Questions tagged [fluctuation-dissipation]
The fluctuation-dissipation tag has no usage guidance.
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Noise spectral density for waveguide: I don't understand this calculation
In Introduction to Quantum Noise, Measurement and Amplification, on page 64 is computed the power spectral density of noise on a classical waveguide. I am really struggling to understand a step of the ...
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Good references for linear response theory
I am looking for good references for linear response theory. I have seen this https://nptel.ac.in/courses/115/106/115106091/ which looks nice but probably a little long (going into too many details).
...
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Fluctuation for diffusion flux (Fick's law)
I am trying to write the formulation for fluctuation in diffusion flux (Fick's law):
$$ \vec{j}= - \rho D\vec{\nabla} c $$
Then I describe fluctuation in concentration and density as the following: ...
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2answers
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Fluctuation dissipation theorem : how to identify the response variable and the force in general?
I fully re-edited my question
I have a super basic question. Note that I am just beginning to learn linear response theory.
General context:
If I consider a linear, time invariant, causal system, ...
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1answer
40 views
The fluctuation-dissipation theorem
In Giuliani & Vignale's Quantum Theory of the Electron Liquid, in page 126, they point out that the absorption and emission spectra are related by $$S_{AA^\dagger}(-\omega)=e^{-\beta\hbar\omega}S_{...
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Fluctuation-dissipation theorem out of equilibrium
Are there generally accepted formulations of the fluctuation-dissipation theorem out of equilibrium?
Background: Fluctuation-Dissipation Theorem in the Keldysh Formalism
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Problem in derivation of Smoluchowski Equation
I am trying to derive Smoluchowski equation using Fokker Planck equation. I am following the book ''Non Equilibrium Statistical Mechanics'' by Robert Zwanzig. I am attaching a screenshot of a few ...
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1answer
277 views
Does the fluctuations-dissipation theorem hold in active matter for macroscopic physical quantities?
I am trying to understand how the fluctuationādissipation theorem applies to active matter.
I simulated a system with active motors which may consume energy from the environment to move and exert ...
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47 views
Where does differntial equation of covariance matrix come from?
Does anyone know where the differential equation of covariance matrix comes from?
$$\frac{dC(t)}{dt}=AC(t)+C(t)A^T+D$$
where $C$ is the covariance matrix, $A$ is the drift matrix, and $D$ is the ...
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1answer
155 views
Fluctuation-Dissipation Theorem in the Keldysh Formalism
In Kamenev's book Field Theory of Non-Equilibrium Systems (he also has lecture notes online here, which contains the relevant statement on pg. 17), he states that the following equation
$$G^K(\epsilon)...
3
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2answers
342 views
Equivalence of thermodynamic ensembles
It is often argued that thermodynamic ensembles are equivalent in the sense that no matter what ensemble one uses for the calculations, one should end up in the same macroscopic equations of state. ...
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33 views
What does stochastic nature of work (quantum scale) really mean?
Fluctuation theorems are (also) concerned with defining work in the non-equilibrium regime.
Now I've read that in regimes where Fluctuations become very strong (which I assume are the non-...
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101 views
Is entropy change always zero after a quasi-static evolution?
If I am thinking in terms of a idealized, perfect carnot cycle I know that in sum
$$\Delta S_{\mathrm{total}} = 0.\tag{1}$$
But that does not mean that there is no entropy generated during the ...
3
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1answer
49 views
What does $\delta$ represents in FLUCTUATION-DISSIPATION THEOREM?
i am trying to follow the following tutorial. I keep seeing $\delta$ over functions such as $\delta F(x)=F(x)-\langle F(x)\rangle_t$ (Eq 14.4) in this and in other tutorials and questions here. What ...
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1answer
63 views
Can one formulate a fluctuation-dissipation theorem in presence of non-Gaussian noise sources?
The fluctuation dissipation theorem relates the linear response of a system to Gaussian fluctuations. The natural question that comes to my mind is the possible derivation of an analogous FDT in ...
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277 views
Exact solution for non-linear Fokker-Planck equation
I'm searching for exact (analytical) results for FP equation in 2 variables (such as $x$ and $p$ in 1D) with a steady state. Kramer's like (with force due to confining potential, such as harmonic ...
