# What is Relaxation time: Definition and 26 Discussions

In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium.
Each relaxation process can be categorized
by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp(-t/τ) (exponential decay).

View More On Wikipedia.org
1. ### Spin-Lattice and Spin-Spin Relaxation Time Question

Please refer to the homework statement. Or, if one would like to put it in other words, how would I go about finding ##T_2## if I know the delay time between 90-degree and 180-degree pulses? Is there an equation that helps solve this succinctly?
2. ### Relaxation time and average electron velocity in Drude model

If τ is the relaxation time, τ means, on average the time between two collisions for an electron moving under a constant electric field inside a metal. Now according to the assumptions of drude model, the electron acquires an additional velocity of \frac{-eEt}{m}where t is the time elapsed since...
3. ### Relation between spin dephasing time T2* and spin relaxation time

Homework Statement: spin dephasing time Homework Equations: spin relaxation time Hello, i have seen the next equation that relates the spin dephasing time of an ensemble of électrons T2* with the spin relaxation of a single electron T2, and I would like to know how it was deduced/proposed...
4. ### Relation between conductance and dielectric relaxation time

I am studying about dielectric materials and their relaxation properties. There are several ranges of electromagnetic frequencies where different material show different kinds of resonance starting from molecular to atomic motions. Based on the frequency dependence of the imaginary part of the...
5. ### Temperature dependence of relaxation time T1 vs T2

Hi, when we assume a obejct with increasing dynamics with increasing temperature, the longitudinal relaxation time T1 should decrease. Since we have, let's say at a frequency 100 MHz , more fluctuations of B0. Ok, then the transversal relaxation time T2 must increase with increasing...
6. ### Estimating Resistivity of Amorphous Metal - Condensed Matter

Homework Statement Estimate the resistivity of an amorphous metal whose mean free path is of the order of an atomic spacing. Compare your answer to crystalline copper.Homework Equations VF = h(bar) KF / m VF = l / τ ρ = m / n e2 τ The Attempt at a Solution I think my real issue with this...
7. ### Relaxation Time in Damped Harmonic Oscillators

Relaxation time is defined as the time taken for mechanical energy to decay to 1/e of its original value. Why do we take a specific ratio of 1/e? What is its significance?
8. ### Relaxation time approximation and ideal hydrodynamics

Homework Statement please check attachment Homework Equations please check attachment The Attempt at a Solution since the deviation from f_0 to f is linear then we can write f=f_0 + C where C is some constant this should be enough to prove the first question (i think so) for the second...
9. ### Drude model relaxation time approximation

In the Drude model of the free electron gas to explain the conduction of a metal, the relaxation time approximation that the electron has a collision in an infinitesimal time interval ##dt##is ##dt/\tau##. It can be shown that the mean time between collisions is ##tau##. If we choose an...
10. ### About Relaxation Time Approximation

I have seriously stocked in the subject below. According to Ashcrift & Mermin (chapter 13): If the electrons about r have equilibrium distribution appropriate to local temperature T(r), g_n (r,k,t)=g_n^o (r,k)=\frac {1}{ exp^{(\epsilon_n (k) -\mu (r))/kT} +1} (formula 13.2) then...
11. ### MRI excitation time vs relaxation time

So.. if you apply a fluctuating magnetic field to an atom at its correct resonance frequency, its pole will go out of alignment of the applied field. How long does it take for the proton/electron to go 90 degrees out of the applied field vs how long it takes to return
12. ### Fitting Pulsed NMR Data for Spin-Lattice Relaxation Time (T1)

Hello, I didn't know where else to post this so here it goes ... I have collected data from a pulsed NMR experiment to calculate the value of the spin-lattice relaxation time (T1). Now I'm asked to fit the data using a function of the form V(t) = V_0*(1 - 2*exp(-t/T1)). But I'm not really...
13. ### Effect of cross-linking/fillers on relaxation time

Hello all I'm glad to join the forums and having the opportunity of having some scientific discussions I'd like to discuss with you the effect of cross-linking or adding fillers to the relaxation of a polymer I believe that they have the same effect..as both lead to the restriction of...
14. ### Boltzmann Transport Equation : Hall Effect in the Relaxation Time Approximation

Hello everyone! I have been on this website for quite a while, and found some interesting answers to many questions, and I decided to create an account to seek you help with a particular issue I encountered in my assignment. Please have a read, and thank you for any input! Homework...
15. ### Calculating resistivity from relaxation time.

