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

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177 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 ...
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104 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.
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88 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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151 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( ...
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125 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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31 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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278 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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72 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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96 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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133 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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135 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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103 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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90 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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100 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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183 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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24 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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15 views

Microscopic definition/expression of/for the heat current

Often I see the following microscopic definition/expression of/for a heat current due to an external field $$ {\bf j}_Q = 2 \int \frac{\text{d}{\bf k}}{(2\pi)^3} \frac{\hbar {\bf k}}{m} ...
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34 views

Understanding the mean square displacement in molecular dynamics

In a Molecular Dynamics (MD) simulation, the mean square displacement $\text{MSD}$ is given by $$\text{MSD}(\delta t) = \left\langle\left|\vec{r}(\delta t)-\vec{r}(0)\right|^2\right\rangle,$$ where ...
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17 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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27 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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32 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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13 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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14 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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33 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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33 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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37 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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60 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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40 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 ...
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69 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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38 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 ...
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21 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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50 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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35 views

Spin version of Maxwell's demon: Where's the energy?

I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a ...
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249 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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35 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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134 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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49 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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58 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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57 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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76 views

thermoelectric effect

The Absolute Seebeck effect states that an electric potential (voltage) is produced to any isolated conducting when subject to a temperature gradient.But why? My view of this is that when you apply ...
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37 views

Relation between bonded and non bonded interactions

I came across parameterizing a finitely extensible model for polymers. The maximum stretch length is approximately 3.5 in sigma units. This means that the bonded interaction energy will have a maximum ...
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57 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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53 views

Probability of exceeding $A_0$ (Helmholtz free energy)

I'm not very good at this and need some guidance. I got an expression for Helmholtz free energy $A(R)$, where $R$ is the radius of a spherical core. I need to know the probability for $A>A_0$. ...
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41 views

Estimating magnitude of error in the simplified Debye heat capacity

If you recall, there are two separate Debye cut-off frequencies that correspond to the longitudinal and transverse modes of vibration. Taking this into account, one can generalize the Debye heat ...
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429 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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110 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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55 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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60 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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184 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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120 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 ...