Related papers: Orthogonality Catastrophe Revisited
For every $2$-regular graph $F$ of order $v$, the Oberwolfach problem $OP(F)$ asks whether there is a $2$-factorization of $K_v$ ($v$ odd) or $K_v$ minus a $1$-factor ($v$ even) into copies of $F$. Posed by Ringel in 1967 and extensively…
In this paper we demonstrate that the selection of events with different multiplicities of produced particles, leads to the violation of the azimuthal angular symmetry, $\phi \to \pi - \phi$. We find for LHC and lower energies, that this…
We investigate the nonequilibrium dynamics of a groundstate fermionic many body gas subjected to a quench between parameter regimes of a topologically nontrivial Hamiltonian. By focusing on the role of the chiral edge states inherent to the…
Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation…
For N impenetrable particles in one dimension where only the nearest and next-to-nearest neighbours interact, we obtain the complete spectrum both on a line and on a circle. Further, we establish a mapping between these N-body problems and…
The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy…
Recent developments identify pole-skipping as a `smoking-gun' signature of the hydrodynamic nature of chaos, offering an alternative way to probe quantum chaos in addition to the out-of-time-ordered correlator (OTOC). We study the quantum…
The excitation of a slow extraordinary wave in a overdense plasma from an ordinary wave impinging on the critical layer in the plane spanned by the density gradient and magnetic field is solved analytically by formulating the problem in…
While highly successful, density functional theory is known to have limitations owing to its neglect of many-body electron-electron interactions. This neglect leads to errors in the single-particle energies, leading to underestimated band…
It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and…
In this work, we study optical self-focusing that leads to collapse events for the time-independent model of co-propagating beams with different wavelengths. We show that collapse events depend on the combined critical power of two beams…
The conditions under which a linear anisotropic polarization element orthogonalizes several polarization states of input totally polarized light were studied in the paper. The criterion for orthogonalization was obtained in the form of…
Orthogonality of eigenstates of different energies and its implications in potential scattering are unlabeled. Scalar products of scattering states of different energies are found to have finite non-orthogonal terms in potentials of finite…
We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely,…
We present the results of generalized measurements of optical polarization designed to provide one of three or four distinct outcomes. This has allowed us to discriminate between nonorthogonal polarization states with an error probability…
We investigate multiple orthogonal polynomials associated with the system of measures obtained by applying a Christoffel transform to each of the orthogonality measures. We present an algorithm for computing the transformed recurrence…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
The use of proper orthogonal decomposition (POD) to explore the complex fluid flows that are common in engineering applications is increasing and has yielded new physical insights. However, for most engineering systems the dimension of the…
In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are…
This work discusses gravothermal catastrophe in astrophysical systems and provides an analytic collapse solution which exhibits many of the catastrophe properties. The system collapses into a trapped surface with outgoing energy radiated to…