Questions tagged [perturbation-theory]
Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.
1,331 questions
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Perturbations in the inflaton field before inflation
The recent papers I've read concerning perturbations that generate cosmic structures later on were careful to state that these perturbations in the inflaton field are generated during inflation. But ...
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Scattering states and 2nd-order perturbation theory of a bound state
It is known that, in quantum mechanics, the standard 2nd-order perturbation theory (and beyond) depends on summing over intermediate states. My question is over the range of this sum: for systems ...
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Confusion regarding Weinberg's proof of constant tensor perturbation on superhorizon scales
In Weinberg's "Damping of Tensor Modes in Cosmology" arXiv:astro-ph/0306304, he claims to show in the appendix that "$h_{ij}$ becomes time-independent as the wavelength of a mode leaves ...
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Rigorous pedagogical references on Epstein-Glaser's causal perturbation theory
I'm interested in learning the Epstein-Glaser approach to renormalization, also called causal perturbation theory. The most authoritative pedagogical reference I have found so far is the book Finite ...
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Polarisability of the hydrogen atom from second-order Rayleigh-Schrodinger perturbation theory
I am trying to work out the polarisability of the ground state hydrogen atom using second-order Rayleigh-Schrodinger perturbation theory, including the unbound states. I know the angular part can be ...
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Diagrammatic Calculation of Anderson localization
I'm current following Piers Coleman's Many-Body Physics to understand the diagrammatic method for Anderson localization (weak localization)
The diagrams are as follows.
where the dashed line is the ...
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Validity of the perturbation theory in the presence of degeneracy in electron-phonon systems
In electron-phonon coupling system, the total hamiltonian of the system can be written as:
$$
\hat{H}=\hat{H}_0+\hat{V}
$$
where $\hat{H}_0$ is the hamiltonian of free electrons and phonons.
$$
H_0=\...
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Boundary effects on energy spectrum
If I have two systems whose spectra are known exactly (the systems are CFTs with the energies characterized by a set of integers $\{Q1,m1\}$ and $\{Q2,m2\}$) and the leading irrelevant operator that ...
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Examples of computations of real processes in QCD
As far as I understand, most of asymptotic states in QCD are bound states (hadrons). Bound states cannot be studied by perturbative methods of Feynman diagrams. In standard textbooks I looked at I did ...
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Perturbation of the form $H'=i\lambda[A,H_0]$
Recall the correction to the wavefunction up to first order is\begin{align*}\psi_n=\psi_n^{(0)}+\sum_{m\neq n}\frac{\langle\psi_m^0|H_1|\psi_n^0\rangle}{E_n^0-E_m^0}\psi_m^{(0)}\end{align*}
suppose ...
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Phase transition of shift of energy level under small perturbation in random matrix theory
I'm a mathematician and I'm thinking about a question in random matrix theory.
Suppose $H_0$ is a $N\times N$ GUE random matrix (variance of each element is $\frac{1}{N}$). We consider a small ...
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Corrections to the hydrogen atom energy levels induced by spin-related perturbation operators
Consider a perturbation in the hydrogen system: $V=-g_p^{e}g_{s}^{p}\frac{\hbar^2}{8\pi m_e}{\sigma}_e\cdot\hat{r}\left( \frac{1}{r^2}+\frac{1}{\lambda r}\right)\mathrm{e}^{-r/\lambda}$, where $\...
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Why don't all quantum systems undergo exponential decay?
In the section "Energy Shift and Decay Width" of Modern Quantum Mechanics by Sakurai he shows that the probability for a system to remain in eigenstate $\lvert i \rangle$ of unperturbed ...
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Diagrammatic representation Cosmological Perturbation Theory - Symmetry factors
The proper question I would like to ask is very short, but I need some "preamble" to introduce it. Sorry if it results quite long, but it is for sake of clarity.
I am studying cosmological ...
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Are the eigenstates of a holomorphic Hamiltonian holomorphic?
In Kato's book Perturbation Theory for Linear Operators, Chapter 2, Section 6.2, it is claimed that, for a Hamiltonian which is a holomorphic function of a real parameter $x$ (i.e. a time-dependent ...
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