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The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

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Canonical ensemble and Quantum field theory

As we all know in Canonical ensemble number is fixed. It is a closed system. But can one use canonical with quantum field theory? Particularly case like heavy ion collision, where the number is not ...
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32 views

Elitzur theorem and the Ising model

I was recently studying the Elitzur theorem and its application to the Ising model on Kogut: An introduction to lattice gauge theories and spin systems, chapter $5$C. I was wondering how he obtain $\...
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probability density distribution: From free diffusion to presence of a barrier

I am a biologist and I am not very comfortable with statistical mechanics. However, I want to learn and I am trying to understand. I just need some clues from people that handle these topics easily. ...
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19 views

Topological soliton objects in Minkowski v.s. Euclidean spacetime?

What makes the distinctions between the soliton objects in Minkowski or in Euclidean spacetime? It looks that usually, the Euclidean path integral is easier to be performed in many cases. In fact, ...
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1answer
44 views

Physical Realization of Three-Level System

I have come across the Hamiltonian (where $\varepsilon,\Delta\geq0$) in one of my problem sets: $$H= \left(\begin{array}{c c c} 0&0&0\\ 0&\varepsilon-\Delta&0\\ 0&0&\...
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Example calculation of increase in accessible states upon reimposing constraints in an isolated system?

Can you show me some example calculations of where the accessible states of a system increase upon reimposing the constraints of an isolated system (like moving the piston in a cylinder back to its ...
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1answer
50 views

What is the role of temperature in photon shot noise departing from Poisson?

I am trying to understand the physics behind photon shot noise and have two sources. The first is from "Photon Transfer" by James Janesick which has he following bit on photon shot noise. Signal ...
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37 views

statistical definition of the temperature, the thermal energy and the pressure for an non-ideal gas

I recently realised that my definition (and understanding) of the temperature was only valid for a ideal gas: $T=\frac{2}{3 k_B}\int (u-v)^2f(v)dv$ where $u$ is the mean (or global) velocity of a ...
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63 views

If the moon produced energy like the Sun would it radiate the same energy and light on Earth as the Sun? [on hold]

I would like to know if the moon where to shine like the sun would the Earth get the same energy and light as it is getting now from the Sun?
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41 views

Statistical mechanics with a freely variable parameter

I would prefer to limit this question to the microcanonical ensemble for ease. I'm particularly interested in the limit that there is no intrinsic cost to introducing particles into a system, in the ...
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18 views

Grand-canonical ensemble for antiparticles

For a system of interaction free identical fermions/bosons in thermodynamic equilibrium, the average number of particles in a single-particle state $i$ is given by, $$n_i=\frac{1}{e^{\beta (\epsilon_i-...
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18 views

To prove the Lorentz invariance of density distribution functions for massless particles in phase space

One defines the density distribution function of a collection of $N$ particles in phase space as follows, $$f(\vec{x},\vec{p},t)=\sum_{i=1}^N\delta^{(3)}(\vec{x}-\vec{x}_i)\delta^{(3)}(\vec{p}-\vec{p}...
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2answers
57 views

Existence of conduction electrons in pure Si at room temperature

Silicon has a bandgap of ~1.1 eV whereas the room temperature thermal energy is ~0.04 eV. But we still find electrons in the conduction band for a pure silicon wafer, away from any radiation. I ...
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1answer
25 views

How calculate pipe thickness from moment of inertia

I am creating a parametric spreadsheet to predict the behaviour of a sign post when subject to a specified wind speed for a uni assignment . Currently half way through creating the spreadsheet and one ...
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1answer
349 views

Is spontaneous symmetry breaking robust against weak perturbations to the Hamiltonian?

Setup Suppose we have some Hamiltonian $H$ which is known to exhibit spontaneous symmetry breaking (SSB), at least in some parameter regime. For simplicity, we might consider the 2D Ising model below ...
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2answers
99 views

Understanding statistical mechanics for a non-physicist [duplicate]

I study statistics and not physics, but I am interested in the role probabilities have within physics, e.g. within classical mechanics. I wonder whether it is possible to understand classical ...
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2answers
157 views

Why aren't Maxwell-Boltzmann statistics used in general cases?

From Probability Theory Vol. 1 Feller Section 2 Chapter 5: Maxwell-Boltzaman distribution: consider $r$ indistinguishable balls and $n$ cells. Assuming that all $n^r$ possible placements are ...
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1answer
31 views

Is there any difference between radial distribution function and pair correlation function?

