Relaxation after the quench Sample Clauses

Relaxation after the quench. − 𝓨 In a while after the quench the system relaxes and approaches a thermal state. To demonstrate that, we rotate the time frame t, t′ in the numerically computed Green’s functions towards τ = t t′, = (t + t′)/2 and make a Fourier transform along τ . Indeed, the system returns to a nearly-thermal state if the extended fluctuation dissipation relation iGK(ω, 𝓨 ) = tanh ω − µ˜(𝓨 ) (5.12) A(ω, 𝓨 ) 2T˜(𝓨 ) ˜is the SYK spectral function. In contrast to the equilibrium case, the extended is fulfilled at frequencies in the vicinity of µ, where A(ω, 𝓨 ) = −2ImGR(ω, 𝓨 ) fluctuation dissipation relation (5.12) is manifestly time dependent via the “centre ˜𝓨 of mass” coordinate which enters the effective temperature T and chemical potential µ. Overall, the ratio (5.12) determines the effective distribution function µ˜, T ), where n F is the Fermi distribution function.
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