Divergences in open quantum systems

Agón, Cesar; Lawrence, Albion

doi:10.1007/jhep04(2018)008

Title: Divergences in open quantum systems

Abstract

Here, we show that for cubic scalar field theories in five and more spacetime dimensions, and for the T = 0 limit of the Caldeira-Leggett model, the quantum master equation for long-wavelength modes initially unentangled from short-distance modes, and at second order in perturbation theory, contains divergences in the non-Hamiltonian terms. These divergences ensure that the equations of motion for expectation values of composite operators closes on expectation values of renormalized operators. Along the way we show that initial “jolt” singularities which occur in the equations of motion for operators linear in the fundamental variables persist for quadratic operators, and are removed if one chooses an initial state projected onto low energies, following the Born-Oppenheimer approximation.

Authors:

Agón, Cesar ^[1]; Lawrence, Albion ^[2]

Brandeis Univ., Waltham, MA (United States). Martin Fisher School of Physics; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; State Univ. of New York (SUNY), Plattsburgh, NY (United States). C.N. Yang Inst. for Theoretical Physics
Brandeis Univ., Waltham, MA (United States). Martin Fisher School of Physics

Publication Date:: 2018-04-03

Research Org.:: Brandeis Univ., Waltham, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1503319

Grant/Contract Number:: SC0009987

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Quantum Dissipative Systems; Renormalization Group

Citation Formats


                    Agón, Cesar, and Lawrence, Albion. Divergences in open quantum systems.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep04(2018)008.

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                    Agón, Cesar, & Lawrence, Albion. Divergences in open quantum systems.  United States.  https://doi.org/10.1007/jhep04(2018)008

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                    Agón, Cesar, and Lawrence, Albion. Tue .  
"Divergences in open quantum systems".  United States.  https://doi.org/10.1007/jhep04(2018)008.  https://www.osti.gov/servlets/purl/1503319.

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@article{osti_1503319,

  title        = {Divergences in open quantum systems},

  author       = {Agón, Cesar and Lawrence, Albion},

  abstractNote = {Here, we show that for cubic scalar field theories in five and more spacetime dimensions, and for the T = 0 limit of the Caldeira-Leggett model, the quantum master equation for long-wavelength modes initially unentangled from short-distance modes, and at second order in perturbation theory, contains divergences in the non-Hamiltonian terms. These divergences ensure that the equations of motion for expectation values of composite operators closes on expectation values of renormalized operators. Along the way we show that initial “jolt” singularities which occur in the equations of motion for operators linear in the fundamental variables persist for quadratic operators, and are removed if one chooses an initial state projected onto low energies, following the Born-Oppenheimer approximation.},

  doi          = {10.1007/jhep04(2018)008},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 4,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {4}

}

Copy to clipboard

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Open quantum dynamics induced by light scalar fields
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Title: Divergences in open quantum systems

Abstract

Citation Formats

Quantum disentangled liquids journal, October 2014

Initial Conditions for Inflation journal, November 2002

Decoherence of inflationary primordial fluctuations journal, March 2008

Memory Effects in Irreversible Thermodynamics journal, November 1961

Path integral approach to quantum Brownian motion journal, September 1983

Universality in fast quantum quenches journal, February 2015

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation journal, January 2016

Influence action and decoherence of hydrodynamic modes journal, February 1999

Universal Scaling in Fast Quantum Quenches in Conformal Field Theories journal, April 2014

Exact diagonalization of two quantum models for the damped harmonic oscillator journal, January 2000

The Quantum-Statistical Theory of Transport Phenomena, I: On the Boltzmann-Uehling-Uhlenbeck Equation journal, September 1952

Emergent Newtonian dynamics and the geometric origin of mass journal, June 2014

Hydrodynamic transport coefficients in relativistic scalar field theory journal, September 1995

Renormalization in open quantum field theory. Part I. Scalar field theory journal, November 2017

Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology journal, October 2001

Ensemble Method in the Theory of Irreversibility journal, November 1960

Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions journal, March 2014

Holographic interpretations of the renormalization group journal, January 2013

The Theory of a General Quantum System Interacting with a Linear Dissipative System journal, April 2000

Hamiltonian formulation of Wilson's lattice gauge theories journal, January 1975

Relativistic hydrodynamics from the projection operator method journal, February 2013

From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory journal, May 1996

On quantum statistical mechanics of non-Hamiltonian systems journal, December 1972

