The Loschmidt spectral form factor

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] %$, for H1 − H2 small. If the...
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Autor*in:	Winer, Michael [verfasserIn] Swingle, Brian

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Effective Field Theories Field Theory Hydrodynamics Nonperturbative Effects Random Systems

Anmerkung:	© The Author(s) 2022

Übergeordnetes Werk:	Enthalten in: Journal of high energy physics - Berlin : Springer, 1997, 2022(2022), 10 vom: 20. Okt.
Übergeordnetes Werk:	volume:2022 ; year:2022 ; number:10 ; day:20 ; month:10

Links:	Volltext

DOI / URN:	10.1007/JHEP10(2022)137

Katalog-ID:	SPR048426199

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520			\|a 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] %$, for H1 − H2 small. If the ensemble average of the SFF is the variance of the density fluctuations for a single Hamiltonian drawn from the ensemble, the averaged Loschmidt SFF is the covariance for two Hamiltonians drawn from a correlated ensemble. This object is a time-domain version of the parametric correlations studied in the quantum chaos and random matrix literatures. We show analytically that the averaged Loschmidt SFF is proportional to eiλTT for a complex rate λ with a positive imaginary part, showing in a quantitative way that the long-time details of the spectrum are exponentially more sensitive to perturbations than the short-time properties. We calculate λ in a number of cases, including random matrix theory, theories with a single localized defect, and hydrodynamic theories.
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allfields	10.1007/JHEP10(2022)137 doi (DE-627)SPR048426199 (SPR)JHEP10(2022)137-e DE-627 ger DE-627 rakwb eng Winer, Michael verfasserin aut The Loschmidt spectral form factor 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor, %$ \textrm{tr}\left[{e}^{i{H}_1T}\right]\textrm{tr}\left[{e}^{-i{H}_2T}\right] %$, 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. Effective Field Theories (dpeaa)DE-He213 Field Theory Hydrodynamics (dpeaa)DE-He213 Nonperturbative Effects (dpeaa)DE-He213 Random Systems (dpeaa)DE-He213 Swingle, Brian aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2022(2022), 10 vom: 20. Okt. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2022 year:2022 number:10 day:20 month:10 https://dx.doi.org/10.1007/JHEP10(2022)137 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2022 2022 10 20 10
spelling	10.1007/JHEP10(2022)137 doi (DE-627)SPR048426199 (SPR)JHEP10(2022)137-e DE-627 ger DE-627 rakwb eng Winer, Michael verfasserin aut The Loschmidt spectral form factor 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 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] %$, 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. Effective Field Theories (dpeaa)DE-He213 Field Theory Hydrodynamics (dpeaa)DE-He213 Nonperturbative Effects (dpeaa)DE-He213 Random Systems (dpeaa)DE-He213 Swingle, Brian aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2022(2022), 10 vom: 20. Okt. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2022 year:2022 number:10 day:20 month:10 https://dx.doi.org/10.1007/JHEP10(2022)137 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2022 2022 10 20 10
allfields_unstemmed	10.1007/JHEP10(2022)137 doi (DE-627)SPR048426199 (SPR)JHEP10(2022)137-e DE-627 ger DE-627 rakwb eng Winer, Michael verfasserin aut The Loschmidt spectral form factor 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 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] %$, 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. Effective Field Theories (dpeaa)DE-He213 Field Theory Hydrodynamics (dpeaa)DE-He213 Nonperturbative Effects (dpeaa)DE-He213 Random Systems (dpeaa)DE-He213 Swingle, Brian aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2022(2022), 10 vom: 20. Okt. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2022 year:2022 number:10 day:20 month:10 https://dx.doi.org/10.1007/JHEP10(2022)137 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2022 2022 10 20 10
allfieldsGer	10.1007/JHEP10(2022)137 doi (DE-627)SPR048426199 (SPR)JHEP10(2022)137-e DE-627 ger DE-627 rakwb eng Winer, Michael verfasserin aut The Loschmidt spectral form factor 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 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] %$, 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. Effective Field Theories (dpeaa)DE-He213 Field Theory Hydrodynamics (dpeaa)DE-He213 Nonperturbative Effects (dpeaa)DE-He213 Random Systems (dpeaa)DE-He213 Swingle, Brian aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2022(2022), 10 vom: 20. Okt. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2022 year:2022 number:10 day:20 month:10 https://dx.doi.org/10.1007/JHEP10(2022)137 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2022 2022 10 20 10
