Skip to main content

Questions tagged [bloch-oscillation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
45 views

Choice of axes in resonantly driven two level system

Consider a two-level atom with a transition at angular frequency $\omega_0$ and $\mu_{12}=2 \times 10^{-29} \text{Cm}$ subjected to a sequence of two resonant pulses. The first pulse has electric ...
Anchal Kumar Sharma's user avatar
1 vote
1 answer
49 views

Understanding electric conduction in tight binding model

Let's consider a system of free electrons moving in a one dimensional lattice with dispersion $\varepsilon(k) = -2t\cos{ka}$, ($a$ is the lattice spacing and $t$ the hopping amplitude). Let's now ...
Matteo's user avatar
  • 3,014
1 vote
2 answers
75 views

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 ...
Nicolas Schmid's user avatar
0 votes
0 answers
43 views

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 ...
Bohan Xu's user avatar
  • 708
2 votes
1 answer
95 views

Is current density independent of applied fields for Bloch electrons?

Following Ashcroft-Mermin chapter 12 the semiclassical dynamics is governed by $ \dot{\vec{r}} = \vec{v}_n(\vec{k}) = \frac{1}{\hbar}\frac{\partial \epsilon_n(\vec{k})}{\partial \vec{k}} $ and $ \hbar ...
Uphyscs's user avatar
  • 51
1 vote
1 answer
159 views

Solving Schrodinger Equation for scattering off a periodic potential

I am interesting in solving the time-independent Schrodinger equation (TISE) for the scenario where we have an electron plane wave of fixed energy incident upon a potential that is infinite and ...
bdforbes's user avatar
4 votes
1 answer
546 views

Matrix elements $\langle n,k|x|n',k'\rangle$ for Bloch states

I believe this is just elementary QM, but I'm getting awfully confused. The question is drawn from this paper on Wannier-Stark localization (but is self-contained): https://iopscience.iop.org/article/...
dsfkgjn's user avatar
  • 107
1 vote
1 answer
183 views

How to proove that a Bloch state is periodic in reciprocal space? Two Bloch states with wavevector $k$ and $k + (2\pi/a)$ are identical?

I have been trying to prove that two Bloch states with wavector k and k + (2pi/a) are identical, as the book says: can anyone help me? I have look at some more sources in the solid-state physics, and ...
Who's user avatar
  • 155
1 vote
2 answers
327 views

Ballistic Transport and Bloch Oscillations Contradiction

My question is as follows, below this I have included derivations of both effects: The derivation of Bloch Oscillations implies that in a perfect crystal we will not have net current flow when an ...
safcphysics's user avatar
10 votes
1 answer
3k views

What exactly is Crystal Momentum, $\hbar k$?

The title says it all really. Does this mean that the crystal is moving? From my notes, I read that The effect of an external force on an electron in the crystal is to change the crystal momentum $\...
N. Gin labs's user avatar
6 votes
3 answers
2k views

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 ...
Fred's user avatar
  • 195
2 votes
2 answers
281 views

In the context of bloch waves, where does the formula $| k \rangle = A\sum_{X} e^{ikX} |X \rangle$ come from?

I am following a course on condensed matter physics. In our lecture notes, the lecturer has postulated the following formula in the context of Bloch waves: $$| k \rangle = A\sum_{X} e^{ikX} |X \rangle$...
Mikkel Rev's user avatar
  • 1,356
1 vote
1 answer
600 views

Reduced wave vector using Bloch's theorem

In every solid state physics book it says that the wave vectors appearing in Bloch's theorem can be confined to the first Brillouin zone and provide a hint on how to show this. Most of the times this ...
Pablo Bähler's user avatar
3 votes
2 answers
742 views

Two different expressions for Rabi Frequency (on resonance)

I've been searching through several articles and books and I found two different expressions for the Rabi Frequency on the semiclassical rotating-wave approximation, and they are different by a factor ...
Igor César De Almeida's user avatar
0 votes
1 answer
1k views

Dispersion relation from Hamiltonian

Note: This is obviously for homework so I'm not asking for the answer to be spoon fed, I'm just not understanding the steps I have to take. I have a fairly simple Hamiltonian for a ring tight binding ...
user1543042's user avatar
2 votes
1 answer
773 views

Bloch waves at large momenta

I am trying to come to grip with some solid state theory. Bloch waves, energy eigenstates for hamiltonians with lattice periodic potential in $\mathbb R^d$, are frequently written as $$\phi_{n,k}(r)=e^...
plm's user avatar
  • 191
1 vote
0 answers
239 views

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 ...
Kloudpaper's user avatar
4 votes
1 answer
648 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'...
The Quantum Physicist's user avatar
2 votes
1 answer
346 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 ...
Koby Yavilberg's user avatar
25 votes
4 answers
1k views

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 ...
Alex Eftimiades's user avatar
6 votes
3 answers
2k views

How does Bloch's theorem generalize to a finite sized crystal?

I would be fine with a one dimensional lattice for the purpose of answering this question. I am trying to figure out what more general theorem (if any) gives Bloch's theorem as the number of unit ...
Alex Eftimiades's user avatar
3 votes
2 answers
432 views

Bloch oscillations - Scattering to other bands

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 ...
felix's user avatar
  • 1,776