# Questions tagged [bloch-oscillation]

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### Why is the relaxation of coherence rate half the spontaneous emission rate?

Consider a two-level atom of which the lower and upper levels are denoted, respectively, a and b. If spontaneous emission from the upper to the lower level is the only source of relaxation, then the ...
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### How can linear response give DC conductivity when the formalism doesn't have dissipation at all?

A lot of textbook or lecture note that teach linear response theory would calculate AC conductivity first and then say that the DC conductivity can be obtained from taking the limit of frequency to ...
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### Peierls Substitution with Time-Dependent Vector Potential

My question is whether Peierls substitution really holds true for time-dependent electromagnetic (EM) potentials and, if yes, why. To implement an electromagnetic field in a condensed matter system ...
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### How the Bloch sphere of a Hahn echo in NMR looks like? 90-t-90-t-echo

I have tried to find in the literature a proper nice and beautiful Bloch sphere to describe the trajectory of a nuclear spin, starting in z-axis, using a pulse sequence of an initial 90º pulse with ...
632 views

### Advanced atomic physics: From Liouville Equations to the Bloch equations

I'm trying to derive the Bloch equations from the Liouville equation. This should be possible according to this paper, which discusses higher order Bloch equations (second order spherical tensors). I'...
335 views

### Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential, for example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x)$$ with $V(x+a) = V(x)$ where $a$ is the lattice ...
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### Crystal momentum and the vector potential

I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase ...
In the free electron approximation, a Bloch state $|k\rangle$ is the linear superposition of free plane wave states $\sum_G C_G(k) |k+G\rangle$, where $G$ are the conjugate lattice. Since the ...