20.500.12556/RUL-182235 Boom and bust cycles due to pseudospectra of matrices with unimodular spectra We discuss dynamics obtained by increasing powers of non-normal matrices that are roots of the identity and therefore have all eigenvalues on the unit circle. Naively, one would expect that the matrix elements of high powers of the matrix asymptotically cannot grow as one increases the power. We demonstrate that, rather counterintuitively, a completely opposite behavior is possible. In the limit of infinitely large matrices, one can have an exponential growth. For finite matrices, this exponential growth is part of a repeating cycles of exponential growth followed by an exponential decay. The effect can occur for strongly non-normal matrices if the spectrum is different than the pseudospectrum, with the exponential growth rate being given by the pseudospectrum. We show that this effect appears in a class of transfer matrices appearing in studies of two-dimensional non-interacting systems, for a matrix describing the Ehrenfest urn, as well as in previously observed purity dynamics in a staircase random circuit. pseudospectrum non-normal matrices exponential growth psevdospekter nenormalna matrika eksponentna rast true false true Angleški jezik Slovenski jezik Članek v reviji 2026-05-05 08:20:04 2026-05-05 08:20:06 2026-05-13 04:51:31 0000-00-00 00:00:00 2025 0 0 15 str. no. 29, art. 295202 Vol. 58 Jul. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 1751-8121 10.1088/1751-8121/aded52 276509187 Bhat_2025_J._Phys._A__Math._Theor._58_295202.pdf Bhat_2025_J._Phys._A__Math._Theor._58_295202.pdf 1 1AE5AA3CA3F4E04B3A99B6A89F9914F4 bf30fc19cba72a7487f945f09e583d42b300a42377aa5ac7b498a99033d9e55f b073e503-4dd1-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233711 https://iopscience.iop.org/article/10.1088/1751-8121/aded52 1 2fe38f94-484a-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233304 Fakulteta za matematiko in fiziko 0 0 0