Extreme decoherence and quantum chaos Adolfo d del C Campo DIPC - - PowerPoint PPT Presentation

Extreme decoherence and quantum chaos

Adolfo d del C Campo DIPC & & Ike kerbasque Bilbao, S Spain QI QIST2019 Yuka kawa I Institute f for T Theoretical P Physics, Kyoto U University, M May 2 29th

th, 2

2019

Adolfo d del C Campo

Adolfo d del C Campo

QST group from Boston to Bilbao

Adolfo d del C Campo

QST group from Boston to Bilbao

A Chenu AdC F Gomez-Ruiz L Dupays Dr N Gentil TY Huang J Zhu

• Dr. LP Garcia-Pintos Prof Zhenyu Xu

Research

Quantum open Systems Time, Quantum Speed Limits & Metrology Quantum Control: Shortcuts to Adiabaticity Dynamics of phase transitions: Kibble Zurek mechanism Quantum Computation: adiabatic, open Quantum Thermodynamics: engines, finite-time Trapped ions, cold atoms Integrable models, RMT, …

Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu

Adolfo d del C Campo

Open Quantum Systems: Decoherence

e.g. Zurek, Physics Today

Contents

u Extreme decoherence

Noise as a resource for Open Quantum Systems Noise coupled to local interactions Noise coupled to Random Matrix Theory

u Work statistics of complex systems

Loschmidt echo and p(W) P(W) and scrambling Work pdf & chaos/RMT Work pdf for time-reversal

Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu

System of interest embedded in an environment: composite system-environment Reduced dynamics via master equation Markovian limit: Universal Lindblad form

Adolfo d del C Campo

Open Quantum Systems

ρ(t) = ˆ USE(t, 0)ρS(0) ⊗ ρE ˆ USE(t, 0)† d dtρS = −i ~ h ˆ HS, ρS i + X

α

γα  LαρSL†

α − 1

2

• L†

αLα, ρS

• d

dtρS = −i ~ h ˆ HS, ρS i + D(ρS)

Adolfo d del C Campo

Open Quantum Systems: Decoherence

e.g. Zurek, Physics Today

Decay of coherences of density matrix, e.g. of a Schrodinger cat state

ψ0(x) = Nσ  e− (x−r)2

2σ2

+ e− (x+r)2

2σ2

Adolfo d del C Campo

Open Quantum Systems: Decoherence

e.g. Zurek, Physics Today

Decay of coherences of density matrix, e.g. of a Schrodinger cat state Quantum Brownian Motion Decoherence time in the high-temperature limit

τD = λ2

β

2γ∆x2

d dtρS(t) = 1 i~[H, ρS(t)] − iγ ~ [x, {p, ρS(t)}] − 2mγkBT ~2 [x, [x, ρS(t)]]

Adolfo d del C Campo

Decoherence from Quantum Decay: Fidelity

Survival probability Master equation Short time decay Universal decoherence time for Markovian evolutions

S(t) := F[ρS(0), ρS(t)] = hΨ0|ρS(t)|Ψ0i d dtρS = −i ~ h ˆ HS, ρS i + X

α

γα  LαρSL†

α − 1

2

• L†

αLα, ρS

• τD =

1 P

α γαCov

⇣ Lα, L†

α

⌘ Cov(A, B) = hABi hAihBi

• M. Beau, J. Kiukas, I. L. Egusquiza, AdC, Phys. Rev. Lett. 119, 130401 (2017)

S(t) = 1 − t τD + O(t2)

Adolfo d del C Campo

Purity Master equation Short time decay Universal decoherence time & rate

d dtρS = −i ~ h ˆ HS, ρS i + X

α

γα  LαρSL†

α − 1

2

• L†

αLα, ρS

• τD =

1 P

α γαCov

⇣ Lα, L†

α

⌘

• M. Beau, J. Kiukas, I. L. Egusquiza, AdC, Phys. Rev. Lett. 119, 130401 (2017)

Pt = P0[1 − Dt + O(t2)]

D = 2 P0 1 τD

Decoherence from Quantum Decay: Purity

Pt = trρ2

S ∈ [1/d, 1]

Adolfo d del C Campo

Decoherence from Quantum Decay

Survival probability Quantum Brownian motion Short time decay Recover Zurek’s estimate for decoherence time

