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The compactification introduces periodic boundary conditions, and therefore the momentum in the extra dimension can take only discrete values. A particle that propagates in the extra compactified dime …

The Boltzmann Equation from Quantum Field Theory We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described …

Consider the transmission function $T(x,y)$, equal to unity when $(x,y)$ is inside an aperture and equal to zero outside. (The apertures lie on a screen in the $x,y$ plane, and I am assuming monochrom …

Perhaps we can approach something like an answer, by following the lines set out in Ritter's exposition of geometric quantization (2002). Geometric quantization works because the Heisenberg equations …

The differential equation for $u(\bf{r})$ allows for a radial solution $u(r)$, depending only on the norm $r=|\bf{r}|$ of the vector $\bf{r}$. For such a solution we can perform the angular integratio …

A mathematical proof of Hawking's area theorem has been given by Chruściel, Delay, Galloway, and Howard, in Regularity of Horizons and The Area Theorem (2001). The proof identifies the conditions und …

For a "canonical" list of references you might consult 50 Years of Anderson Localization. In addition to the Aizenman-Molchanov paper mentioned by Christian Remling, the earlier Fröhlich-Spencer work …

The transpose map, and other positive maps, play a key role in quantum information theory, as detectors of entanglement, see On the structure of entanglement witnesses and new class of positive indeco …

So there are two parameters $\alpha$ and $\beta$ and a function $V(\alpha,\beta)$, obtained from your first equation by substituting $S=\alpha^2/\beta$ and $\mu=2\beta/\alpha$. With some effort we can …

This B.A. thesis, Self-Adjointness and the Renormalization of Singular Potentials by S. Gopalakrishnan (2006) might be what you are looking for. The inverse square potential (attractive and repulsive) …

the decay time in your "simple case" is well approximated by the large-$M$ limit [*] $$\lim_{M\rightarrow\infty}M\sigma\tau=2.84$$ here is a plot of $$f_M(s)=\left.\frac{F_M(t)}{1-F_M(\infty)}\righ …

I interpret your question as a query into a mathematical formulation of quantum decoherence, which is the process by which a partial trace of the quantum mechanical density operator $\hat\rho$ reduces …

You don't really need quantum mechanics to address this issue, in classical mechanics you would ask whether time and energy can be thought of as canonically conjugate variables (because quantization w …

Well, the absolute value squared of a wave packet $\Psi_t(x)$ has the interpretation of a time-dependent probability distribution $P_t(x)=|\Psi_t(x)|^2$ for the stochastic variable $x$ (position on a …

A question along these lines was asked recently to two eminent mathematical physicists, Mel Levy and Elliott Lieb, and here is their wish list of open problems in many-electron theory.