I have understood the part that for solids pair correlation function is the measure of the probability of finding the center of another particle in the neighborhood of a given particle. On the other ...
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1answer
35 views

Is it possible to efficiently update the ground state of an Ising lattice after a local change in the fields?

The Hamiltonian of an Ising model can be written as: $$H(\mathbf s) = \sum_{i<j}J_{ij}s_i s_j + \sum_i h_i s_i$$ where $s_i \in \{0,1\}$ are the spins on each site. The ground state is the spin ...
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20 views

Transverse Ising model in continuum limit

Recently I have read "Analyzing the two dimensional Ising model with conformal fi eld theory" by Paolo Molignini, but I don't understand clearly manipulations in the section about continuum limit of ...
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40 views

What is the meaning of negative frequency in $\chi^{\prime\prime}(-\omega)$?

The imaginary part $\chi^{\prime\prime}(\omega)$ of the generalized susceptibility $\chi(\omega)$ is an odd function of $\omega$ i.e., $$\chi^{\prime\prime}(\omega)=-\chi^{\prime\prime}(-\omega).$$ ...
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1answer
22 views

Time evolution of a projected mixed state

Suppose a quantum system (non-interacting) at finite temperature ($\beta^{-1}$). I want to know how to compute the transition probability between two degrees of freedom ($u$ and $v$) at two different ...
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137 views

How could the universe's expansion “remove the mean gravitational potential”?

I'm citing W. C. Saslaw's The Distribution of the Galaxies: Gravitational Clustering in Cosmology, chapter 25, where he adresses (what seems to be a Newtonian approximation of) the thermodynamic ...
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1answer
70 views

Analyticity of the generalized susceptibility in the linear response theory

In linear response theory, the generalized susceptibility $\chi(\omega)$ is defined as $$\chi(\omega)=\int\limits_{0}^{\infty}\phi(t) e^{i\omega t} dt, ~~t\geq 0\tag{1}$$ where $\phi(t)$ is the ...
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2answers
84 views

Deviation from Linear response in metals and Ohm's law

In metals, Ohm's law is an example of a linear response i.e., $I\propto V$ where $I$ is the current (response) due to the applied voltage $V$ (external force). For metals, can we have a breakdown of ...
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1answer
57 views

Are density matrices symmetric? [closed]

The context is that I want to simplify an expression like $$ \mathrm{Trace}[\rho_1 \rho_2 \rho_3] + \mathrm{Trace}[\rho_2 \rho_1 \rho_3] $$ (Note that the second term is not a cyclic permutation of ...
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2answers
174 views

If spontaneous symmetry breaking only occurs in infinite systems, why do we observe similar effects in finite systems?

Background No SSB in finite systems Consider a system interacting with a heat bath at inverse temperature $\beta$, with the resultant dynamics of the system described by a Liouvillian superoperator $...
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1answer
39 views

Specific Heat and melting of ice [duplicate]

If ice contained in a beaker starts melting, then why does temperature remains constant. Is there a way to understand this phenomenon using the concept of specific heat.
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2answers
67 views

Microstates - Why Position and Momentum?

Why is it that when we discuss the microstate of a system of particles, we use Position and Momentum? How does Position and Momentum tell us everything we need to know about a single particle? I've ...
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2answers
62 views

Why is it necessary to irreversibly erase a memory?

I know that the most accepted resolution of the Maxwell's demon paradox was proposed by Landauer and revolves around the fact that the demon's memory is finite and will have to be erased at some point....
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2answers
231 views

How can we justify, in deriving quantum statistics, the use of Stirling approximation in the form $\ln(x!)\approx x \ln x - x$?

At first sight one can say "why not to use only one term, or maybe three or more terms"? Why use two terms? I see that books (see for example good books like Griffiths quantum mechanics or Atkins ...
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In Monte Carlo integration for Molecular dynamics simulation, why is a Boltzmann distribution assumed?

