Random phase approximation study of one-dimensional fermions after a quantum quench

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Results are presented for a two-point correlation function of a spin-chain after a quantum quench for an intermediate time regime where inelastic effects are weak. A Callan-Symanzik like equation for the correlation function is explicitly constructed which is used to show the appearance of three distinct scaling regimes. One is for spatial separations within a light-cone, the second is for spatial separations on the light-cone, and the third is for spatial separations outside the light-cone. In these three regimes, the correlation function is found to decay with power-laws with nonequilibrium exponents that differ from those in equilibrium, as well as from those obtained from quenches in a quadratic Luttinger liquid theory. A detailed discussion is presented on how the existence of scaling depends on the properties of the initial state before the quench.

Section: Model and A Brief Discussion Of Resultsmentioning

confidence: 99%

Correlation functions in the prethermalized regime after a quantum quench of a spin chain

Mitra

2013

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“…This central region grows with time, with the remaining parts of the wire acting essentially as reservoirs. At large times a translational invariant CCSS is locally observed [26][27][28][29][30][31][32][33][34][35]. Interestingly, some of the properties of the CCSS created in this way, in particular the momentum-resolved electronic distribution, are similar to the CCSS obtained using a Landauer description [26,[29][30][31][32][33]36].…”

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confidence: 87%

Steady-state properties of a nonequilibrium Fermi gas

Ribeiro¹

2017

The current-carrying steady-state that arises in the middle of a metallic wire connected to macroscopic leads is characterized regarding its response functions, correlations and entanglement entropy. The spectral function and the dynamical structure factor show clear non-equilibrium signatures accessible by state-of-the-art techniques. In contrast with the equilibrium case, the entanglement entropy is extensive with logarithmic corrections at zero-temperature that depend on the wire-leads coupling and, in a non-analytic way, on voltage. This shows that some robust universal quantities found in gapless equilibrium phases do not persist away from equilibrium.PACS numbers: 05.60.Gg, 05.70.Ln Current-carrying steady-states (CCSS) are characterized by a steady flow of equilibrium-conserved quantities, such as energy, spin or charge. Of direct relevance to transport experiments are steady currents generated by coupling a system to reservoirs at different thermodynamic potentials. The resulting CCSS are thermodynamically unbalanced, i.e. do not fulfill equilibrium fluctuation dissipation relations [1,2]. CCSS in one or quasi-onedimensional systems are of relevance in many fields, including charge and spin transport in electronic devices and in cold atom setups.Due to kinetic constraints, accounting for relaxation in one dimension requires to go beyond 2-body interaction terms and explicitly account for 3-and higher-body collisions [3][4][5] and thus may be neglected for weakly interacting clean samples. For non-interacting electrons on a wire, ideal reservoirs can be mimicked by injecting particles from plus and minus infinity with a given energy distributions [6][7][8][9]. This ideal conditions, alluded to as Landauer reservoirs [10,11], yield to a local energy distribution function that is the average of those of the leads. A series of studies featuring non-equilibrium Luttinger liquids [12][13][14][15][16][17] found that interaction-induced dephasing may smear the local energy distribution even in the absence of relaxation. In the presence of a strong enough relaxation the system is expected to equilibrate locally. Treatments based on the Boltzaman equation have been used to obtain the distribution function of the charge carriers in this regime [3][4][5][18][19][20].Experiments featuring CCSS, designed to access the local energy distribution of charge caries, were performed using tunneling spectroscopy in mesoscopic wires [21][22][23] and carbon nanotubes [24]. The local energy distribution, measured in the center of the wire, was reported to exhibit a characteristic double step form resulting from contribution of both Fermi functions of the electronic leads. The sharp steps seen at low temperatures are smeared out as temperature increases or in the presence of electron-electron interactions, disorder or electron-phonon coupling.The study of current-carrying states recently became available for cold atomic setups [25]. Mainly motivated by these advances, a rather different body of works investigated the time evo...

“…The dissipation thus shares features with Landau damping where plasmons acquire a finite lifetime. 32 It also shares similarities with turbulent systems that are known to exhibit the well known Kolmogorov cascades where energy is passed down from large scale structures to small scale structures. 33 We believe that this type of behavior and mechanism for thermalization, unraveled in a controlled way on the particular system we study, is quite general.…”

Section: Introductionmentioning

confidence: 93%

“…The above mechanism for thermalization arising due to an exchange of energy between long wavelength and short wavelength modes appears to be rather generic, and may even be recovered in a quench involving fermions. 32 In particular in Ref. 32 the effect of weak interactions on a system of one-dimensional fermions that are in a nonequilibrium state due to an initial quench was studied using the random phase approximation (RPA).…”

Section: B Flow Far From the Critical Pointmentioning

confidence: 99%

Thermalization and dissipation in out-of-equilibrium quantum systems: A perturbative renormalization group approach

Mitra

Giamarchi

2012

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A perturbative renormalization group approach is employed to study the effect of a periodic potential on a system of one-dimensional bosons in a nonequilibrium steady state due to an initial interaction quench. The renormalization group flows are modified significantly from the well-known equilibrium Berezinski-KosterlitzThouless form. They show several new features such as a generation of an effective temperature, generation of dissipation, as well as a change in the location of the quantum critical point separating the weak-and strong-coupling phases. Detailed results on the weak-coupling side of the phase diagram are presented, such as the renormalization of the parameters and the asymptotic behavior of the correlation functions. The physical origin of the generated temperature and friction is discussed.