Questions tagged [fluctuation-dissipation]
The fluctuation-dissipation tag has no usage guidance.
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Time evolution operator with chemical potential
In the Bruus and Flensberg textbook, section 1.5, it is mentioned that
Basically, the result obtained from the canonical ensemble is carried over to the grand canonical ensemble by the substitution $...
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Virial theorem for momentum fluctuations
In the paper https://journals.aps.org/pr/abstract/10.1103/PhysRev.109.1464 Lebowitz attempted to derive an estimation of the magnitude of center of mass momentum fluctuations in the presence of ...
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Spontaneous emission as dissipation and fluctuation
Suppose we have some sort of medium and we want to build an effective theory of light inside. Of course we want to calculation the dielectric constant, which in turn is determined by the ...
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Why do statistical physics and thermodynamics care about fluctuations?
Fluctuation seems to be an eternal theme in the study of statistical physics and thermodynamics, why do we need to care about it? Just for stability?
Any comments would be appreciated
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Suscpectibility in Ising networks
I am struggling to find good references on how the susceptibility described phase transitions in Ising networks. First of all i struggle to find a good defintion for the susceptibility.
I understood ...
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A simple picture for work fluctuation relations?
One possible formulation of the second law of thermodynamics is that the work extracted during the change of a thermodynamic system between two thermodynamic states is at most equal to the free energy ...
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Relation between power dissipation and imag part of susceptibility [duplicate]
I am trying to understand the following relation between power dissipation and the imaginary part of the susceptibility, from Sethna's Statistical Mechanics textbook. Why does the integral equal the ...
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Why the mass minimize the energy?
I have been reading the book named "Entropy, Order Parameters and Complexity" and there is an example that confuses me.
A mass $m$ hangs on the end of a spring with spring constant $K$ and
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Deriving the fluctuation-dissipation theorem
In the derivation of the classical version of the fluctuation-dissipation theorem here, they expand the equilibrium distribution function (with Hamiltonian $H(x) = H_{0}(x) - f_{0}x$)
$$ W(x, 0) = \...
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Wiki video shows that vacuum fluctuations exist, despite that vacuum fluctuations do not exist
I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually ...
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Fluctuation-dissipation and lesser Green's function
I learned from a lecture that $G^{<}=-f(\epsilon)(G^r-G^a)$ is a type of fluctuation-dissipation theorem. However as far as I know the fluctuation-dissipation theorem is stated as $S(\omega)=2\hbar(...
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Ito-Stratonovich drift term for spatial white noise
Suppose I have a Langevin equation with multiplicative noise of the form
$$ \dot{x} = f(x) + g(x)\eta(t) $$
where $ \eta(t) $ is a Gaussian white noise with zero average, unit strength, and delta ...
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Use equipatition theorem when studying Brownian motion [duplicate]
Not a physicist so excuse my ignorance.
I am currently studying introductory topics on Brownian mechanics. Utilizing the Langevin equation for a Brownian particle submerged in a fluid with no external ...
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How to evaluate the integral of velocity autocorrelation function for calculating the diffusion coefficient
I am reading Kubo's review article "The fluctuation-dissipation theorem" (http://www-f1.ijs.si/~ramsak/km1/kubo.pdf)
Could someone help me with how Eq. 2.5 is derived? I am confused with how ...
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What is the fractional frequency stability of a thermal damped harmonic oscillator?
Suppose I have a lightly driven (classical) damped harmonic oscillator at temperature $T$. Suppose $\omega$ and $Q$ are specified as well as the mean energy $\bar{E}$ in the oscillator due to the ...
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Does an electron undergo a form of Brownian motion in the vacuum?
There are some questions on StackExchange such as this one
Brownian Motion in Vacuum
asking about Brownian motion in the vacuum. There are related papers such as this one:
https://arxiv.org/abs/quant-...
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Onsager's hypothesis: why is true that correlations decay with increasing time?
I am studying from Chandler's book (Introduction to Modern Statistical Mechanics) the fluctuation-dissipation theorem. Before introducing it, the book states something without really demonstrating it. ...
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Deriving black body law from fluctuation-dissipation theorem?
Is it possible to prove the Blackbody radiation law using the fluctuation-dissipation theorem?
Has it been done, or is there some reason why it wouldn't work? I would appreciate if you could point me ...
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Heat capacity in statistical mechanics
A known result from statistical mechanics is the following fluctuation-dissipation relation:
\begin{equation}
\frac{\partial^2S}{\partial E^2} = - \frac{1}{C_v T^2} \tag{1}
\end{equation}
where $C_v$ ...
