comparing the mechanical properties in the film with the properties in the bulk polymer. ...
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31 views

The relationship between the two statistical mechanical definitions of entropy

It seems like similar questions have been asked here; hopefully my question is not a duplicate. I am reading my textbook on the statistical mechanical definitions of entropy, and I am very confused ...
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51 views

Partition function microcanonical ensemble

I was wondering if there is a way to understand the partition function for a microcanonical ensemble $$\mathcal Z(E)=\sum_{\text{microstate $i$ with energy $E$}} w_i$$ as a limit of the continuous ...
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20 views

Screened potential of charged impurity in a 2-dimentional electron gas

What's the analytical relation of screened potential of charged impurity in a 2-dimentional electron gas?
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69 views

Boltzmann distribution - statistical mechanics

I have just followed a derivation of the Boltzmann distribution which I have never seen before, and I must say it is really intuitive. However I have a question as to how we can think of the Boltzmann ...
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51 views

validity of Kramers-Kronig relations for all systems

Are Kramers-Kronig relations valid for all physical systems that obey causality? I came across this example http://journals.aps.org/prb/pdf/10.1103/PhysRevB.83.165119 where the authors say that though ...
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48 views

Euler Equation Arbitrary Quantities

I have a question about the Euler equation. For some state I can write down: $$ U = TS - pV + \mu N$$ In this equation $T$, $p$, $V$, and $N$ are directly measurable so they have fixed values. ...
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64 views

Retarded thermal Green function

I'm working with finite temperature field theory, but I'm having problems understanding the retarded Green's function in this formalism. I'm reading Niemi and Semenoff's article "Finite Temperature ...
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33 views

How do you obtain the fluctuation spectrum of a tubular membrane?

I am reading through a paper. A tubular membrane, submitted to tension $\sigma$ acting as a Lagrange multiplier to conserve area, fluctuates around a cylindrical shape of length L and radius R. ...
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46 views

Entropy of an oscillator in Einstein's solid

This is a homework problem and I need help with it. A solid's (Einstein's model) oscillators are in the first excited state on average. How much entropy does one oscillator have? What I've tried so ...
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59 views

Thermal fluctuations in metals

My professor said that the $k_BT$ displacement in the energy levels of the band electrons is due to the space-thermal displacement of the potential of the ion host. I think that this displacement is ...
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60 views

probability of sequence for given rate constants

lets consider a copolymer, $C_{r,s}^A$ containing r number of A monomers and s number of B monomers with A at the reactive end of the polymer. The equilibrium constant for A-A, A-B, B-A, and B-B bonds ...
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35 views

How to calculate the partial entropy in a fully connected ising system

I'm trying to reproduce a calculation that should lead to the partial entropy in a fully connected ising model for the high-temperature range ($\beta < 2$) in the thermodynamic Limit ($N ...
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28 views

Molecular field meaning in Liquid Crystal Theory

Given the Frank-De Gennes free energy $F = \int f(\boldsymbol{p},\nabla\boldsymbol{p}, ...)\ d\boldsymbol{x},$ for liquid crystals (see De Gennes-Prost, p. 107, formula 3.21), the vector ...
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36 views

Wolff vs Swendsen Wang Algorithm

Following the orginal paper of Swendsen Wang, their dynamical critical exponent $z$ is about $z=0.35$, whereas the Wolff Algorithm seems to have $z=1.19$. When I calculate the Correlation time though, ...
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22 views

What is difference and linkage between power law of phase transition in physics and Zipf law in linguistics

There are power law of phase transition in physics and Zipf law in linguistics which are similiar to each other ,and some expert think they are in fact just the same.But the diagrams of them base on ...
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40 views

Can statistical mechanics be formulated generally in terms of phase space?

In many statistical mechanics books, notably Landau and Lifschitz' volume in the course on theoretical physics, the quantities central to statistical mechanics such as entropy are defined in terms of ...
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35 views

state occupation rate $n_{i}=\frac{1}{e^{\beta (\varepsilon _{i}-\mu )}+{[1/-1/0]}}$ & density matrix $\rho _{m}=\frac{e^{-\frac{E_{m}}{kT}}}{Z(T)}$

Three kinds of distributions. The states occupation rates: F.D. $n_{i}=\frac{1}{e^{\beta (\varepsilon _{i}-\mu )}+1}$ B.E. $n_{i}=\frac{1}{e^{\beta (\varepsilon _{i}-\mu )}-1}$ Boltzmann ...
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14 views

Rationale behind the 'joint cavity distribution'?