allfieldsSound	10.1007/JHEP10(2022)137 doi (DE-627)SPR048426199 (SPR)JHEP10(2022)137-e DE-627 ger DE-627 rakwb eng Winer, Michael verfasserin aut The Loschmidt spectral form factor 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 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] %$, 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. Effective Field Theories (dpeaa)DE-He213 Field Theory Hydrodynamics (dpeaa)DE-He213 Nonperturbative Effects (dpeaa)DE-He213 Random Systems (dpeaa)DE-He213 Swingle, Brian aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2022(2022), 10 vom: 20. Okt. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2022 year:2022 number:10 day:20 month:10 https://dx.doi.org/10.1007/JHEP10(2022)137 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2022 2022 10 20 10
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source	Enthalten in Journal of high energy physics 2022(2022), 10 vom: 20. Okt. volume:2022 year:2022 number:10 day:20 month:10
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author	Winer, Michael
spellingShingle	Winer, Michael misc Effective Field Theories misc Field Theory Hydrodynamics misc Nonperturbative Effects misc Random Systems The Loschmidt spectral form factor
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topic_title	The Loschmidt spectral form factor Effective Field Theories (dpeaa)DE-He213 Field Theory Hydrodynamics (dpeaa)DE-He213 Nonperturbative Effects (dpeaa)DE-He213 Random Systems (dpeaa)DE-He213
topic	misc Effective Field Theories misc Field Theory Hydrodynamics misc Nonperturbative Effects misc Random Systems
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title	The Loschmidt spectral form factor
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title_sort	loschmidt spectral form factor
title_auth	The Loschmidt spectral form factor
abstract	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] %$, for H1 − H2 small. If the ensemble average of the SFF is the variance of the density fluctuations for a single Hamiltonian drawn from the ensemble, the averaged Loschmidt SFF is the covariance for two Hamiltonians drawn from a correlated ensemble. This object is a time-domain version of the parametric correlations studied in the quantum chaos and random matrix literatures. We show analytically that the averaged Loschmidt SFF is proportional to eiλTT for a complex rate λ with a positive imaginary part, showing in a quantitative way that the long-time details of the spectrum are exponentially more sensitive to perturbations than the short-time properties. We calculate λ in a number of cases, including random matrix theory, theories with a single localized defect, and hydrodynamic theories. © The Author(s) 2022
abstractGer	Abstract The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor, %$ \textrm{tr}\left[{e}^{i{H}_1T}\right]\textrm{tr}\left[{e}^{-i{H}_2T}\right] %$, for H1 − H2 small. If the ensemble average of the SFF is the variance of the density fluctuations for a single Hamiltonian drawn from the ensemble, the averaged Loschmidt SFF is the covariance for two Hamiltonians drawn from a correlated ensemble. This object is a time-domain version of the parametric correlations studied in the quantum chaos and random matrix literatures. We show analytically that the averaged Loschmidt SFF is proportional to eiλTT for a complex rate λ with a positive imaginary part, showing in a quantitative way that the long-time details of the spectrum are exponentially more sensitive to perturbations than the short-time properties. We calculate λ in a number of cases, including random matrix theory, theories with a single localized defect, and hydrodynamic theories. © The Author(s) 2022
abstract_unstemmed	Abstract The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor, %$ \textrm{tr}\left[{e}^{i{H}_1T}\right]\textrm{tr}\left[{e}^{-i{H}_2T}\right] %$, 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. © The Author(s) 2022
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title_short	The Loschmidt spectral form factor
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