Given the following data on copper, how do i calculate the resistivity? Relaxation time: 2.50e10-14s Density: 8940Kgm-3 molar mass: 63.5g is there an equation for it.
16. ### 1. I need to find the T2 relaxation time of CSF how can i do

1. I need to find the T2 relaxation time of CSF how can i do this? can I use H2O as a surrogate for CSF and obtain the T2 relaxation time that way?
17. ### Spin-spin relaxation time in water

Hey all, I just finished a lab on NMR, and I am looking around for a value to compare my results to. Does anyone know of a place I can find the spin-spin and spin-lattice relaxation times of pure water? I have been googling around with little success so far beyond order of magnitude...
18. ### Relaxation time approximation

I was reading Chpater 13 in A&M solid state physics, which is about relaxation time approximation. But there is one fundamental expression I'm trying to understand. It's the formulation of the relaxation-time approximation (Eq. 13.3). dg = dt/\taug0 But most of other textbooks including...
19. ### Homogeneous and inhomogenous relaxation time

Consider two-level system, the relaxation time (T1) and the coherence relaxation time (T2). I wonder what's the relation between T1, T2 in homogeneous and inhomogeneous case? Here is my thoughts. For inhomogeneous case, all atoms are behave independently, the 'random' phase relation will add...
20. ### Relaxation time and spatial width

Consider a two-level system, let T1 be the relaxation time for the excited system and T2 is the relaxation time for coherence. If we use a Gaussian (with small constant waist w) exp(-x^2/w^2) to shine on the sample, because the waist is small, propably only the atoms around x=0 will be excited...
21. ### Relaxation time approximation

Effective mass and bands in semiconductors In the study of the basic semiconductor physics devices we usually draw flat bands without taking into account the spatial dependence of them. Now why is it correct? I suppose that the "real band diagram" informations are included into the effective...
22. ### What is the definition of momentum relaxation time in semiconductors?

What is a "momentum relaxtion time"? Tried googling it but couldn't get any definitions. Comes from the sentence in a paper on silicon semiconductors: "the momentum relaxation times lies in the subpicosecond regime...as a result free carriers can follow oscillations of an optical wave almost...
23. ### Nuclear magnetic resonance T1 relaxation time definition

Hi all: I have one confused concept about T1 relaxation time in nuclear magnetic resonance field. As we know, fluctuation of local magnetic field inside the sample causes T1 decay in the following RF excitation. Imagine one simple mode, near a gadolinium ion (Gd3+), there is one water...
24. ### Charge Density (Relaxation Time)

Statement: If a volume charge distribution existed inside a conductor at t = 0, the charges would quickly migrate to the outside surfaces due to repulsion. The rate at which the charge density would decrease is given by: \rho_{v}(t) = \rho_{v}(t = 0)e^{-\frac{t}{t_{r}}} where the relaxation...
25. ### Solve initial-value problem for heat equation and find relaxation time

Homework Statement Solve the initial-value problem for the heat equation ut = K\nabla2u in the column 0< x < L1, 0< y < L2 with the boundary conditions u(0,y;t)=0, ux(L1,y,t)=0, u(x,0;t)=0, uy(x,L2;t)=0 and the initial condition u(x,y;0)=1. Find the relaxation time. Can anyone please explain...
26. ### Relaxation time = displacement lifetime of fermi sphere?

Homework Statement I just want to clear this up, I am a little confused: when an electric field is applied there is a force on the electron K-states thus displacing the fermi surface/sphere Is the relaxation time ( \tau)= lifetime of fermi sphere displacement or is lifetime of...