All Questions
Tagged with adiabatic quantum-mechanics
75
questions
3
votes
1
answer
104
views
Adiabatic Approximation in the spin 1/2 System
I am studying the following Hamiltonian:
$$H(t) = \begin{bmatrix}
\frac{t\alpha}{2} & H_{12} \\
H_{12}^* & -\frac{t\alpha}{2} \\
\end{bmatrix}$$
I want to assume that $\...
0
votes
1
answer
165
views
Finite-time effects in Landau Zener
Consider a two level system with a Landau-Zener Hamiltonian of the form
$$\hat{H}=\begin{pmatrix}v t&\beta\\\beta&-v t\end{pmatrix}.$$
The Landau-Zener formula provides a closed form for the ...
- 503
1
vote
0
answers
46
views
Constructing a gapped family of Hamiltonians in the trivial paramagnet
Consider the trivial paramagnet, which has the Hamiltonian $$H = - \sum_i \sigma^x_i$$ Now let's say I have two different Hamiltonians $$H_0 = H + 2\sigma^x_{i_0} \qquad H_1 = H + 2\sigma^x_{i_1}$$ ...
- 737
2
votes
0
answers
165
views
Non-adiabatic evolution and time-dependent adiabatic parameter
I am dealing with the dynamics of a two-bands lattice system. The idea is that you have a lattice model of free fermions, with some hopping amplitudes and on-site energies.The lattice have two fermion ...
- 503
1
vote
1
answer
64
views
Derivative of $c(t)$ in Adiabatic Approximation
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is
$$\begin{aligned}
\dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\...
- 37
3
votes
0
answers
41
views
What is the relation between the Adiabatic Approximation used in quantum chemistry and the one given in QM textbooks?
I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry ...
- 89
2
votes
0
answers
224
views
Understanding adiabatic elimination in three-level system coupled to EM field
I am having some difficulties understanding the "adiabatic elimination" in the context of atomic physics.
In particular, consider a three-level system with states labeled by $|g_1\rangle$, $|...
- 3,014
4
votes
0
answers
265
views
Implement Adiabatic Elimination on Hamiltonians?
Adiabatic elimination is the process of truncating a Hamiltonian's Hilbert space to the "slow" states you care about. You throw out the "fast" eigenstates to produce a smaller ...
- 7,931
3
votes
1
answer
93
views
When applying the adiabatic theorem, why doesn't the gap become doubly exponentially small generically?
Suppose we have a parameterised family of Hamiltonians $H(s)$, $s\in [0,1]$, acting on $n$ spins/qubits. When applying the adiabatic theorem, it is well known that if we wish to remain in the ground ...
- 709
10
votes
1
answer
451
views
Is there a generalization of the adiabatic theorem into a degenerate Hamiltonian?
Adiabatic theorem states that if the Hamiltonian of the system $H(t)$ is slowly changed, and if the initial state is in the $n$th eigenstate of $H(0)$, then the final state will remain in the $n$th ...
- 307
0
votes
1
answer
67
views
Why can't we use the time-dependent Schrödinger equation twice in the adiabatic approximation derivation?
In the standard derivation of the adiabatic approximation (see Sakurai in Modern Quantum Mechanics, Wikipedia) a differential equation for the coefficients is reached as
$$
i\hbar \dot{c}_m(t) + i\...
- 602
1
vote
0
answers
41
views
Adiabatic theorem for stochastic time-dependence
I am trying to derive the adiabatic theorem when my time-dependent Hamiltonian is stochastic and I have a few questions. Usually, one starts with the Schrödinger equation
\begin{equation}
i\frac{d |\...
- 87
0
votes
1
answer
60
views
Adiabatic theorem with stochastic variables
Suppose a system which is driven by a stochastic complex variable $\alpha$(t). Looking at the eigensystem, both eigenvectors and eigenvalues are then stochastic variables. In my case, after building a ...
- 87
1
vote
1
answer
30
views
Where does the lower limit of the integral for the dynamic phase factor come from? [closed]
I'm working on a problem right now where we have to figure out the transition probability between arbitrary excited states of the harmonic oscillator under a small time-dependent perturbation. Its ...
- 11
0
votes
2
answers
105
views
In the adiabatic theorem, how do we know which eigenstate we start on? (STIRAP)
I am aware of the question here, but it doesn't have an answer and also doesn't answer my question. I'm wondering about a specific case in STIRAP, where the 3 eigenstates are $$|\Psi_\pm\rangle = \...
- 700