Coarse graining and decoherence in quantum field theory journal, February 1996

Foundations and measures of quantum non-Markovianity journal, July 2012

Quantum non-Markovianity: characterization, quantification and detection journal, August 2014

The theory of a general quantum system interacting with a linear dissipative system journal, October 1963

An exactly solvable quench protocol for integrable spin models journal, November 2017

The Quantum-statistical Theory of Transport Phenomena, II: On the Theory of Metallic Conductivity journal, May 1953

Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) journal, March 1965

Foundations and Measures of Quantum Non-Markovianity text, January 2012

Relativistic hydrodynamics from projection operator method text, January 2012

Holographic interpretations of the renormalization group text, January 2012

Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions text, January 2013

Emergent Newtonian dynamics and the geometric origin of mass text, January 2013

Universal scaling in fast quantum quenches in conformal field theories text, January 2014

Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation text, January 2015

Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory text, January 1994

Coarse-Grained Effective Action and Renormalization Group Theory in Semiclassical Gravity and Cosmology text, January 2001

Coarse graining and decoherence in quantum field theory text, January 1995

Exact Diagonalization of Two Quantum Models for the Damped Harmonic Oscillator text, January 1999

Open quantum dynamics induced by light scalar fields journal, October 2019

Hot Cosmic Qubits: Late-Time de Sitter Evolution and Critical Slowing Down text, January 2019

Quantum disentangled liquids
journal, October 2014

Initial Conditions for Inflation
journal, November 2002

Decoherence of inflationary primordial fluctuations
journal, March 2008

Memory Effects in Irreversible Thermodynamics
journal, November 1961

Path integral approach to quantum Brownian motion
journal, September 1983

Universality in fast quantum quenches
journal, February 2015

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation
journal, January 2016

Influence action and decoherence of hydrodynamic modes
journal, February 1999

Universal Scaling in Fast Quantum Quenches in Conformal Field Theories
journal, April 2014

Exact diagonalization of two quantum models for the damped harmonic oscillator
journal, January 2000

The Quantum-Statistical Theory of Transport Phenomena, I: On the Boltzmann-Uehling-Uhlenbeck Equation
journal, September 1952

Emergent Newtonian dynamics and the geometric origin of mass
journal, June 2014

Hydrodynamic transport coefficients in relativistic scalar field theory
journal, September 1995

Renormalization in open quantum field theory. Part I. Scalar field theory
journal, November 2017

Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
journal, October 2001

Ensemble Method in the Theory of Irreversibility
journal, November 1960

Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
journal, March 2014

Holographic interpretations of the renormalization group
journal, January 2013

The Theory of a General Quantum System Interacting with a Linear Dissipative System
journal, April 2000

Hamiltonian formulation of Wilson's lattice gauge theories
journal, January 1975

Relativistic hydrodynamics from the projection operator method
journal, February 2013

From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory
journal, May 1996

On quantum statistical mechanics of non-Hamiltonian systems
journal, December 1972

Coarse graining and decoherence in quantum field theory
journal, February 1996

Foundations and measures of quantum non-Markovianity
journal, July 2012

Quantum non-Markovianity: characterization, quantification and detection
journal, August 2014

The theory of a general quantum system interacting with a linear dissipative system
journal, October 1963

An exactly solvable quench protocol for integrable spin models
journal, November 2017

The Quantum-statistical Theory of Transport Phenomena, II: On the Theory of Metallic Conductivity
journal, May 1953

Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
journal, March 1965

Foundations and Measures of Quantum Non-Markovianity
text, January 2012

Relativistic hydrodynamics from projection operator method
text, January 2012

Holographic interpretations of the renormalization group
text, January 2012

Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
text, January 2013

Emergent Newtonian dynamics and the geometric origin of mass
text, January 2013

Universal scaling in fast quantum quenches in conformal field theories
text, January 2014

Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
text, January 2015

Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
text, January 1994

Coarse-Grained Effective Action and Renormalization Group Theory in Semiclassical Gravity and Cosmology
text, January 2001

Coarse graining and decoherence in quantum field theory
text, January 1995

Exact Diagonalization of Two Quantum Models for the Damped Harmonic Oscillator
text, January 1999

Open quantum dynamics induced by light scalar fields
journal, October 2019

Hot Cosmic Qubits: Late-Time de Sitter Evolution and Critical Slowing Down
text, January 2019