I have a question about equation (17) of this paper: http://arxiv.org/pdf/1009.1635v1.pdf First, I was hoping that someone could explain how it is arrived at. Second, I find the notation to be a bit ...
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23 views

Derivation of a formula concerning overlap between spin states

I am reading through Cavagna's Spin glass theory for pedestrians, but I am stuck at equation (35). I'll try to provide a little context. Given two spin configurations $\sigma$ and $\tau$, we define ...
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40 views

Two-dimensional atomic trap--how to set up the problem?

It is possible to trap neutral atoms between two solid surfaces in a potential of the form $V (x, y, z) = ax^2 + by^2$ where a and b are parameters. The allowed space for the gas extends to ...
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56 views

On the relationship between entropy and chaotic noise

I have few conceptual questions related to application of chaos in communications. Kolmogorov-Sinai Entropy1 , Kolmogorov-Sinai Entropy2 and Kolmogorov-Sinai Entropy3 KS is an entropy metric for ...
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50 views

Landau free energy

I am reading the statistical mechanics by Pathria in Chap 12. I have a question about the Landau free energy. What is the physical reasoning for that the free energy could be a functional of the order ...
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91 views

Questions on degenerate ground states and the thermodynamic limit?

For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are: (1) If $H$ has either global $SU(2)$ spin-rotation symmetry or time-reversal ...
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88 views

Occupation probability in grand canonical ensemble

I have a system with energy spectrum which has two groups of $N$ degenerate levels (the gap between them is $E$). There are $N$ non-interacting fermions in the system. What is the occupation factor at ...
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23 views

What is “thermal undulation” in the context of lipid bilayers?

What is thermal undulation in the context of lipid bilayers? Is it another word for "thermal fluctuation"?
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60 views

Weibull distribution

The Weibull distribution probability density is given by: $$f(w,k,\lambda)=\begin{cases}\frac{k}{\lambda}\left(\frac{w}{\lambda}\right)^{k-1}e^{-\left(w/\lambda\right)^k} &w\geq0 \\ 0 & ...
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294 views

Ultra-Relativistic Fermi Gas - Chemical Potential and Energy

I tried deriving the expression for chemical potential of a Relativistic Fermi Gas using asymptotic expansion (for large z) in : $$ N = \frac{V}{h^3}4\pi (KT)^3g_s \int \frac{p^2 dp}{e^{p-\nu}+1} $$ ...
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37 views

Flammability and statistical mechanics

I am wondering to what extent the flammability can be predicted from the statistical properties of an ensemble. Given the partition function of an ensemble, can we in principle predict this property? ...
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272 views

Classical regime for Fermi-Dirac and Bose-Einstein gases

I'm studying statistical mechanics, in particular classical regime for Fermi Dirac and Bose Einstein gases. Time average value for occupation numbers in FDBE statistics: $$ \langle ...
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52 views

What is the probability that all the air ends up in the upper right corner of the room and we suffocate

Since someone commented this on this question(What is the probability of ice in boiling water?), I would like to ask what is the probability that all the air ends up in the upper right corner of the ...
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61 views

What is known about the statistical mechanics of systems with normally distributed energies?

Consider a system taking on N states with energies $\epsilon \sim \mathcal{N}(\mu,\sigma^2)$. Are such systems well-studied in any context? I ask because I'd like to be able to take certain ...
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61 views

Is it possible to derive fermi-dirac or bose-einstein statistics using quantum operator formulations?

I've been looking through theory on identical particles to get a better grasp of the uncertainty principle but it would be very interesting if these results could be extracted from the formalism as ...
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62 views

What is ``thermal" about a thermal quotient of EdS and EAds?

This is in continuation of my previous question and is in reference to this paper. I guess that the authors are interested in $S^n$ and $\mathbb{H}^n$ since these are the Euclideanized versions of ...
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501 views

Density of states of a photon gas in volume V and temperature T

I have a question on the density of states for a photon gas: Suppose I have a photon gas in a box of volume $V$ at temperature $T$. If I enumerate the total number of states accessible to the system ...
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113 views

Why does the cross derivative of the partition function disappear here?

They state that the chemical potential in a canonical ensemble is given by: $$\mu = -kT \frac{\partial{\ln Z(N,V,T)}}{\partial{N}} \tag{1}$$ But if I use the definition of chemical partial (which I ...
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57 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.
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62 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 ...
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199 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 $-\mu {\bf B}$, ...
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130 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 ...