Collapse and revival of the matter wave field of a Bose–Einstein condensate

Greiner, Markus; Mandel, Olaf; Hänsch, Theodor W.; Bloch, Immanuel

doi:10.1038/nature00968

Cited by 1,204 publications

(1,560 citation statements)

References 22 publications

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“…For large U the behavior is different, showing strong so-called collapse-and-revival oscillations with approximate frequency 2π/U . They stem from the vicinity of the atomic limit (i.e., zero hopping amplitude), for which the propagator e −iHt is exactly periodic with period 2π/U [173]. For finite hopping (small compared to U ) these oscillations are damped and decay on timescales of order /bandwidth.…”

Section: Dmft For Nonequilibriummentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

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Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter. Motivation Electronic CorrelationsAlready in 1937, at the outset of modern solid state physics, de Boer and Verwey [1] drew attention to the surprising properties of materials with incompletely filled 3d-bands. This observation prompted Mott and Peierls [2] to discuss the interaction between the electrons. Ever since transition metal oxides (TMOs) were investigated intensively [3]. It is now well-known that in many materials with partially filled electron shells, such as the 3d transition metals V and Ni and their oxides, or 4f rare-earth metals such as Ce, electrons occupy narrow orbitals. The spatial confinement enhances the effect of the Coulomb interaction between the electrons, making them "strongly correlated". Correlation effects can lead to profound quantitative and qualitative changes of the physical properties of electronic systems as compared to non-interacting particles. In particular, they often respond very strongly to changes in external parameters. This is expressed by large renormalizations of the response functions of the system, e.g., of the spin susceptibility and the charge compressibility. In particular, the interplay between the spin, charge and orbital degrees of freedom of the correlated d and f electrons and with the lattice degrees of freedom leads to an amazing multitude of ordering phenomena and other fascinating properties, including high temperature superconductivity, colossal magnetoresistance and Mott metal-insulator transitions [3].arXiv:1109.4833v1 [cond-mat.str-el]

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Section: Dmft For Nonequilibriummentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

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“…As a matter of fact, at the lowest order ω (1) (µ 1 , µ 2 ) and ω ′ (1) (µ 1 , µ 2 ) have the same form in terms of the generating function Ω Ψ0 as for m z = 0. The only difference is in ϕ(µ), which is now different from zero ϕ (1) (µ) = tanh(ζ/2)[d * ρ (1) 0 ](−iµ) . (8.4) …”

Section: Initial States With Nonzero Longitudinal Magnetizationmentioning

confidence: 99%

“…Nonequilibrium dynamics in closed quantum systems, and in particular quantum quenches, have attracted much experimental [1][2][3][4][5][6] and theoretical attention in recent years. There is a growing consensus that integrable models exhibit important differences in behaviour as compared to non-integrable ones 41 .…”

Section: Introductionmentioning

confidence: 99%

Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Fagotti¹,

Eßler²

2013

J. Stat. Mech.

153

257

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We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values, that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.

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“…The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Motivated by recent experimental advances in the field of cold atoms, the theoretical study of the non-equilibrium dynamics of isolated interacting many-body quantum systems is currently receiving increasing attention [1][2][3][4]. Among the several questions that have been addressed, a central one concerns the way in which a macroscopically large isolated system evolving with unitary quantum dynamics from a generic initial state approaches equilibrium.…”

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confidence: 99%

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Contents

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Collapse and revival of the matter wave field of a Bose–Einstein condensate

Cited by 1,204 publications

References 22 publications

Dynamical Mean-Field Theory

Dynamical Mean-Field Theory

Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

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