S(t) := F[ρS(0), ρS(t)] = hΨ0|ρS(t)|Ψ0i S(t) = 1 − t τD + O(t2)

• M. Beau, J. Kiukas, I. L. Egusquiza, AdC, Phys. Rev. Lett. 119, 130401 (2017)

d dtρS(t) = 1 i~[H, ρS(t)] − iγ ~ [x, {p, ρS(t)}] − 2mγkBT ~2 [x, [x, ρS(t)]]

τD = λ2

β

2γ∆x2

Decoherence in Noisy Quantum systems

Adolfo d del C Campo

Adolfo d del C Campo

Sources of noise

System Environment

Adolfo d del C Campo

Sources of noise

Wavefunction Collapse models (GRW theory, Milburn model, …)

• A. Bassi et al. Rev. Mod. Phys. 85, 471

(2013)

• A. Chenu et al., Quantum Simulation of

Generic Many-Body Open System Dynamics Using Classical Noise, PRL 118, 140403 (2017).

• L. P. García-Pintos et al.,

Spontaneous symmetry breaking induced by quantum monitoring, arXiv:1808.08343.

• R. Gambini et al., Fundamental

decoherence from quantum gravity: a pedagogical review, J. Gen Relativ Gravit 39, 1143 (2007).

• I. L. Egusquiza et al., Quantum evolution

according to real clocks, Phys. Rev. A 59, 3236 (1999).

System Environment

Full system Deterministic part + stochastic part with real Gaussian process Stochastic Schrodinger equation Extensive literature

Adolfo d del C Campo

Stochastic Hamiltonians

H(t) = H0(t) + γ(t)V

i d dt|ψ(t)i = [H0(t) + γ(t)V ] |ψ(t)i

• G. J. Milburn, PRA 44, 5401 (1991)
• H. Moya-Cessa, V. Bužek, M. S. Kim, and P. L. Knight, PRA 48, 3900 (1993)
• A. Budini, PRA 64, 052110 (2001)

[…]

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

Noise-Averaged dynamics

Density matrix averaged over realizations Master equation requires stochastic unravelling Simplified via Novikov’s theorem for white noise

Adolfo d del C Campo

d dtρ(t) = −i[H0(t), ρ(t)] − W 2 2 [V, [V, ρ(t)]]

d dtρ(t) = i[H0(t), ρ] Z t dshγ(t)γ(s)i h V, h[ ˆ Ust(t, s)V ˆ U †

st(t, s), ρst(t)]i

i

ρ(t) = hρst(t)i = ⌦ |ψ(t)ihψ(t)| ↵

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

hγ(t)γ(t0)i = W 2δ(t t0)

Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain

Adolfo d del C Campo

Experimental tests?

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HI = − X

i<j

Jij σz

i σz j − h N

X

i=1

σx

i .

Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain

Adolfo d del C Campo

Experimental tests?

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HI = − X

i<j

Jij σz

i σz j − h N

X

i=1

σx

i .

Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain Modulating magnetic field Nonlocal “2-body” dissipator

Adolfo d del C Campo

Experimental tests?

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HI = − X

i<j

Jij σz

i σz j − h N

X

i=1

σx

i .

D[ρ(t)] = −γ X

ij

[σx

i [σx j , ρ(t)]]

τD ∼ 1/N 2

Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain

Adolfo d del C Campo

Experimental tests?

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HI = − X

i<j

Jij σz

i σz j − h N

X

i=1

σx

i .

Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain Modulating ferromagnetic couplings Nonlocal “4-body” dissipator

Adolfo d del C Campo

Experimental tests?

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HI = − X

i<j

Jij σz

i σz j − h N

X

i=1

σx

i .

