# Questions tagged [berry-pancharatnam-phase]

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### What is the logic connection between these two statements?

What is the connection between these two statements: the berry curvature change sign under time-reversal operation If the system has the time-reversal symmetry, then berry curvature is odd in k. ...
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### Calculation of a Berry phase in the Aharonov-Bohm effect

In his seminal paper, where he introduced the concept of geometric phase, Berry investigates, among other things, a quantum system in a box encircling the infinitely thin solenoid carrying flux $\Phi$....
1answer
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### Visual representation of quantum state/phase

Is there a known good way to visualize a quantum state, composed of the sum of eigenstates, with a phase rotating on each state. I am looking for a way to keep up with the state and the phase. In a ...
1answer
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### Aharonov-Bohm phase picked up when a magnetic dipole goes around a charge

When a particle with charge $q$ traverses a loop that encloses a magnetic flux $\Phi$, it picks up a phase $e^{iq\Phi}$ (I have set $c$ and $\hbar=1$). This is the usual Aharonov-Bohm phase. Now, let ...
1answer
279 views

### Questions about Berry Phase

I'm learning about the Berry Phase from the original paper, and from the TIFR Infosys Lectures The Quantum Hall Effect by David Tong (2016). I have some questions regarding the original derivation of ...
1answer
442 views

### Is the non-trivial topology on the torus reflected on the Bloch sphere?

Almost every text on topological insulators have the Bloch sphere example of a two level system showing the non triviality of the bundle of an eigenvector over the sphere: we can't define an ...
1answer
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### Berry Curvature and Curvature Tensor

When the curvature tensor (from Einstein's theory) has a non-zero torsion, it is said to be an antisymmetric tensor in the last two indices composed of the connections of the field. Alternatively, the ...
1answer
221 views

### Berry phase in 2D Harmonic Oscillator

I am trying to figure out the Berry phase in case of 2D Harmonic Oscillator under adiabatic cyclic condition of Hamiltonian. I know that in 1 D since Hamiltonian has only 1 time dependent parameter (...
1answer
306 views

### Importance of the Pancharatnam–Berry Phase

As I understand it, the Pancharatnam–Berry phase first arises in the adiabatic approximation for the evolution of a quantum state. For the evolution of a quantum state parameterized by the set of ...
2answers
403 views

### Effects of Topological Terms: Hopf, $\Theta$, Chern-Simons, WZW, Berry phase term

What are the effects and the differences of Topological Terms? For example, I had known and heard several of them are called Topological, (1) Hopf term, (2) $\Theta$ term, (3) Chern-Simons term,...
1answer
82 views

### Topology of parameter space

How do we decide the topology of the parameter space? Does this topology depends on the Hamiltonian (the form of potential) we are using? I was studying Berry's phase and it involves rotation of the ...
1answer
659 views

### Is my attempt to prove that Berry's phase is quantized in inversion symmetric systems true? Do I violate gauge invariance?

The Berry's or Zak's phase is given as \begin{align*} \gamma & =\oint_\mathrm{BZ}d\mathbf{k}\mathcal{\mathcal{\mathcal{A}}}(\mathbf{k})\ \ \mbox{mod }2\pi\\ & =i\oint_\mathrm{BZ}d\mathbf{k}\...
1answer
311 views

### Flux quantization in a superconductor and Berry phase

In the derivation of flux quantization for a superconducting ring, we say that $$\oint_C \nabla\theta . dl = \theta_{2} - \theta_{1}$$ Then we equate this value to $2\pi n$. The reason cited in ...