Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory
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| Format: | Preprint |
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2025
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| _version_ | 1866914357119549440 |
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| author | He, Peng-Zhang Liu, Lei-Hua Zhang, Hai-Qing Jiang, Qing-Quan |
| author_facet | He, Peng-Zhang Liu, Lei-Hua Zhang, Hai-Qing Jiang, Qing-Quan |
| contents | We study Krylov complexity in Schrödinger field theory in the grand canonical ensemble with chemical potential $μ$, with an emphasis on the qualitatively new features that arise for $μ>0$. In this regime the fermionic Wightman power spectrum is effectively single-sided and sharply truncated at $ω=μ$, which induces a crossover in the Lanczos coefficients {and signals a dynamical transition from a bulk-dominated regime to a spectral-edge-dominated regime}: $b_n$ displays a two-stage linear growth (from an early-time slope $π/β$ to an asymptotic slope $2/β$), while $a_n$ bends from near-zero values to a linear descent with slope $-4/β$. We provide analytic support for the resulting complexity growth from three complementary viewpoints: (i) using an $SL(2,\mathbb{R})$ algebraic construction matched to the asymptotic Lanczos data, we show that the late-time Krylov complexity must grow quadratically, $K(t)\propto t^{2}$; (ii) by analyzing engineered Wightman spectra with controlled decay and truncation, we identify single-sided exponential decay as the key spectral feature responsible for the quadratic asymptotics, while an approximately even two-sided exponential spectrum explains the early-time $K(t)\sim\sinh^{2}(πt/β)$ behavior at large $μ$; (iii) we formulate the problem in terms of orthogonal polynomials and estimate the crossover scale separating the early- and late-stage regimes. Overall, our results help clarify the role of chemical potential and spectral truncation in shaping operator growth and Krylov complexity in this non-relativistic quantum field theory setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory He, Peng-Zhang Liu, Lei-Hua Zhang, Hai-Qing Jiang, Qing-Quan High Energy Physics - Theory Statistical Mechanics We study Krylov complexity in Schrödinger field theory in the grand canonical ensemble with chemical potential $μ$, with an emphasis on the qualitatively new features that arise for $μ>0$. In this regime the fermionic Wightman power spectrum is effectively single-sided and sharply truncated at $ω=μ$, which induces a crossover in the Lanczos coefficients {and signals a dynamical transition from a bulk-dominated regime to a spectral-edge-dominated regime}: $b_n$ displays a two-stage linear growth (from an early-time slope $π/β$ to an asymptotic slope $2/β$), while $a_n$ bends from near-zero values to a linear descent with slope $-4/β$. We provide analytic support for the resulting complexity growth from three complementary viewpoints: (i) using an $SL(2,\mathbb{R})$ algebraic construction matched to the asymptotic Lanczos data, we show that the late-time Krylov complexity must grow quadratically, $K(t)\propto t^{2}$; (ii) by analyzing engineered Wightman spectra with controlled decay and truncation, we identify single-sided exponential decay as the key spectral feature responsible for the quadratic asymptotics, while an approximately even two-sided exponential spectrum explains the early-time $K(t)\sim\sinh^{2}(πt/β)$ behavior at large $μ$; (iii) we formulate the problem in terms of orthogonal polynomials and estimate the crossover scale separating the early- and late-stage regimes. Overall, our results help clarify the role of chemical potential and spectral truncation in shaping operator growth and Krylov complexity in this non-relativistic quantum field theory setting. |
| title | Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2509.14742 |