Long and short time quantum dynamics: III. Transients

Špička, Václav; Velický, B.; Kalvová, A.

doi:10.1016/j.physe.2005.05.016

Cited by 25 publications

(38 citation statements)

References 34 publications

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“…One way this can be further understood is by breaking the self-energy into "dark" and "induced" pieces, following the work bySpicka et al [14][15][16]. Starting from Equation (18) we find…”

Section: Self-consistencymentioning

confidence: 99%

“…In that case, the self-energy gives rise to a line width in the spectrum of a single excitation, as measured, e.g., by equilibrium photoemission spectroscopy. Here, the relation arrives only through copious approximations applied to population dynamics [14][15][16], which occur along an orthogonal direction to t rel . We require the population dynamics to be very slow for this to hold, or for the pump-induced population changes to be extremely small such that only these terms play a role.…”

Section: Self-consistencymentioning

confidence: 99%

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Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

Kemper

Freericks

2016

Entropy

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Abstract:We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions, within the differential equation for the populations, that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here, we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green's functions and self-energies plays a pivotal role in determining these decay rates.

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“…One way this can be further understood is by breaking the self-energy into "dark" and "induced" pieces, following the work bySpicka et al [14][15][16]. Starting from Equation (18) we find…”

Section: Self-consistencymentioning

confidence: 99%

Section: Self-consistencymentioning

confidence: 99%

Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

Kemper

Freericks

2016

Entropy

View full text Add to dashboard Cite

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“…and by approximating the retarded and advanced Green's functions with their Hartree-Fock (HF) values [21][22][23]. This approach is in the spirit of the Boltzmann approach of Ref.…”

mentioning

confidence: 99%

Dynamics of many-body localization

2014

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Following the field theoretic approach of Basko et al., Ann. Phys. 321, 1126(2006, we study in detail the real-time dynamics of a system expected to exhibit many-body localization. In particular, for time scales inaccessible to exact methods, we demonstrate that within the second-Born approximation that the temporal decay of the density-density correlation function is non-exponential and is consistent with a finite value for t → ∞, as expected in a non-ergodic state. This behavior persists over a wide range of disorder and interaction strengths. We discuss the implications of our findings with respect to dynamical phase boundaries based both on exact diagonalization studies and as well as those established by the methods of Ref. 1.It has been known for more than 50 years that noninteracting particles in a one-dimensional disordered system exhibit Anderson localization [2], namely the exponential suppression of transport. While a localized system is non-ergodic and thus does not thermalize, coupling the system to other degrees of freedom with a continuous spectrum, such as a heat bath, allows thermalization to occur via processes such as variable-range hopping [3]. For an isolated many-body system, only interactions between the particles may lead to thermalization. The question of whether or not localization is stable in the presence of interactions was first considered by Fleishman and Anderson [4], who concluded that short-ranged interactions cannot destabilize the insulating phase. A similar and still open question also exists for Bose-Einstein condensates, treated in the framework of the time-dependent Gross-Pitaevskii (or nonlinear Schrödinger) equation [5]. In this case numerics, as well as analytical arguments, suggest a temporally sub-diffusive or even logarithmic thermalization behavior for not very strong interactions [5].Using a diagrammatic approach, Basko et al. argued that for a general class of isolated, disordered and interacting systems, a many-body mobility edge exists, similarly to the Anderson mobility edge in a threedimensional non-interacting system [1]. Namely, a critical energy separates "insulating" and "metallic" eigenstates, which can be distinguished by evaluating the spatial correlations of any local operator. "Metallic" eigenstates will have non-vanishing or slowly decaying correlations, while "insulating" states will have exponentially decaying correlations. By changing the energy (or the micro canonical temperature) of the system across the mobilityedge, the system will undergo an insulator-metal transition. Similar to the Anderson transition, the many-body localization (MBL) transition is a dynamical and not a thermodynamic phenomena [1]. However, the MBL transition is also not a conventional quantum phase transition since the critical energy, which depends on the parameters of the system, may be very far from the ground state. In fact, for systems of bounded energy density (e.g., finite number of states per site), Oganesyan and Huse suggested that the transition will persist up t...

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“…In this paper we consider consequences of the global U͑1͒ symmetry for the properties of the electronic nonequilibrium Green's function [15][16][17][18][19] ͑NGF͒ admitting an arbitrarily large deviation from equilibrium. In a near-equilibrium case, this symmetry is known 2,6,9,10 to lead to a Ward identity connected with particle number conservation and expressing the transport vertex for linear response to a shift in the energy zero ͑or, equivalently, of the chemical potential͒ in terms of the equilibrium self-energy.…”

mentioning

confidence: 99%

“…We derive an extension of this WI to all nonequilibrium processes of the broad switch-on class specified by the Keldysh initial condition: they start at a switch-on instant from equilibrium, which has been formed at an infinitely remote initial time. [15][16][17][18][19] We further derive from the nonequilibrium Ward identity the renormalized semigroup composition rule for nonequilibrium Green's functions ͑NE RSGR͒ accounting for memory and coherence past and future in the system. It is shown that this necessary condition for the WI can also be deduced from the Dyson equation alone, without invoking the gauge invariance explicitly.…”

mentioning

confidence: 99%

Ward identity for nonequilibrium Fermi systems

2008

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A nonequilibrium Ward identity ͑NE WI͒ connecting the scalar transport vertex correction with one-particle self-energy is derived using the global U͑1͒ symmetry of the fermion nonequilibrium Green's functions ͑NGF͒. The nonperturbative derivation does not depend on the details of the many-body system. A renormalized multiplicative composition rule for the NGF, reflecting time coherence, is obtained and related to the NE WI. Applications involve ͑i͒ testing the consistency of approximations shown in the example of a self-consistent Born approximation for disorder scattering, and ͑ii͒ in the general quantum transport theory, the formalism permits one to assess routes to generalized master equations, in particular those based on the generalized Kadanoff-Baym ansatz.

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Long and short time quantum dynamics: III. Transients

Cited by 25 publications

References 34 publications

Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

Dynamics of many-body localization

Ward identity for nonequilibrium Fermi systems

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