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2answers
135 views
Fluctuation-dissipation theorem for velocities
I am given the following problem about fluctuation dissipation theorem:
Consider an external force $f(t)= \frac{f_0}{2}(e^{i\omega_0 t}+e^{-i\omega_0 t})$ acting on a particle with momentum $p=mv$ in ...
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1answer
98 views
How to determine the off-diagonal term of magnetic susceptibility tensor from fluctations?
I have run a Monte Carlo simulation of the classical Heisenberg model (in the future I am planning to add other interaction terms). I would like to extract information about the property of the system ...
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1answer
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What is the fluctuation-dissipation relation for non-quadratic kinetic energies?
Recently I tried to get in touch with some statistical mechanics. I am completely new to the field and hence many things are unclear to me. Currently, I have a question regarding the dissipation-...
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205 views
What causes viscosity of a fluid?
Consider a fluid like water. Intuitively I would say that its viscosity is caused by intermolecular interactions among its molecules.
But the Einstein-Smoluchowski relation (and the Fluctuation-...
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1answer
103 views
Thermodynamics Help - Reading through Landau and Lifshitz
I am reading Landau and Lifshitz and I am confused about two steps in the Fluctuation theory chapter. They occur just before Eqn. 3 in "Fluctuations of the fundamental thermodynamic quantities". Here ...
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1answer
203 views
Fluctuations in Fluctuation Dissipation theorem
In the derivation of the Fluctuation-Dissipation theorem. We encounter an identity
$$ \langle\delta A(t) \delta B(0) \rangle = \langle A(t)B(0)\rangle-\langle A \rangle\langle B\rangle$$
where
$$\...
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1answer
176 views
Fluctuation dissipation on a ring?
The integral fluctuation theorem is given by:
$$\left< e^{-R}\right>=1\tag{0}$$
where:
$$R\equiv \ln \left( \frac{p_0(\vec n_0) p[\vec n(\tau),\vec c(\tau)]}{p_f(\vec n) \cdot p[\tilde n(\tau),\...
asked Feb 2 '18 at 19:48
Quantum spaghettification
5,8917 gold badges35 silver badges107 bronze badges
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1answer
134 views
Fluctuations of free energy in quantum statistical mechanics
I want to calculate the fluctuation of the mean value of the free energy, $\langle F \rangle$, which I denote as $(\Delta F)^2 = \langle F^2\rangle - \langle F\rangle^2$. Since I have calculated the ...
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0answers
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Thermal fluctuations in orientation of point particles
I am modeling group of point particles with 6 degrees of freedom each - 3 positional degrees of freedom and 3 orientational degrees of freedom. So, each particle has 3 position coordinates and a unit ...
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Fluctuation-dissipation theorem for the acoustic equation
Recently I discovered a paper by R. Snieder on the extraction of the acoustic Green function from cross-correlations of the acoustic noise. What differs this paper from other papers on the subject, is ...
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Is there an equivalency between fluctuation and effective degrees of freedom?
Is it possible to use the fluctuation-dissipation theorem to introduce a new "fictitious" degree of freedom (d.o.f) for an existing coordinate/d.o.f which fluctuates a lot?
Consider a non ...
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1answer
432 views
How does the fluctuation theorem dissipation function become entropy?
In "The Fluctuation Theorem" by Evans and Searles, they derive the transient fluctuation theorem from Liouville's theorem (pg 1541). Following their notation $ \Gamma = (\vec{q}, \vec{p}) $, they use ...
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1answer
89 views
Can we take $\sigma^2_N=\frac{\kappa_T}{\beta V}N^2$ to be an example of the fluctuation-dissipation theorem?
In statistical mechanics, the relation $\sigma^2_E=\langle E^2\rangle-\langle E\rangle^2=k_BT^2C_v$ is interpreted ad one of the examples of fluctuation-dissipation theorem. The fluctuation in energy ...
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143 views
Does the Lindblad equation satisfy a fluctuation dissipation relation?
The fluctuation dissipation relation is usually stated in terms of an identity that relates the retarded, advanced and either the Keldysh or time-ordered correlators. This is easily enforced in ...
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1answer
57 views
DPD weight function
I was wondering about the connection between the weight function of the random force and the conservative force between DPD particles in a standard DPD simulation. Both usually have the form [Groot ...
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1answer
608 views
Fluctuation-dissipation theorem in QFT
If I understand correctly, the fluctuation-dissipation theorem (fdt) in QFT technically arises because of $\pm i\epsilon$ - infinitesimally small summand in the denominator of spectral representation ...
