Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains

Denis, Zakari; Wimberger, Sandro

doi:10.3390/condmat3010002

Cited by 5 publications

(3 citation statements)

References 44 publications

(73 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us also mention that the master Eq. ( 5) is used as the starting point in many papers on conductivity with bosonic and fermionic carriers [14][15][16], where in the latter case the bosonic annihilation and creation operator should be substituted by fermionic ones.…”

Section: Master Equationmentioning

confidence: 99%

Landauer-Büttiker equation for bosonic carriers

2018

Self Cite

View full text Add to dashboard Cite

We study the current of Bose particles between two reservoirs connected by a one-dimensional channel. We analyze the problem from first principles by considering a microscopic model of conductivity in the noninteracting limit. Equations for the transient and the stationary current are derived analytically. The asymptotic current has a form similar to the Landauer-Büttiker equation for electronic current in mesoscopic devices.

show abstract

Section: Master Equationmentioning

confidence: 99%

Landauer-Büttiker equation for bosonic carriers

2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…in contact with an environment) evaluating out-of-equilibrium two-time correlations has proven extremely challenging. Most works have instead focused on characterizing the non-equilibrium dynamics of open systems by considering the universal scaling behavior of simpler observables or the propagation of single-time correlations [8,9], by using various approximate approaches to evaluate two-time correlations [10][11][12][13][14][15], or by considering small many-body quantum systems [16].…”

mentioning

confidence: 99%

Evolution of two-time correlations in dissipative quantum spin systems: Aging and hierarchical dynamics

et al. 2019

View full text Add to dashboard Cite

We consider the evolution of two-time correlations in the quantum XXZ spin-chain in contact with an environment causing dephasing. Extending quasi-exact time-dependent matrix product state techniques to consider the dynamics of two-time correlations within dissipative systems, we uncover the full quantum behavior for these correlations along all spin directions. Together with insights from adiabatic elimination and kinetic Monte Carlo, we identify three dynamical regimes. For initial times, their evolution is dominated by the system unitary dynamics and depends on the initial state and the Hamiltonian parameters. For weak spin-spin interaction anisotropy, after this initial dynamical regime, two-time correlations enter an algebraic scaling regime signaling the breakdown of time-translation invariance and the emergence of aging. For stronger interaction anisotropy, these correlations first go through a stretched exponential regime before entering the algebraic one. Such complex relaxation arises due to the competition between the proliferation dynamics of energetically costly excitations and their motion. As a result, dissipative heating dynamics of spin systems can be used to probe the entire spectrum of the underlying Hamiltonian.Two-time correlations are powerful tools to capture the fundamental dynamical features of many-body systems both in and away from equilibrium. These correlation functions are of the form B(t 2 )A(t 1 ) where A and B are operators, t 1 and t 2 are two different times, and . . . = tr(ρ . . . ) is the average over the density matrix ρ of a given system. Numerous experimental techniques have been developed to probe these correlations measuring the response of many-body systems. A non-exhaustive list includes ARPES [1], neutron scattering [2] or conductivity and magnetization measurements in solids [3], and radiofrequency [4], Raman, Bragg [5] (and references therein) or modulation spectroscopy [6] in cold gases. In equilibrium, these experimental methods provide information on various spectral features such as collective excitations and bound states. Whereas away from equilibrium, these techniques are employed to identify the formation of dynamically induced states in isolated quantum systems subjected to an external parameter change, and to capture, using for example magnetic susceptibility measurements, the aging dynamics of classical spin glasses [7].Theoretically, two-time correlations have been studied in isolated many-body quantum systems (i.e. not in contact with an environment), both in and far from equilibrium. However, for open many-body quantum systems (i.e. in contact with an environment) evaluating out-of-equilibrium two-time correlations has proven extremely challenging. Most works have instead focused on characterizing the non-equilibrium dynamics of open systems by considering the universal scaling behavior of simpler observables or the propagation of single-time correlations [8,9], by using various approximate approaches to evaluate two-time correlations [10][11][12][13][14...

show abstract

“…Correlations of order one or two have been, however, the most frequently measured correlations. Recently, there has been immense progress in recipes for measuring higher-order correlations [10] to the ultimate goals of non-destructively exploring quantum systems [3,11] and achieving quantum-field tomography [12]. In order to explore the quantum coherence properties of massive particles, it has been possible to observe higher-order correlations up to the sixth order [13].…”

Section: Introductionmentioning

confidence: 99%

Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems

Wamba,

Pelster

2020

Preprint

View full text Add to dashboard Cite

We formulate an exact spacetime mapping between the N -point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A 94, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a D-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary N -point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schrödinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the N -point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.

show abstract

Two-Time Correlation Functions in Dissipative and Interacting Bose–Hubbard Chains

Cited by 5 publications

References 44 publications

Landauer-Büttiker equation for bosonic carriers

Landauer-Büttiker equation for bosonic carriers

Evolution of two-time correlations in dissipative quantum spin systems: Aging and hierarchical dynamics

Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems

Contact Info

Product

Resources

About