We study the spectral form factor (SFF) for hydrodynamic systems with a sound pole, a large class including any fluid with momentum conservation and energy conservation, or any extended system with spontaneously broken continuous symmetry. We study such systems in a finite volume cavity and find that the logarithm of the hydrodynamic enhancement to the SFF is closely related to the spectral form factor of a quantum particle moving in the selfsame cavity. Depending upon the dimensionality and nature of the effective single-particle physics, these systems exhibit a range of behaviors including an intricate resonance phenomenon, emergent integrability in the SFF, and anomalously large fluctuations of the SFF.We study the spectral form factor (SFF) for hydrodynamic systems with a sound pole, a large class including any fluid with momentum conservation and energy conservation, or any extended system with spontaneously broken continuous symmetry. We study such systems in a finite volume cavity and find that the logarithm of the hydrodynamic enhancement to the SFF is closely related to the spectral form factor of a quantum particle moving in the selfsame cavity. Depending upon the dimensionality and nature of the effective single-particle physics, these systems exhibit a range of behaviors including an intricate resonance phenomenon, emergent integrability in the SFF, and anomalously large fluctuations of the SFF.

arXiv:2211.09134Physical review. B./Physical review. BAug 25, 20237 citations

Spectral form factors of topological phases

Anurag Sarkar, Subrata Pachhal, Adhip Agarwala +1 more

Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of such systems in a variety of strongly interacting quantum theories, in this work, we study their behavior in short-range entangled topological phases, particularly focusing on the role of symmetry-protected topological zero modes. We show, using both analytical and numerical methods, how the existence of such zero modes in any representative system can mask the SFF with large period (akin to generalized Rabi) oscillations, hiding any behavior arising from the bulk of the spectrum. Moreover, in a quenched disordered system, these zero modes fundamentally change the late-time universal behavior reflecting the chaotic signatures of the zero-energy manifold. Our study uncovers the rich physics underlying the interplay of chaotic signatures and topological characteristics in a quantum system.Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of such systems in a variety of strongly interacting quantum theories, in this work, we study their behavior in short-range entangled topological phases, particularly focusing on the role of symmetry-protected topological zero modes. We show, using both analytical and numerical methods, how the existence of such zero modes in any representative system can mask the SFF with large period (akin to generalized Rabi) oscillations, hiding any behavior arising from the bulk of the spectrum. Moreover, in a quenched disordered system, these zero modes fundamentally change the late-time universal behavior reflecting the chaotic signatures of the zero-energy manifold. Our study uncovers the rich physics underlying the interplay of chaotic signatures and topological characteristics in a quantum system.

arXiv:2306.13138Physical review. B./Physical review. BApr 9, 20244 citations

Quantum Entanglement Theory

Michigan State University Press eBooksJan 1, 20260 citations

Quantum entanglement and its applications

Shengjun Wu

Jan 1, 20030 citations

The Loschmidt spectral form factor

Michael Winer, Brian G. Swingle

Abstract The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor, $\textrm{tr}\left[{e}^{i{H}_1T}\right]\textrm{tr}\left[{e}^{-i{H}_2T}\right]$ tr e i H 1 T tr e − i H 2 T , for H1 − H2 small. If the ensemble average of the SFF is the variance of the density fluctuations for a single Hamiltonian drawn from the ensemble, the averaged Loschmidt SFF is the covariance for two Hamiltonians drawn from a correlated ensemble. This object is a time-domain version of the parametric correlations studied in the quantum chaos and random matrix literatures. We show analytically that the averaged Loschmidt SFF is proportional to eiλTT for a complex rate λ with a positive imaginary part, showing in a quantitative way that the long-time details of the spectrum are exponentially more sensitive to perturbations than the short-time properties. We calculate λ in a number of cases, including random matrix theory, theories with a single localized defect, and hydrodynamic theories.Abstract The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor, $$ \textrm{tr}\left[{e}^{i{H}_1T}\right]\textrm{tr}\left[{e}^{-i{H}_2T}\right] $$ tr e i H 1 T tr e − i H 2 T , for H1 − H2 small. If the ensemble average of the SFF is the variance of the density fluctuations for a single Hamiltonian drawn from the ensemble, the averaged Loschmidt SFF is the covariance for two Hamiltonians drawn from a correlated ensemble. This object is a time-domain version of the parametric correlations studied in the quantum chaos and random matrix literatures. We show analytically that the averaged Loschmidt SFF is proportional to eiλTT for a complex rate λ with a positive imaginary part, showing in a quantitative way that the long-time details of the spectrum are exponentially more sensitive to perturbations than the short-time properties. We calculate λ in a number of cases, including random matrix theory, theories with a single localized defect, and hydrodynamic theories.

arXiv:2206.00677Journal of High Energy PhysicsOct 20, 20228 citations

Abstract The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor,

\textrm{tr}\left[{e}^{i{H}_1T}\right]\textrm{tr}\left[{e}^{-i{H}_2T}\right]

tr e i H 1 T tr e − i H 2 T , for H1 − H2 small. If the ensemble average of the SFF is the variance of the density fluctuations for a single Hamiltonian drawn from the ensemble, the averaged Loschmidt SFF is the covariance for two Hamiltonians drawn from a correlated ensemble. This object is a time-domain version of the parametric correlations studied in the quantum chaos and random matrix literatures. We show analytically that the averaged Loschmidt SFF is proportional to eiλTT for a complex rate λ with a positive imaginary part, showing in a quantitative way that the long-time details of the spectrum are exponentially more sensitive to perturbations than the short-time properties. We calculate λ in a number of cases, including random matrix theory, theories with a single localized defect, and hydrodynamic theories.