D[ρ(t)] = −γ X

i<j

X

i0<j0

⇥ σz

i σz j ,

⇥ σz

i0σz j0, ρ(t)

⇤⇤ τD ∼ 1/N 4

Stochastic Hamiltonian k-body operators “2k-body” dissipators Double sum over indices vs usual single sum ~ correlated environment

Adolfo d del C Campo

Stochastic k-body Hamiltonians

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HS(t) = ˆ HT (t) + X

α

λα(t) ˆ Lα

[ ˆ P, ˆ Lα] = 0, ˆ Lα = X

i1<···<ik

L(α,k)

i1,...,ik

D(ρ) = − X

α

X

i1<···<ik

X

i0

1<···<i0 k

γα 2 [L(α,k)

i1,...,ik, [L(α,k) i0

1,...,i0 k, ρ]]

Stochastic Hamiltonian k-body operators “2k-body” dissipators Polynomial scaling

Adolfo d del C Campo

Stochastic k-body Hamiltonians

• A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017)

ˆ HS(t) = ˆ HT (t) + X

α

λα(t) ˆ Lα

[ ˆ P, ˆ Lα] = 0, ˆ Lα = X

i1<···<ik

L(α,k)

i1,...,ik

τD ∼ 1/N 2k

Extreme Decoherence

Adolfo d del C Campo

Chaotic systems as a paradigm of complex systems and test-bed for information scrambling Described by Random Matrix Theory Ensembles of random matrices Gaussian Unitary Ensembles (GUE): Hermitian Hamiltonians Gaussian Orthogonal Ensembles (GOE): Real Symmetric Hamiltonians with time-reversal symm

Chaos & Complex systems

Adolfo d del C Campo

Heavy Nucleus Systems

Density of states: Universal for large Hilbert space dimension “d” Eigenvalues spacing

Chaos & Complex systems

Adolfo d del C Campo

N=100 (GUE) ρ(E) = √ 2d π s 1 − ✓ E √ 2d ◆2

Stochastic Hamiltonian RMT-body operators Decoherence rate?

Adolfo d del C Campo

Stochastic k-body Hamiltonians

ˆ HS(t) = ˆ HT (t) + X

α

λα(t) ˆ Lα

[ ˆ P, ˆ Lα] = 0, ˆ Lα = X

i1<···<ik

L(α,k)

i1,...,ik

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

GUE average

Adolfo d del C Campo

Stoch RMT Hamiltonians: noise & ensemble averages

hf(X)iGUE := Z

d

Y

k=1

dxk%GUE(x1, . . . , xd) hf(X)iHaar

hf(X)iHaar := Z

U(d)

f(UHU −1)dµ(U)

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

GUE average Decoherence rate of “fixed” initial state

Adolfo d del C Campo

Stoch RMT Hamiltonians: noise & ensemble averages

hf(X)iGUE := Z

d

Y

k=1

dxk%GUE(x1, . . . , xd) hf(X)iHaar

hf(X)iHaar := Z

U(d)

f(UHU −1)dµ(U)

DGUE = 2d d + 1 X

µ

γµhvarρβ=0(Vµ)iGUE ' Γd Γ = X

µ

γµ

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

Noise-averaged master equation Decoherence rate Exponential dependence on particle number! Extreme decoherence

Adolfo d del C Campo

Decoherence rate in RMT: GUE

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

Ensemble average

d dtρ(t) = 1 i~[ ˆ HT , ρ(t)] − X

α

λα(t)[ˆ Lα, [ˆ Lα, ρ(t)]]

D = 2 P0 1 τD = X

α

λα(t)∆ˆ L2

α

ˆ Lα ∈ GUE(d)

DGUE ∼ Γd ∼ 2N

Γ = X

α

λα

Stochastic k-body Hamiltonians lead to k-body Lindblad operators Decoherence rate scales polynomially on system size

Adolfo d del C Campo

k-body Stochastic Hamiltonians & Lindbladians

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

2-body 4-body 3-body ( ) Not Extreme!

Two copies of the system, independent fluctuations

Adolfo d del C Campo

Entangled states: the thermofield double state

˜ Ht = H ⊗ 1 + 1 ⊗ H + ~√γ(ξL

t H ⊗ 1 + 1 ⊗ ξR t H)

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

Two copies of the system, independent fluctuations Lindblad operators Initial state: purified thermal density matrix, defined via the Hamiltonian (not fixed)

Adolfo d del C Campo

Entangled states: the thermofield double state

˜ Ht = H ⊗ 1 + 1 ⊗ H + ~√γ(ξL

t H ⊗ 1 + 1 ⊗ ξR t H)