In statistical physics, The calculation of partition function for an ensemble takes a Boltzmann's distribution of the Hamiltonian. Similarly, In Monte-Carlo integration of Molecular Dynamics ...
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1answer
32 views

Temperature relaxation from kinetic equation

Suppose we have the kinetic equation $$ \frac{\partial f}{\partial t}=-\frac{f-f_0}\tau $$ for the electron distribution function in momentum space $f(\mathbf{k},t)$. Here $\tau$ is the relaxation ...
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2answers
41 views

Probability in canonical ensemble

For a system in thermal contact with reservoir (bath) at constant temperature, why in text books like Modern Statistical Mechanics (Chandler), they use the notion that the probability of the system ...
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1answer
35 views

Equipartition of energy and degrees of freedom in Diatomic gas [duplicate]

Suppose we have a gas of $N$ diatomic molecules (ex $O_2$) with one-molecule hamiltonian being: $$\mathcal{H} = \frac{\vec{p}_1^2}{2m}+\frac{\vec{p}_2^2}{2m} + V(r_{rel}) $$ Where $r_{rel}$ is the ...
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Reverse task of a Markov Chain Monte Carlo: How to sample distributions/Hamiltonians if one certain realisation is known?

We know MCMC can be used to sample realisations once a probability distribution(or Hamiltonian from which a probability distribution is derived) is given. But if one certain realisation is already ...
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35 views

How does the Dirac equation follow from the algebra of order and disorder operators in the Ising model?

In his book "Statistical Field Theory", Mussardo derives the Dirac equation for the Majorana fermions in the scaling limit of the Ising model. He does this by defining order operators (the Pauli ...
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2answers
60 views

Dark current and thermal excitation in CCDs

In charge-coupled devices (CCDs), doped semiconductors are used to produce an electronic signal from incoming photons - the underlying principle being the photoelectric effect. This simple law tells ...
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1answer
57 views

How presence of metastable state ensure that there is first order phase transition?

Recently, I took a lecture in which professor showed a graph which was similar to following figure Professor told that if there is a metastable state, it means that there must be some kind of first ...
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1answer
63 views

Relation between The speed and Temperature of the molecule

I'm fully aware of Gay-Lussacs Law, but when I was reading Feynman Lectures on Physics volume 1, sir said that the temperature and the speed of the gas (Ideal Gas) are proportional to each other. But ...
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1answer
82 views

Momentum transport equation

In the derivation of the momentum transport equation in Kirkwood's paper (https://aip.scitation.org/doi/10.1063/1.1747782), I am stuck at a particular point in the derivation. The rate of change of ...
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28 views

Phase transition between two CFTs

If we start with a CFT (say CFT$_1$) and deform it by some relevant operator, in the IR we can get another CFT (say CFT$_2$). This is flowing from one CFT to another. I was wondering whether there ...
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1answer
182 views

Binning or just skipping values in a simulation to avoid autocorrelation

Given a set of data from a generic Montecarlo simulation $x_i$, $(1=1,...,N)$, autocorrelation is expected to happen between data points within relaxation time $\tau$ (correlation time) distance ...
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1answer
30 views

Planck law near absolute zero

Is the Planck law of radiation valid even for $T$ near absolute zero? Why can we be sure that the mean photon number inside a black body is zero for $T\to 0$?
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1answer
43 views

Maxwell's velocity/speed distribution

Maxwell's speed distribution for gas in thermal equilibrium follows: $$f(v)=\left(\frac{M_g}{2k_bT_g}\right)^{\frac{3}{2}}\exp\left(-\frac{M_gv^2}{2k_bT_g}\right)$$ Three queries: $1.$Was this ...
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Where does this $dy$ come from?

CONTEXT: Large Deviation Theory Textbook: Perspectives on Statistical Mechanics, Yoshitsugu Oono For i.i.d. stochastic variables $\{X_n\}$, the rate function (or large deviation function) $I(y)$ is ...
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1answer
45 views

Particle current density expression

I was reading the paper https://doi.org/10.1063/1.1747782 by Irving and kirkwood and came across an expression called particle current density and is given as follows $$j(r,r^{\prime};t)= \sum \sum_{k\...
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25 views

Maxwell-Boltzman speed distribution

For a class assignment, I have to do a Barnes-Hut Galaxy simulation. The assignment includes: The dots' velocities following the Maxwell distribution with typical velocity of $$v={\left<v\right&...
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How does the virial expansion converging, mean that there is no phase transition?

I have a question regarding how the virial expansion relates to phase transition. I watch the lecture https://www.coursera.org/learn/statistical-mechanics/lecture/1a5Di/tutorial-3-algorithms-exact-...
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1answer
49 views

Is partition function algorithm-dependent or configuration-dependent?

I am reading this resource to learn statistical mechanics: http://blancopeck.net/Statistics.pdf I am trying to learn about the partition function, which as I understand it, is equal to the number of ...