Landauer, Kubo, and microcanonical approaches to quantum transport and noise: A comparison and implications for cold-atom dynamics

Chien, Chih-Chun; Ventra, Massimiliano Di; Zwolak, Michael

doi:10.1103/physreva.90.023624

Cited by 40 publications

(60 citation statements)

References 48 publications

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“…We verify that the proper change of basis provides a direct transformation between their and our kernels. We reproduce results on the average number of particles and its variance [34][35][36] (see also a numerical study in [37]) and on the Loschmidt echo [36] in the absence of the defect, as well as on the current for the infinite temperature initial state in the presence of the defect [38]. Known asymptotic results for the entanglement entropy [39][40][41] are also reproduced.…”

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confidence: 62%

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

2020

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We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

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confidence: 62%

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

2020

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“…In this setting, a transition from ballistic to diffusive transport across the junction was recently demonstrated [48]. Other studies have investigated light cone velocities [49], entanglement spreading [50], nonequilibrium steady states [51], the time evolution of two chains at different temperatures [52][53][54][55][56], the comparison between Landauer, Kubo, and microcanonical descriptions [57], and the emergent hydrodynamics [58,59]. Furthermore, in line with the results obtained for the Markov case in the low bias regime, ballistic to diffusive transport was found in the limit of infinite temperatures [60].…”

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confidence: 94%

A nonequilibrium quantum phase transition in strongly coupled spin chains

Mascarenhas

Giudice

Savona

2017

Quantum

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We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Timedependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport regimes.Nonequilibrium phase transitions have emerged as critical phenomena that may underpin novel forms of universality, departing significantly from transitions that are driven by thermal or quantum fluctuations [1]. A prototypical setting for these critical phenomena is that of transport in one-dimensional systems, and in particular many-body spin chains such as the spin-1/2 XXZ chain. This model system is known to provide an accurate description of real materials [2][3][4][5] and can also be quantum-simulated in superconducting circuits [6][7][8]. With the outstanding developments and control in trapped ions and ultracold atoms in optical lattices [9][10][11][12][13][14][15][16][17][18][19][20][21][22] and molecules [23][24][25], similar models can also be simulated in such architectures.Transport through the XXZ spin chain has been investigated in several studies, both from the perspective of linear response (i.e., the Kubo formalism) [26][27][28][29][30] and from the point of view of quench-induced dynamics [31][32][33][34]. These works have highlighted the possibility of both ballistic and diffusive transport of the spin current and characterized the transition between the different regimes.More recently, the study of nonequilibrium critical phenomena has been extended to open quantum systems, where the nonequilibrium character is induced by coupling the system to several external reservoirs [35]. Theoretical investigation of open quantum systems is ultimately motivated by the inherently open nature of several modern experimental platforms [36], which are typically subject to external drive, dissipation and dephasing. One of the main goals of these studies is to investigate the possibility of critical phenomena that differ substantially from those occurring in closed, Hamiltonian systems, possibly leading to the emergence of new universality classes [35].In the context of open quantum systems, the problem of spin transport has been addressed by assuming boundary driven spin chains, i.e. chains in which only the first and last spins are coupled to external environments which induce the necessary bias to trigger transport. Boundary driven many-body systems are rapidly emerging as a n...

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“…At t = 0 the left half is filled and the right half is empty. The ballistic transport of fermions clearly shows a light-cone structure [20,41] with the outermost wavefront showing a constant maximal propogating speed. For different geometries the maximal speeds are different, and there are equivalent ways for measuring them.…”

Section: Resultsmentioning

confidence: 99%

“…As illustrated by the matter-wave example, transport of fermionic atoms is closely related to electronic transport in nanoscale and mesoscopic systems [20,21,23,24]. For instance, when ultracold fermions are driven out of equilibrium in a one-dimensional optical lattice, a quasi-steady state current with a constant magnitude for a period of time emerges, which is the precursor of the steady-state current (in the thermodynamic limit) found in biased solid-state systems [25,26].…”

Section: Introductionmentioning

confidence: 99%

Matter-wave propagation in optical lattices: geometrical and flat-band effects

Metcalf

Chern

Ventra

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

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The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of propagation of matter-waves as a function of the lattice geometry. To address this issue, we have investigated theoretically the quantum transport of non-interacting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square lattice has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Possible realizations of those dynamical phenomena are discussed.

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Landauer, Kubo, and microcanonical approaches to quantum transport and noise: A comparison and implications for cold-atom dynamics

Cited by 40 publications

References 48 publications

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

A nonequilibrium quantum phase transition in strongly coupled spin chains

Matter-wave propagation in optical lattices: geometrical and flat-band effects

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