˜ V1 = H ⊗ 1 ˜ V2 = 1 ⊗ H |Φ0i := 1 p Z(β) X

k

e−

βEk 2

|ki |ki

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

Time-dependent density matrix Decay of the purity Decoherence rate

Adolfo d del C Campo

Entangled states: exact evolution

ρt = 1 Z(β) X

j,k

e− β

2 (Ej+Ek)−i 2t ~ (Ej−Ek)−γt(Ej+Ek)2|ji|jihk|hk|

Pt = r 1 8πγt Z ∞

−∞

e− y2

8γt

• Z(β − iy)

Z(β)

• 2

˜ D = 4γvarρβ(H) = 4γ d2 dβ2 ln [Z(β)]

Adolfo d del C Campo

Entangled states: exact evolution

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

Adolfo d del C Campo

Entangled states: exact evolution

P∞ = Z(2β)/Z(β)2

• Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019)

• Z. Xu, L. P. García-Pintos, A. Chenu, and A. del Campo, PRL 122, 014103 (2019).

) )

Adolfo d del C Campo

Entangled states: decoherence rate

• Z. Xu, L. P. García-Pintos, A. Chenu, and A. del Campo, PRL 122, 014103 (2019)

Adolfo d del C Campo

Thermofield double states: decoherence rate

For a TDS extreme decoherence is restricted to infinite temperature or small system sizes

Decoherence rate proportional to heat capacity of CFT Heat capacity proportional to entropy/scales with #dof [Papadodimas & Raju]

• Z. Xu, L. P. García-Pintos, A. Chenu, and A. del Campo, PRL 122, 014103 (2019).

Adolfo d del C Campo

Black holes in AdS/CFT: decoherence rate

˜ D = 4γC/(kBβ2)

Contents

Noise a resource for quantum simulation of open systems

In Local Interactions

polynomial scaling of decoherence rate with system size In RMT Operators exponential scaling of decoherence rate with system size

Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu

Xu et al., PRL 122, 014103 (2019) Chenu et al. PRL 118, 140403 (2017); 119,130401 (2017)

Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu

Part II Work statistics in complex systems & information scrambling

• A. Chenu, I. L. Egusquiza, J. Molina-Vilaplana, AdC, Sci. Rep. 8, 12634 (2018)
• A. Chenu, J. Molina-Vilaplana, AdC, Quantum 3, 127 (2019)

Driven isolated system Unitary evolution: physical time of evolution “s” Work probability distribution

Work pdf

Adolfo d del C Campo

ˆ Hs = X

n

Es

n|nsihns|

ˆ U(τ) = T exp  −i Z τ ds ˆ Hs

• pτ(W) =

X

n,m

p0

n pτ m|nδ

⇥ W −

• Eτ

m − E0 n

⇤

• J. Kurchan, ArXiv:0007360 (2000); P. Talkner, E. Lutz, P. Hanggi, PRE 75, 050102(R) (2007)

Fourier transform = moment-generating function Variable “t” different from the physical time of evolution “s” Explicit expression resembles a Loschmidt echo

Work pdf: characteristic function

Adolfo d del C Campo

• J. Kurchan, ArXiv:0007360 (2000); P. Talkner, E. Lutz, P. Hanggi, PRE 75, 050102(R) (2007)

χ(t, τ) = Z ∞

−∞

dWpτ(W) eiW t. χ(t, τ) = X

n

p0

nhn0|eit ˆ Heff

τ e−it ˆ

H0|n0i

ˆ Heff

τ

= ˆ U †(τ) ˆ Hτ ˆ U(τ)

Silva 2008: If system prepared in an eigenstate at s=0 sudden quench think of “t” as a second time of evolution in a Loschmidt echo Avoids explicit computation of transition probabilities in

From Work pdf to dynamics

Adolfo d del C Campo

• A. Silva, PRL 101, 120603 (2008)

χ(t, τ) = hn0|eit ˆ

Hτ e−it ˆ H0|n0i

pτ(W) = X

n,m

p0

n pτ m|nδ

⇥ W −

• Eτ

m − E0 n

⇤

Chenu et al 2017: Purification of arbitrary initial mixed state purification

From Work pdf to dynamics: arbitrary setting

Adolfo d del C Campo

ρ0 ! |Ψ0i = X

n

p p0

n |n0iL ⌦ |n0iR

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); Quantum 3, 127 (2019)

Chenu et al 2017: Purification of arbitrary initial mixed state purification Characteristic function as a Loschmidt echo amplitude

From Work pdf to dynamics: arbitrary setting

Adolfo d del C Campo

ρ0 ! |Ψ0i = X

n

p p0

n |n0iL ⌦ |n0iR

χ(t, τ) = X

n

p0

nhn0|eit ˆ Heff

τ e−it ˆ

H0|n0i

= hΨ0|Ψti = hΨ0|e+it ˆ

Heff

τ e−it ˆ

H0 ⌦ 1R|Ψ0i

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); Quantum 3, 127 (2019)

Chenu et al 2017: Purification of arbitrary initial mixed state purification Characteristic function as a Loschmidt echo amplitude Loschmidt echo

From Work pdf to dynamics: arbitrary setting

Adolfo d del C Campo

ρ0 ! |Ψ0i = X

n

p p0

n |n0iL ⌦ |n0iR

χ(t, τ) = X

n

p0

nhn0|eit ˆ Heff

τ e−it ˆ

H0|n0i

= hΨ0|Ψti = hΨ0|e+it ˆ

Heff

τ e−it ˆ

H0 ⌦ 1R|Ψ0i

L(t) = |hΨ0|Ψti|2 =

• Z ∞

−∞

dWpτ(W) eiW t

• 2
• A. Chenu et al., Sci. Rep. 8, 12634 (2018); Quantum 3, 127 (2019)

Scrambling: Spreading of quantum correlations across many degrees of freedom Papadodimas-Raju: decay dynamics of purified state, e.g., survival amplitude

Work statistics and information scrambling

Adolfo d del C Campo

L(t) = |hΨ0|Ψti|2 = |hΨ0| ˆ UL(t, 0) ⌦ 1R|Ψ0i|2

K Papadodimas, S. Raju, PRL 115, 211601 (2015)

Scrambling: Spreading of quantum correlations across many degrees of freedom Papadodimas-Raju: decay dynamics of purified state, e.g., survival amplitude Decay dynamics in Loschmidt echo Scrambling from work pdf

Work statistics and information scrambling

Adolfo d del C Campo

L(t) = |hΨ0|Ψti|2 = |hΨ0| ˆ UL(t, 0) ⌦ 1R|Ψ0i|2

L(t) = |hΨ0|Ψti|2 =

• Z ∞

−∞

dWpτ(W) eiW t

• 2

ˆ UL(t, 0) = e+it ˆ

Heff

τ e−it ˆ

H0

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); Quantum 3, 127 (2019)

AdC, J. Molina-Vilaplana, J. Sonner, PRD 95, 126008 (2017)

Chaotic systems as a paradigm of complex systems and test-bed for information scrambling Described by Random Matrix Theory Ensembles of random matrices Gaussian Unitary Ensembles (GUE): Hermitian Hamiltonians Gaussian Orthogonal Ensembles (GOE): Real Symmetric Hamiltonians with time-reversal symm

Chaos & Complex systems

Adolfo d del C Campo

Heavy Nucleus Systems

Example: Quantum quenches between two RMT Hamiltonians

• A. Chenu et al. Quantum work statistics, Loschmidt echo and information scrambling,

arXiv:1711.01277

• A. Chenu et al.

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems arXiv:1804.09188 See related work: RMT large N asymptotics: M. Łobejko, J. Łuczka, P. Talkner PRE 95, 052137 (2017) Disordered many-body systems: Y Zheng and D. Poletti, arXiv:1806.02555

Work pdf & RMT

Adolfo d del C Campo

Initial thermal state Sudden quench:

Chaos & Complex systems

Adolfo d del C Campo

|Ψ0i = 1 p Z(β) X

n

e− β

2 ˆ

H0 ⊗ 1R |n0iL ⌦ |n0iR

• A. Chenu et al., Quantum 3, 127 (2019)

