Boom and bust cycles due to pseudospectra of matrices with unimodular spectra

Bhat, Junaid Majeed (avtor), Bensa, Jaš (avtor), Žnidarič, Marko (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: pseudospectrum, non-normal matrices, exponential growth
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: 15 str.
• Številčenje: Vol. 58, no. 29, art. 295202
• PID: 20.500.12556/RUL-182235
• UDK: 512
• ISSN pri članku: 1751-8121
• DOI: 10.1088/1751-8121/aded52
• COBISS.SI-ID: 276509187
• Datum objave v RUL: 05.05.2026

Gradivo je del revije

• Naslov: Journal of physics. A, Mathematical and theoretical
• Skrajšan naslov: J. phys., A, Math. theor.
• Založnik: IOP Publishing
• ISSN: 1751-8121
• COBISS.SI-ID: 3763226

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: psevdospekter, nenormalna matrika, eksponentna rast

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: J1-4385
• Naslov: Kvantna večdelčna fizika in nehermitskost

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika