and connected by a Fermi-liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling

V

. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature

{T}^{*}(V)\ensuremath{\sim}{V}^{4}

is parametrically enhanced with respect to the linear-

T

behavior expected in systems with quasiparticles. Interestingly, below

{T}^{*}(V)

the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the bath and becomes non-Fermi liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure

\mathcal{J}=\mathrm{\ensuremath{\Phi}}({T}_{L})\ensuremath{-}\mathrm{\ensuremath{\Phi}}({T}_{R})

, with

\mathrm{\ensuremath{\Phi}}(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}

and power law crossing over from

\ensuremath{\gamma}=3/2

\ensuremath{\gamma}=2

below

{T}^{*}

DOI: 10.1103/physrevb.108.115120

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{T}_{L}\ensuremath{\ne}{T}_{R}

and connected by a Fermi-liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling

V

. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature

{T}^{*}(V)\ensuremath{\sim}{V}^{4}

is parametrically enhanced with respect to the linear-

T

behavior expected in systems with quasiparticles. Interestingly, below

{T}^{*}(V)

\mathcal{J}=\mathrm{\ensuremath{\Phi}}({T}_{L})\ensuremath{-}\mathrm{\ensuremath{\Phi}}({T}_{R})

, with

\mathrm{\ensuremath{\Phi}}(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}

and power law crossing over from

\ensuremath{\gamma}=3/2

\ensuremath{\gamma}=2

below

{T}^{*}

T_L\neq T_R

and connected by a Fermi-Liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling

V

. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature

T^*(V)\sim V^4

is parametrically enhanced with respect to the linear-

T

behavior expected in systems with quasiparticles. Interestingly, below

T^*(V)

the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the strange bath and becomes Non-Fermi-Liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure

\mathcal{J}=Φ(T_L)-Φ(T_R)

, with

Φ(T)\sim T^γ

and power law crossing over from

γ=3/2

γ=2

below

T^*

\sqrt{T}

-dependence at relatively high temperature to a linear T-dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.

\\mathcal{N}=2

theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable

t

J

model of electrons with an SYK-like form. We find a

\\mathbb{Z}_2

fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.