ˆ H0 → ˆ Hf ˆ H0, ˆ Hf ∈ GUE(N)

hL(t)i

Short-times Long-times

Chaos & Complex systems

Adolfo d del C Campo

1 0.01 0.1 1 10 100 0.001 0.01 0.1 1 0.01 0.1 1 10 100

hL(t)iGUE = ⌦ et2σ2

W +O(t4)↵

et2hσ2

W i+O(t4)

hL(t)iGUE ! hZ(2β)i hZ(β)2i 2 (N + 1) hL(t)i

• A. Chenu et al., Quantum 3, 127 (2019)

Time-reversal operation Negation of system Hamiltonian (e.g. in GOE) Loschmidt echo from partitio function Work pdf Mean work

Work for time-reversal operation

Adolfo d del C Campo

L(t) = |hΨ0|Ψ0(t)i|2 =

• Z (β + i2t)

Z (β)

• 2

hWi = 2h ˆ H0iβ p(W) = 1 2 hρ(E)iβ

• E=−W/2
• A. Chenu et al., Sci. Rep. 8, 12634 (2018)

ˆ H0 → ˆ Hf = − ˆ H0 ˆ H0 ∈ GOE(N)

Loschmidt echo, work pdf and scrambling

Adolfo d del C Campo

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); A. Chenu et al., Quantum 3, 127 (2019)

L(t) = |hTDS(0)|TDS(t)i|2 =

• Z

dWp(W)eiW t

• 2

=

• Z(β + i2t)

Z(β)

• 2

ˆ H0 → ˆ Hf = − ˆ H0 ˆ H0 ∈ GOE(N)

GUE averaged Loschmidt echo Spectral form factor

Loschmidt echo, work pdf and scrambling

Adolfo d del C Campo

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); A. Chenu et al., Quantum 3, 127 (2019)

hL(t)i = 1 hZ(β)2i 1 N 21 ⇣ g(0, t)g(β, t) + NhZ(2β)i 1 N hZ(2β)ig(0, t) 1 N g(β, t)N ⌘

g(β, t) ⌘ hZ(β + it)Z(β it)i

ˆ H0 → ˆ Hf ˆ H0, ˆ Hf ∈ GUE(N)

GUE averaged Loschmidt echo: infinite temperature Frame potential

Loschmidt echo, work pdf and scrambling

Adolfo d del C Campo

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); A. Chenu et al., Quantum 3, 127 (2019)

F(k)

E

= Z

ˆ A, ˆ B∈E

D ˆ AD ˆ B

• tr ˆ

A† ˆ B

• 2k

hL(t)i = 1 N 2 F(1)

GUE(t)

(β = 0)

GUE averaged Loschmidt echo: infinite temperature Frame potential

Loschmidt echo, work pdf and scrambling

Adolfo d del C Campo

• A. Chenu et al., Sci. Rep. 8, 12634 (2018); A. Chenu et al., Quantum 3, 127 (2019)

F(k)

E

= Z

ˆ A, ˆ B∈E

D ˆ AD ˆ B

• tr ˆ

A† ˆ B

• 2k

hL(t)i = 1 N 2 F(1)

GUE(t)

(β = 0)

Cotler et al JHEP 1711 (2017) 048

Summary

u Extreme decoherence

Noise as a resource for QOS Noise coupled to local interactions Noise coupled to RMT

u Work statistics of complex systems

Loschmidt echo and p(W) P(W) and scrambling Work pdf & chaos/RMT Work pdf for time-reversal

Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu

The DIPC-Bilbao Group

Aurelia Chenu (group co-leader)

• Dr. Gentil Neto

Leonce Dupays Tanyou Huang Jinxiun Zhou Fernando Gomez Ruiz (UMass => Bilbao)

• Dr. Luis Pedro Garcia-Pintos (UMass)
• Prof. Diego Tielas (UMass => La Plata)
• Prof. Zhenyu Xu (UMass => Soochow)

Adolfo d del C Campo: ad adolfo.delcam ampo@gmai ail.com

Collaborators

Jiashu Cao (MIT) Íñigo L. Egusquiza (Bilbao) Chuan-Feng Li (Hefei) Norman Margolus (MIT) Javier Molina-Vilaplana (Cartagena) Julian Sonner (Geneve) Masahito Ueda (Tokyo) Haibin Wu (ECNU) Wojciech H Zurek (LANL)