Recap Stat Phys II
Mastering Stochastic Processes: A Quiz
Test your knowledge of advanced concepts in statistical physics with our stimulating quiz! Dive deep into stochastic processes, Gaussian distributions, and Langevin equations while assessing your understanding and retention of these critical topics.
Challenge yourself with questions covering:
- Gaussian white noise
- Fokker-Planck equations
- Equipartition theorem
- Fluctuation-dissipation theorem
A stochastic process is called Gaussian if
Only the first and second moment are nonzero.
Only the first and second central moment are nonzero
Only the first and second cumulant are nonzero.
All higher moments vanish.
Gaussian white noise
Is a stochastic process with zero mean and delta-correlated noise.
Is Markovian.
Has higher cumulants which are delta-correlated.
Is a stochastic process with non-zero mean and delta-correlated noise.
The Fourier-transform of the autocorrelation function
Is always constant.
Is the noise spectral density.
Is not defined for a non-white noise process.
Is constant for Gaussian white noise.
What is added to promote an equation of motion to a Langevin equation?
Damping.
Noise source (stochastic force).
Damping and noise source (stochastic force).
Delta function.
Imagine the stochastic force in a Langevin question as a series of delta-peaks, so called jumps. The Stratanovich interpretation assumes that the correlation function is evaluated
Before the arrival of a jump.
After the arrival of a jump.
At the mean of before and after the jump.
A non-Markovian Langevin equation
Has fluctuating quantities which are Gaussian white noise.
Has no fluctuating quantities which are Gaussian white noise
Is characterized by a memory Kernel.
Has no fluctuating quantities.
A Fokker Planck equation
Describes the time-evolution of a density distribution.
is characterized via a drift and a diffusion term.
Is not normalized.
Is always linear.
A Smulochowski equation
Is as exact as a Fokker Planck equation.
Is only a good approximation for strongly damped systems.
The equipartition theorem states
That energy is shared equally amongst all energetically accessible degrees of freedom of a system
That energy is shared not equally amongst all energetically accessible degrees of freedom of a system.
States that energy is shared equally amongst all energetically accessible kinetic degrees of freedom of a system.
States that energy is shared equally amongst all energetically accessible potential degrees of freedom of a system
The fluctuation-dissipation theorem states
That a process which dissipates heat is always associated with thermal fluctuations
That a process which dissipates energy is always associated with a stochastic force
That a process which dissipates energy is never associated with a stochastic force
That every process is dissipative.
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