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1answer
505 views
Heat capacity and fluctuation-dissipation theorem, meaning of energy fluctuations?
I have read that from the fluctuation-dissipation theorem that the heat capacity is proportional to energy fluctuations (or populations fluctuations). In this context what is the meaning of 'energy ...
asked Apr 16 '16 at 4:42
Quantum spaghettification
5,8917 gold badges35 silver badges107 bronze badges
3
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0answers
144 views
Second law of thermodynamics in linear response theory
I am wondering about the appearance of irreversibility in the response functions or equivalently the correlation functions in a statistical mechanics system. The main principle that I have seen where ...
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1answer
322 views
Massless brownian particle Langevin equation and FDT
Given the Langevin equation of a massless brownian particle:
$$
\gamma \dot{x}=\eta,
$$
where $\gamma$ is the friction coefficent and $\eta$ the noise ($\langle\eta \rangle =0$ and $\langle\eta(t)\...
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2answers
320 views
how to simulate a steep potential barrier in langevin equation
When simulating a Langevin equation, how is a vertical potential barrier handled?
I have the time overdamped evolution of the position $x$, described by
$\gamma\frac{dx}{dt}=-V'(x)+\eta(t)$
where $...
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1answer
386 views
alternative derivation of Einstein relation
Is there a derivation of the EinsteināSmoluchowski relation without the assumption of the Boltzmann distribution? Every time I see a derivation, it always assumes the Boltzmann distribution, such as ...
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1answer
219 views
Confused by Langevin Equation
Trying to understand the Langevin Equation. In particular, this passage from a Wikipedia article has me confused (section: "Thermal Noise in an Electrical Resistor"):
$\frac{dU}{dt} =-\frac{U}{RC}+...
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1answer
619 views
Drag force acting on a disk in a 2D system
I have a 2-dimensional system with behavior governed by Langevin dynamics in which disks (circles) move through a fluid. In the Langevin equation, there is a velocity-dependent term that accounts for ...
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1answer
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Does the skin effect, eddy current / hysteresis losses contribute to Johnson noise in an inductor?
Based on my very basic understanding of the Johnson noise, it's not just a DC phenomena, but should change with frequency in a system, where there is a frequency dependent, real component to the ...
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What information is contained in the quantum spectral density?
Consider a harmonic oscillator system with Hamiltonian
$$\hat{H} = \frac{1}{2} A \hat{u}^2 + \frac{1}{2} B \hat{v}^2 \qquad
[\hat{u}, \hat{v}]=i \gamma $$
where $A$, $B$, and $\gamma$ are all real.
...
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Why should $\langle xf_r\rangle=0$ but $\langle\dot{x}f_r\rangle\ne 0$?
All the $\langle\rangle$ in this question is the mean value theorem over a large number of experiments.
Consider a Brownian particle moving in a liquid with the viscosity $\mu$. The equation of ...
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0answers
248 views
Fluctuation-dissipation in a quantum Ising Model
For the classical Ising model, the fluctuation-dissipation theorem tells us that the Magnetic susceptibility is proportional to the variance of the magnetization. Is there an equivalent relation for ...
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1answer
251 views
Is it possible to eliminate Van der Waals interactions?
I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...
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Fluctuation Dissipation Theorem [closed]
I take this course at university called Waves and Optics, and a few lectures ago our teacher talked about the Fluctuation Dissipation theorem but I didn't really understand it. The math behind it is a ...
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598 views
Nonequilibrium thermodynamics in a Boltzmann picture
The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so ...
4
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1answer
227 views
Quantum fluctuations in a classical domain?
"In the presence of chaos, even small ļ¬uctuations
(including quantum ļ¬uctuations) can be ampliļ¬ed to produce large uncertainties in later
behavior"(http://arxiv.org/pdf/gr-qc/9210010v2.pdf)
Is there ...
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1answer
375 views
Stokes-Einstein's formula results in incorrect units for rotational drag coefficient
The Stokes-Einstein-Sutherland relationship,
$$D = \frac{kT}{ 6 \pi \eta a}$$
where $D$ is the translational diffusivity is well known. A similar relationship is used to calculate the rotational ...
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2answers
765 views
Error in variance
I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
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1answer
381 views
Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation
Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
