universality and dynamic localization in kibble- zurek
DESCRIPTION
Universality and Dynamic Localization in Kibble- Zurek. Michael Kolodrubetz Boston University In collaboration with: B.K. Clark, D. Huse (Princeton) A. Polkovnikov , A. Katz (BU). Kibble- Zurek Scaling. Disordered. Ordered. Kibble- Zurek scaling. Ramp rate. - PowerPoint PPT PresentationTRANSCRIPT
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UNIVERSALITY AND DYNAMIC LOCALIZATION IN KIBBLE-ZUREKMichael Kolodrubetz
Boston University
In collaboration with: B.K. Clark, D. Huse (Princeton)A. Polkovnikov, A. Katz (BU)
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KIBBLE-ZUREK SCALING
Disordered Ordered
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KIBBLE-ZUREK SCALING
Ramp rate
Kibble-ZurekRamp through the critical
point at a constant, finite rate
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KIBBLE-ZUREK SCALING
Ramp rate
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KIBBLE-ZUREK SCALING
Ramp rate
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KIBBLE-ZUREK SCALING
Ramp rate
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KIBBLE-ZUREK SCALING
Ramp rate
Fall out ofequilibrium
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KIBBLE-ZUREK SCALING
Ramp rate
Fall out ofequilibrium
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Recent work: Kibble-Zurek rampsshow non-equilibrium scaling (in the limit of slow ramps)
[Chandran et. al., Deng et. al., etc.]
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KIBBLE-ZUREK SCALING
Recent work: Kibble-Zurek rampsshow non-equilibrium scaling (in the limit of slow ramps) More predictions than just defect production!
[Chandran et. al., Deng et. al., etc.]
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KIBBLE-ZUREK SCALING
Excess heat
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
SchrödingerEquation
ORObservable
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KIBBLE-ZUREK SCALING
SchrödingerEquation
ORObservable
Fixed
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KIBBLE-ZUREK SCALING
SchrödingerEquation
ORObservable
Fixed
Universaldynamics!=
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TRANSVERSE-FIELD ISING CHAIN
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TRANSVERSE-FIELD ISING CHAIN
Paramagnet (PM) Ferromagnet (FM)
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TRANSVERSE-FIELD ISING CHAIN
Paramagnet (PM) Ferromagnet (FM)
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Ramp rate
Slower
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KIBBLE-ZUREK SCALING
Excess heat
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
Dynamics does not depend on ramp
rate!
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory
Part II: Kibble-Zurek with a dynamic field
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal?
Part II: Kibble-Zurek with a dynamic field
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UNIVERSALITY
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
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UNIVERSALITY
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
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UNIVERSALITY
or
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
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UNIVERSALITY
or
Ramp the tilt linearly in time
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
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UNIVERSALITY
or
Ramp the tilt linearly in time: Solve numerically
with DMRG
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
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UNIVERSALITY
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UNIVERSALITY
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UNIVERSALITY
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UNIVERSALITY
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UNIVERSALITY
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UNIVERSALITY
Dynamics are
universal!
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs
Part II: Kibble-Zurek with a dynamic field
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Non-trivial scaling functions
Part II: Kibble-Zurek with a dynamic field
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NON-EQUILIBRIUM PROPERTIES
Spin-spin correlation function
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NON-EQUILIBRIUM PROPERTIES
Thermal
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NON-EQUILIBRIUM PROPERTIES
Kibble-Z
urek
Thermal
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NON-EQUILIBRIUM PROPERTIES
Kibble-Z
urek
Thermal
Antiferromagnetic
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NON-EQUILIBRIUM PROPERTIES
Antiferromagnetic
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal
Part II: Kibble-Zurek with a dynamic field
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field Motivating example: 4 theory
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
“Inflaton”
“Higgs field”
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DYNAMIC-FIELD KIBBLE-ZUREK
“Inflaton”
“Higgs field”
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
When does field get trapped?
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
Dynamics dominated by critical behavior
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREK
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DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
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DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
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DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption
Should work equally well for Higgs, etc.
![Page 140: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/140.jpg)
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption
Should work equally well for Higgs, etc. Do dynamics show scaling collapse?
![Page 141: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/141.jpg)
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption
Should work equally well for Higgs, etc. Do dynamics show scaling collapse?
Expect scaling for
![Page 142: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/142.jpg)
DYNAMIC-FIELD KIBBLE-ZUREK
Scaling hypothesisInitial momentum is the
relevant scale for dynamics
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DYNAMIC-FIELD KIBBLE-ZUREK
Scaling hypothesisInitial momentum is the
relevant scale for dynamics
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DYNAMIC-FIELD KIBBLE-ZUREK
Scaling hypothesisInitial momentum is the
relevant scale for dynamics
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse
![Page 146: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/146.jpg)
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Effect of ground state potential?
![Page 147: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/147.jpg)
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Effect of ground state potential
Is RG relevant
![Page 148: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/148.jpg)
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling
functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Effect of ground state potential
Is RG relevant Trapping in certain regimes
![Page 149: Universality and Dynamic Localization in Kibble- Zurek](https://reader033.vdocument.in/reader033/viewer/2022050819/56814e67550346895dbc04a7/html5/thumbnails/149.jpg)
DYNAMIC-FIELD KIBBLE-ZUREK
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OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling functions? Finite size scaling, dephasing, experiments…
Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Trapping can occur with ground state potential In progress: scaling with potential, emergent
mass, 4 theory, inflationary models…
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SUMMARY
Part I: Universality of Kibble-Zurek scaling
Part II: Kibble-Zurek with a dynamic field
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TRANSVERSE-FIELD ISING CHAIN
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TRANSVERSE-FIELD ISING CHAIN
phase
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TRANSVERSE-FIELD ISING CHAIN
phase
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EQUILIBRIUM SCALING
“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
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EQUILIBRIUM SCALING
Low energy, long wavelength theory?
“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
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EQUILIBRIUM SCALING
Low energy, long wavelength theory
“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
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KIBBLE-ZUREK SCALING
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KIBBLE-ZUREK SCALING
Low energy, long wavelength theory?
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KIBBLE-ZUREK SCALING
Low energy, long wavelength theory?
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KIBBLE-ZUREK SCALING
Low energy, long wavelength theory
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
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NON-EQUILIBRIUM PROPERTIES
Inverted
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DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
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DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
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DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
“Friction” = back-action of spins on field
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DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
“Friction” = back-action of spins on field Mass is extensive ( ) Mean-field coupling between field and spins
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DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
“Friction” = back-action of spins on field Mass is extensive ( ) Mean-field coupling between field and spins
What happens when field tries to
pass through the critical point?