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Clarification regarding Kubo formula and fluctuation-dissipation theorem
In the Wikipedia article for Fluctuation-dissipation theorem, under the section for the derivation in the quantum case, the Kubo formula is quoted.
\begin{align*}
\chi(t-t') = \frac{i}{\hbar} \theta(t ...
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Intuition about non-equilibrium Green functions
In the following paper by Fotso and Freericks, the definitions of the Green functions are given as
\begin{align}
G^<(t,t') &= i \langle c^\dagger(t') c(t) \rangle \\
G^R(t,t') &= -i \theta(...
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Is there a fermionic fluctuation-dissipation theorem?
Question: is there any fermionic version of the fluctuation–dissipation theorem?
Context:
In classical physics, the fluctuation–dissipation theorem is roughly written as
$$\langle x(t)x(t')\rangle = 2\...
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Consistency of Lindblad-type operator evolution equations
One frequently comes across Lindblad-type operator evolution equations in the Heisenberg picture of the form
$$
\frac{\mathrm{d}}{\mathrm{d}t} A =\mathcal{L}^{\dagger}(A),
$$
where the adjoint ...
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Autocorrelation and variance: can the fluctuation-dissipation theorem actually be written in terms of fluctuations?
I am considering the theorem in a statistical mechanics context, but I suppose the question could be extended to other fields where it applies as well.
If we have a system with property $A$ and apply ...
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Does the fluctuation-dissipation (FD) relation $\sigma_E^2=k_BT^2C_V$ arise as a special case of the FD theorem?
The classical fluctuation-dissipation theorem states that the power spectral density $S_{\eta\eta}(\omega)$ of a classical random variable $\eta(t)$ is given by $$S_{\eta\eta}(\omega)=\frac{2k_BT}{\...
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Can a broken egg spontaneously reassemble itself (as in the video)?
According to the fluctuation theorem, the second law of thermodynamics is a statistical law. Violations at the micro scale, therefore, certainly have a non-zero probability. However, the application ...
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How to derive the response function of $m\ddot x + \gamma \dot x + kx = f$?
In a lecture on fluctuation-dissipation theorem, it is stated that
EOM: $m\ddot x + \gamma \dot x + kx = f$
Response function $\chi(\omega) = (-m \omega^2 + i\gamma \omega +
> k)^{-1}$
However, I ...
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Fluctuation-Dissipation Relation for Quantum Phase Transitions
I am looking for a formulation for the fluctuation-dissipation relation connecting the correlation related quantities with the thermodynamic functions at the quantum critical point.
The fluctuation-...
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Is it possible to use fluid dynamics to trade in the financial market?
I read somewhere that there is an investment fund in the USA which in its trading decisions uses physical laws of hydrodynamics. I asked my physicist friend, on the account of what is really in ...
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Spectral density of fluctuations (white noise/delta-correlated process)
Let I be the current flowing across some junction as a result of N charge carriers of charge q. And let $\langle I (t) \rangle$ be its average.
Assume a particle number distribution such that its ...
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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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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 $$
Then I describe fluctuation in concentration and density as the following: ...
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Fluctuation dissipation theorem : how to identify the response variable and the force in general?
I fully re-edited my question
I have a super basic question. Note that I am just beginning to learn linear response theory.
General context:
If I consider a linear, time invariant, causal system, ...
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The fluctuation-dissipation theorem
In Giuliani & Vignale's Quantum Theory of the Electron Liquid, in page 126, they point out that the absorption and emission spectra are related by $$S_{AA^\dagger}(-\omega)=e^{-\beta\hbar\omega}S_{...
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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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Does the fluctuations-dissipation theorem hold in active matter for macroscopic physical quantities?
I am trying to understand how the fluctuation–dissipation 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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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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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
$$G^K(\epsilon)...
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Equivalence of thermodynamic ensembles
It is often argued that thermodynamic ensembles are equivalent in the sense that no matter what ensemble one uses for the calculations, one should end up in the same macroscopic equations of state. ...
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What does stochastic nature of work (quantum scale) really mean?
Fluctuation theorems are (also) concerned with defining work in the non-equilibrium regime.
Now I've read that in regimes where Fluctuations become very strong (which I assume are the non-...
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Is entropy change always zero after a quasi-static evolution?
If I am thinking in terms of a idealized, perfect carnot cycle I know that in sum
$$\Delta S_{\mathrm{total}} = 0.\tag{1}$$
But that does not mean that there is no entropy generated during the ...
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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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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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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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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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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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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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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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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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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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