Zeta functions for the spectrum of the non-commutative harmonic oscillators

Takashi Ichinose, Masato Wakayama

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

This paper investigates the spectral zeta function of the non-commutative harmonic oscillator studied in [PW1, 2]. It is shown, as one of the basic analytic properties, that the spectral zeta function is extended to a meromorphic function in the whole complex plane with a simple pole at s=1, and further that it has a zero at all non-positive even integers, i.e. at s=0 and at those negative even integers where the Riemann zeta function has the so-called trivial zeros. As a by-product of the study, both the upper and the lower bounds are also given for the first eigenvalue of the non-commutative harmonic oscillator.

Original languageEnglish
Pages (from-to)697-739
Number of pages43
JournalCommunications in Mathematical Physics
Volume258
Issue number3
DOIs
Publication statusPublished - Sep 1 2005

Fingerprint

Harmonic Oscillator
Riemann zeta function
harmonic oscillators
Spectral Function
integers
meromorphic functions
Integer
First Eigenvalue
Zero
Meromorphic Function
Argand diagram
Pole
Trivial
eigenvalues
poles
Lower bound

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Zeta functions for the spectrum of the non-commutative harmonic oscillators. / Ichinose, Takashi; Wakayama, Masato.

In: Communications in Mathematical Physics, Vol. 258, No. 3, 01.09.2005, p. 697-739.

Research output: Contribution to journalArticle

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